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Re: [EM] (3) MJ -- The easiest method to 'tolerate'

C.Benham

Tue, Sep 6, 2016 8:23 PM

On 9/6/2016 10:47 AM, steve bosworth wrote:

S: For B&L, the grades used are not ‘magically standardized’ but
culturally determined by human definitions and practices, e.g. at
least from our school days we all are prompted to develop our own
understanding of such common words as EXCELLENT, VERY GOOD, etc., i.e.
as used in the various contexts in which we are called upon to
evaluate proposals, decisions, performances, etc.Do we disagree about
this?

C: Yes. Candidates for political office are in a different category.

Suppose there are several candidates and in your sincere opinion they
are all very bad and deserve the lowest possible grade but one is
significantly even worse than the others.

Would you (a) abstain from voting, or (b) turn up and give all the
candidates the lowest rating or (c) give the bottom-most rating only to
the worst candidate and "insincerely"
give the other bad candidates a higher rating?

Chris Benham

*From:*C.Benham cbenham@adam.com.au
Sent: Saturday, September 3, 2016 10:13 PM
To: Kevin Venzke; steve bosworth; election-methods@lists.electorama.com
Subject: Re: [EM] (3) MJ -- The easiest method to 'tolerate'

Hi C. Benham and everyone,

C: [C. Benham wrote:] An election for a powerful political office
isn't a jury-like
collaboration among voters to select the best winner. Rather it is
competition between factions of voters who are trying to elect their
favourites and/or prevent the election of some candidate
they consider relatively bad.

S:Perhaps we do not entirely disagree as you also want the ‘best
winner’ to be elected.However, we would seem to disagree if, as a
democrat, you are really saying that you do not want the winner to be
the one who is most highly valued by a majority of the voters.Of
course, different citizens will have different ideas about what an
EXCELLENT candidate would look like and MJ allows each voter honestly
(or dishonestly) to ‘evaluate’ each candidate using a rich common
language, i.e. to ‘grade’ each to the extent that each does or does
not come close to being EXCELLENT.By discovering the one candidate
whose majority ‘median-grade’ is highest, MJ most efficiently allows a
society to discover that most highly valued winner. This is partly
because ‘majorities of grades are … considerably more discerning
decisions than are majorities of preferences’ (Belinski & Laraki,
/Majority Judgment/, p.283). Do we disagree?

Also, to the extent that I understand your IBIFA method as contrasted
to MJ, IBIFA 1): is more likely to prompt voters to ‘rank’ rather than
to ‘evaluate’ the competing candidates, and 2): its reasons for its
different stages of rules for discovering its winner are more complex
and less obvious than the reasons for MJ’s count.’ 3): Also, as
explained by B&L, IBIFA (as a ‘point-summing method’) is more
vulnerable to strategic ‘manipulation’, as well as to Condorcet ties
and Arrow’s paradoxes. In this last regard, do you see any flaws in
B&L’s argument that MJ is entirely strategy-proof with regard to
grading?Also, in contrast to the many ways that all the ‘point-summing
methods’ offer opportunities for voters to ‘manipulate’ the results,
do you see any flaws in their mathematical proof that MJ is almost
‘half’ as vulnerable in this regard, i.e. if and when MJ ballots might
be used to ‘rank’ rather than to ‘grade’ the candidates (see pp.14,
15, 189-198, 282-292)?

S:With regard to your example (below), I also see X as winning by
MJ.X’s median grade is ‘b’ [or Very Good’] while Y’s is ‘c’ [or Good],
i.e. 51% of the ‘grades’ evaluated X as Very Good, while 51% of the
grades evaluated Y only as Good.What is the problem with this?

You suggest below:‘The 11 who voted Ya,Xb and the 11 who voted Yc, Xf
might wish they had "lied" and voted like the rest of Y's
supporters.’However, please also note that the 11 who voted Ya,Xb’
also agreed that X is Very Good, and thus it is only ‘the 11 who voted
Yc, Xf’ who presumably will be less satisfied with X’s win.

C: But suppose that MJ is used and the voters give their sincere absolute
ratings (on some magically standardised scale, independent
of the actual candidates).

C: Say there are candidates X and Y and voters rate them on A-B-C-D-E-F
grading ballots.

40: X a, Yf
11: Ya, Xb
38: Ya, Xf
11: Yc, Xf

60% of these voters prefer Y to X but MJ elects X. Is this really the
best result? The 11 who voted Ya,Xb and the 11 who voted Yc, Xf
might wish they had "lied" and voted like the rest of Y's supporters.

I like expressive ballots and there's no reason why IBIFA can't also use
6-slot ratings ballots. Here it elects Y. Whenever the winners of
IBIFA and MJ (or Bucklin or MCA or Range) differ the IBIFA winner will
pairwise-beat the other.

http://wiki.electorama.com/wiki/IBIFA

Chris Benham

http://wiki.electorama.com/wiki/IBIFA

From: C.Benham cbenham@adam.com.au
Sent: Saturday, September 3, 2016 10:13 PM
To: Kevin Venzke; steve bosworth; election-methods@lists.electorama.com
Subject: Re: [EM] (3) MJ -- The easiest method to 'tolerate'
Steve,

An election for a powerful political office isn't a jury-like
collaboration among voters to select the best winner. Rather it is
competition between factions of voters who are trying to elect their
favourites and/or prevent the election of some candidate
they consider relatively bad.

But suppose that MJ is used and the voters give their sincere absolute
ratings (on some magically standardised scale, independent
of the actual candidates).

Say there are candidates X and Y and voters rate them on A-B-C-D-E-F
grading ballots.

40: X a, Yf
11: Ya, Xb
38: Ya, Xf
11: Yc, Xf

http://wiki.electorama.com/wiki/IBIFA

Chris Benham

http://wiki.electorama.com/wiki/IBIFA

On 9/4/2016 4:35 AM, Kevin Venzke wrote:

Hi Steve,

I wrote a full response but then trimmed sections to reduce

redundancy. There is still a fair amount.

Steve wrote:

At the same time, I see B&L as correctly assuming (with E. J.

Nanson ) that the ‘object of … an election is to select …

some candidate who shall, in the opinion of a majority of the

electors, be most fit for the post….(p.209). I also find

it hard to disagree with B&L’s following 2 assertions: ‘Clearly ….

majorities of grades are … considerably more discerning

decisions than are majorities of preferences’ (p.283); Therefore,

‘A method [of voting] should elicit the honest expression of

voters’ opinions as inputs, for the aim of an election is to

produce outputs which represent as [well] as possible the true

wishes of societies and of juries’ (p.352).

I agree that a method should elicit the honest expression of

opinions as inputs, but I believe they should do that by making

it in the voter's strategic interest to express them.

Consequently, I see MJ as always having the advantage over

competing methods by allowing each voter clearly to express his

or her evaluation of each candidate. MJ invites each voter to

‘grade’ each candidate as being either EXCELLENT, VERY GOOD,

...

And I will say again that I don't feel it is sufficient to simply

"allow" and "invite" these things.

K: The notion that the voter should rate [evaluate] candidates

independently of how they rated other candidates is basically

true. But this applies both to sincere voters and to voters

interested in maximizing the effect of their vote. If the latter

voters conclude (as I believe they usually should) that only the

two extreme ratings can maximize the effect of their vote,

then they should only use the two extreme ratings.

S: Depending on their own scale of values, I accept that some voter

may validly choose to use only these two ‘extreme

ratings’. However, MJ also allows other voters who may have a

greater knowledge of the different qualities of the candidates,

appropriately from their point of view, to use all 6 grades

accurately to evaluate each candidate.

Well, strategic voters don't have different scales of values or

inferior knowledge of the different candidates. They are simply

trying to maximize the effect of their vote given the method's rules.

If a voter sees 6 candidates
as EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, and to REJECT,

respectively, she may see that to reject all except her excellent

candidate might allow her rejected candidate to win, rather than

her very good, good, or acceptable candidate. Why should she

take this risk [...]

But this risk is exactly what strategic voting aims to reduce.

and thus also to choose not to contribute honestly to the discovery

of the socially most valued winner?

If I could disagree with only one thing it would be this notion,

that voters care about discovering the best winner, as opposed

to trying to get their preferred candidates elected.

K: Relatedly, I don't see it as an inherently valuable feature of a

method for voters to be able to "clearly express his

or her evaluation" of a candidate, without it actually being in

their strategic interest to do that.

S: Surely, to the extent that citizens might evaluate all the

candidates honestly, this would help greatly to inform all

candidates and the public both about the real values held by

citizens and the perceived value of each candidate. Perhaps

most importantly, it would also have the best chance of electing

the candidate with the qualities needed successfully to

face her official challenges.
If so, contrary to what you say several paragraphs below, this

inclines me to say that each voter usually should grade

each candidate on their own merits, not ‘rate’ or rank each in

relation to one another.

"Should" in what sense? If voters don't want the method to violate

Arrow/IIA then they "should" decline to rate anybody

EXCELLENT if there is no EXCELLENT candidate. But the strategic

voter "should" not refrain from this, if his concern is to

get the best outcome for himself.

On the other hand, if a voter or a group
of voters wish to manipulate the MJ ballot to maximize the chances

of their favorite candidate winning (i.e. by attempting to

translate the ‘grades’ into ‘rankings’), MJ’s method of electing a

winner only by his highest median-grade minimizes ‘cheating’,

‘minimizes the probability that a judge may be found who can

effectively raise or lower the grade in the worst case’ (p.212).

MJ reduces such opportunities almost by ‘half’ (pp. 15, 197, 282),

i.e. it is still only ‘partially strategy-proof-in ranking’

(pp.15, 245). Do you see any errors in B&L’s mathematical proofs

of the above claims.

Is this quote the basis of claims that MJ reduces manipulability?

Because most methods don't even have the mechanism

discussed... Like I've said, I understand this claim as a comparison

to Range, but not much else.

S: MJ avoids Arrow’s paradoxes. Do you disagree?

K: [….] This is not a particularly impressive way to evade Arrow

because practically speaking voters under rated methods

should be expected to rate candidates differently based on which

other candidates are in the race.

S: Up until now, I thought you were using ‘rate’ as equivalent to

‘grade’ but now you seem to be using it as equivalent

to ‘rank’.

No, rate means grade. I am not using it here to mean rank.

As I understand it, MJ’s design prompts each citizen to ‘grade’

each candidate with respect only to her own concept of

what her EXCELLENT candidate would be. Each candidate can be

judged on their own merits in the light of each voter’s own

criteria, not in the light of who else is running. Thus, while

rankings can be deduced from grades, grading is not ranking.

The MJ winner is intended not to be decided by ranking.

Yes, that is MJ's intention, and if people do that (rate in

comparison to a hypothetical candidate that might not be in

the race), then it does not run afoul of Arrow/IIA. However, if

voters do the strategically obvious thing of rating their

favorite candidate EXCELLENT even if he is not exactly excellent,

then in effect the method will not be independent of

irrelevant alternatives, and the method isn't dodging Arrow in any

meaningful way.

K: The alternative is that many voters will choose not to rate

any candidate "excellent" or "rejected."

S: I agree that this is one ‘option’ among many but I do not see

why you say it is ‘the alternative’, as if this option

is the only option or the one that should be preferred.

I am speaking of something that is either true or false:

True means: Some voters use the top and bottom grades even if the

best/worst candidates do not deserve them

False means: No voters ever assign grades outside the range that the

actual candidates actually merit

If the case is "True" then the method isn't avoiding Arrow in a

practical sense. It will have the same issues with

irrelevant alternatives that rank methods do.

K: But I think even sincere-minded voters will be inclined to make

sure somebody is getting those ratings.

S: Yes, especially if they see them as deserving these different

grades.

Yes, that is obvious ("those ratings" referring to the top and

bottom ones). I'm saying I think sincere-minded voters

will probably use the top and bottom ratings even when no candidate

actually deserves them.

K: But under MJ all the ratings [gradings] are independent. The

only reason for a strategic-minded MJ voter to rate B

between A and C is if he has peculiarly good information about what

(final) score for B will be good enough to beat C but

not so good that it creates a problem for A.

S: Yes, but with MJ he is less like to have such ‘peculiarly good

information’. MJ makes it less likely that this

‘strategic-minded voter’ will be able to make this calculation with

confidence.

Completely agree. However, while I am saying that this means the

strategic voter cannot calculate any good way to use the

intermediate ratings, you want to take it further:

Therefore, he is more likely simply to grade the candidates

‘honestly’, [...]

I don't believe this is true. I think the strategic voter can do

better than that. I think I've probably done simulations

on the exact question, I should probably check or make a new one...

S: > Currently, these features incline me to see MJ as the best

method for electing a President. However, you do not seem

to agree, given your next sentence, even though ‘approval voting’

does not allow each voter to express the deferent

intensities with which
they might approve of the different candidates:

K: >This is because in the scenario I discuss below, MJ would offer

different intensities, but nobody (who knew what they

were doing) would use them.
S: Given that MJ offers something like half the scope for

manipulation, I would like to understand why you still think a

knowing MJ voter would choose not to use the different intensities

it offers.

At the same time, no method allows a voter to ‘know what they are

doing’,

By "know what they are doing" I'm talking about understanding the

strategy of a method.

Regarding "half the scope for manipulation" I would need to

understand what that is referring to, if it's the thing quoted

above, or something else. As someone who has created simulations to

measure strategic incentive, I don't feel like much

can be summarized with that kind of language. The claim could well

be true in proper context; for example as I was saying

above, I see that a strategic voter will have a very hard time

making intelligent use of intermediate grades, and by that I

certainly mean to include the idea of manipulating the outcome with

them. On the other hand if "manipulation" includes such

simple strategies as using only the extreme grades, then I don't

think MJ compares that well.

K: That transforms the method into Approval. You are right, that

I’m not certain that Approval (be it actual Approval or

MJ that turned into Approval) is the best method for electing a

president.

S: Again, am I correct in believing that whenever MJ might be

‘turned into Approval’, this use could still allow only

half the manipulation offered by actual Approval?

Well, two-slot MJ, two-slot Range, and Approval are exactly the same

method, so the answer must be no, no matter what the

manipulability claim is.

Also, given that Approval does not allow any voter to express different
intensities of approval, I would like to understand why you might

still consider it to be the ‘best’.

I might but probably wouldn't deem it best. I've already explained

why I prefer it to MJ: MJ "allows" and "invites" voters

to fill out the ballot in a way that is probably not strategically

ideal. That feels deceptive to me, in that less savvy

voters could be at a disadvantage.

K: If [MJ] voters have this perception and respond with this

behavior, then the method is just an overly complicated form

of approval voting.
S: But do you agree that this is a largely mistaken ‘perception’?

Not really.

In any case, if some citizens make this mistake, they
could only blame themselves for failing both to take advantage of

the opportunity to help elect the most valued candidate

by honestly evaluating all of them, and perhaps to have partly

wasted their vote by voting strategically but only with

half a chance of being successful in their own eyes. Consequently,

we could argue that MJ at least has the clear virtue

over the ‘traditional’ methods of most certainly offering these

democratic advantages most completely to citizens.

But I don't view it as a mistake.

K: In that case, I'd rather just use approval, because it's

clearer what's going on.

S: As I see it, no method allows us to know exactly the motives or

calculations which each voter is making when they

vote. However, is it not true that citizens are more like to

‘evaluate’ the candidates, given that MJ’s ballots alone

asks for these grades?

Once again, just because you ask for the grades doesn't mean you're

going to get them or that the voter should (per his

own interests) want to give them to you. It is trivially true that

if the grades aren't present on the ballot then

nobody gets to submit them, of course.

At the same time, I would like to understand why you might ‘rather’

use an ‘impoverished’ method like APPROVAL rather

than MJ which is ‘rich’ with the above opportunities.

I think the "opportunities" are not likely an advantage for those

who take them.

K: If I understand correctly, Orsay was a poll with no stakes. I

would be curious to know whether/how the voters were

told how the ballots would be counted.
S: In this regard, you may wish to consider Belinski’s following

report on page 255 in his book with Laraki (B&L:

Majority Judgment): ‘The experiment—the ballot and the method of

ranking—was explained to potential participants well

before election day in individual letters, an article in the town’s

quarterly magazine, posters, and an evening presentation

open to all.’ Also, on page 17, B&L report their following

instructions to the participants in their different October 2008

experiment conducted on the Web: ‘You will be asked to evaluate in

a language of grades. A candidate’s majority-grade is

the middlemost of her/his grades… The candidates are ranked

according to their majority-grades.’

S: While B&L openly accept that a binding election was not at

‘stake’, I see that experiment as surely providing some

empirical evidence that goes some why to suggesting how people

would use the MJ ballot in an actual election. Of course,

better empirical evidence would be provided, at least by a ‘trial’

adoption of MJ for some actual elections.

Thank you for this summary.

K: In any case, don't think I am saying that under MJ, voters would

all become strategic and this would make the outcomes

worse. I actually think it would make the outcomes better. (As in

"more plausible," if the voters had been a legislature.)

The downside of the voters being strategic is just that the

different rating [grading] options become pointless. So my

criticism is not that MJ is bad, it's that it is needlessly

complicated for what it might and hopefully would turn into.

S: Yes, MJ offers ‘different rating [grading] options’, and much

less scope for manipulation. Admittedly, the counting

of MJ is slightly more complicated than simply summing approvals or

scores. However, is not MJ’s potential for periodically

and more precisely informing all citizens and candidates about the

actual intensities with which the many different scales of

values and concerns that actually exist within one’s society an

additional benefit well worth this slight additional

complication, e.g. a complication which is also much less than any

Condorcet methods or IRV?

But it would only do that (i.e. "more precisely informing all

citizens and candidates about the actual intensities.....")

if voters use it as intended. I don't think they would. If you want

to say that Approval isn't going to produce a lot of

information on the preferences, I will totally agree, and agree that

it's not ideal, but I don't think the conclusion to draw

is that MJ is better than Approval.

Later-no-harm (IRV satisfies, MJ and MAM don't).

I am going to trim your argument from B&L because the point of

disagreement becomes quickly obvious and has little to

do with LNHarm itself:

B&L admit and address this theoretical failure and explain
why it is unimportant in practice (pp.285-287). I will try to

explain why.

[...]

Thus, by the 1st voter now ‘giving a more ‘positive rating [than

before (i.e. Good rather than

Poor) to her] less-preferred candidate’, this has caused her

‘more-preferred candidate to lose. This criterion presumes

that this result would not have been 1st voter’s intention. It

assumes that each voter is only interested in maximizing

the chances that the candidate she personally most favors will be

the winner. B&L see this as the flawed assumption made

by advocates of the ‘traditional methods’.
Instead, B&L assume that voters want the winner to be the candidate

most highly valued by a majority of all the voters.

I think this is bizarre and unrealistic. It's hard for me to believe

that somebody thinks this is what motivates voters.

The premise would render moot all concerns, not just about LNHarm,

but about probably all strategy criteria and

guarantees. This is such an unbridgeable gap that I guess we may

soon be able to wrap up this discussion.

At the same time, do you disagree with Belinski’s claims both
1. that MJ discovery of the winner only by his median grade

makes it only half as like that one voter changing her

grade for one candidate will change who is the winner, and
2. that with many candidates and millions of voters, it is

‘almost certain’ that any manipulation sought by such

changes would not be successful?

compared to Range? maybe. Otherwise the question is not clear
Depends what you mean by manipulation. With some limited

definition I might agree (see earlier thoughts in this post).

The (seeming) incompatibility that frustrates me the most is that

between minimal defense and LNHarm.

S: In practice, there should be no need for such ‘frustration’ if

you answers ‘yes’ to both questions posed by the last

sentence in my immediately above paragraph.

Were those questions related to LNHarm? Are you perhaps implying

that if a voter truncates due a LNHarm concern that

this counts as "manipulation," and would not likely be "successful"?

If so, I don't agree with that at all; truncation

under MJ will have a similar effect as under many other methods.

K: Of the three methods (MAM, IRV, MJ) I would pick MAM. I'm not

sure if I prefer MJ to IRV. Even if we replace MJ in the

question with Approval, I am not sure.
S: Given my above points plus the fact that MAM gives each voter

less opportunity to express the different intensities of

support they might have for the different candidates, and the much

greater difficulty that ordinary citizens would have in

understanding exactly how MAM is counted, I would like to

understand why you would ‘prefer’ MAM over MJ.

I grant that MAM is harder to understand, but I think it gets more

mileage out of its complexity than MJ gets out of its.

When it comes to expressiveness, I think that practically speaking

MAM is actually better than MJ, due to the scenario that

MJ turns into Approval and consequently expresses very little.

K: [….] Otherwise, I'm afraid of Approval's potential to produce

results that appear arbitrary and inconclusive (fragmented

electorate, unconvincing winner).

K: In general I feel that election methods should produce an

outcome that would be plausible if the voters had been able

to gather and vote in person, just as a legislature.

K: For example, MJ violates Condorcet Loser. In theory it can

elect a candidate who could not win head-to-head against any

of the other candidates. It is not likely that a legislature would

settle on an outcome that could not survive a one-on-one

vote against any of the other options.

S: Contrary to B&L’s belief, your worry here regarding Condorcet

seems to assume that ‘preferences’ are more important

than ‘evaluations’. However, if all MJ voters equally distributed

their EXCELLENTs between all the candidates except the

one candidate to which they all gave VERY GOOD, why would you (or a

legislature) be justified in not seeing the one with

all these VERY GOODs as the appropriate winner? This is an example

of the fact that MJ seems naturally to discover the

most valued candidate unless every voter grades all the candidates

exactly in the same way.

S: Why would you not see MJ as ‘plausible’ in this sense? For

example, a legislature could elect its prime minister

in a parliamentary system using MJ. In the extremely unlikely

event that this might result in an MJ tie, it could be

quickly resolved by electing one winner by a head to head vote.

I.e. after discovering to 2 candidates to be equally

qualified, the winner would be the one ‘preferred’ by the majority

for whatever reason.

Let me clarify my thought experiment. I'm not saying to imagine

using MJ (or another method) being used in a legislature.

Legislators talk to each other, gauge support for positions, and

vote yea or nay on specific proposals (or they delay

and don't vote at all), usually ending up with a majority approving

a single outcome. I'm saying take the cast ballots

for an electorate, and the method's outcome, and ask whether a

traditional legislature could have realistically arrived

at the same outcome using the same proportions of voters. If it

doesn't make sense, then somebody probably has a basis

to complain about the method and undermine the legitimacy of the winner.

Now why do I say to do this, and why I do not care about

"preferences" vs "evaluations":

Legislatures normally function according to majority rule. The

electorate is basically a legislature that can't fit in

a single room, so they have to record their voting instructions on a

ballot paper. If majority rule is violated in a

legislature, people will cry foul. It shouldn't be expected to be

different for an electorate (this is my opinion). So I

say that a good way to minimize strategy complaints/concerns is to

make sure the interpretation of the ballots produces

an outcome that would be plausible if the electorate had actually

met in a room.

K: Also, suppose that an MJ voter doesn't like any candidate and

his best rating awarded is "acceptable." In so doing he

can actually cause his "favorite" candidate to lose to somebody

else. I would expect a legislator to understand the risk

of this happening
and not cast votes that could have such an effect.
S: Yes, in this context, if he greatly fears any other candidate

winning, rationally he should give his ‘favorite’ an

excellent and reject the rest.

Glad we agree. Note that it is this behavior (rating a sub-par

candidate differently based on whether there are any

better candidates in the race) that raises issues with Arrow.

Kevin

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On 9/6/2016 10:47 AM, steve bosworth wrote: > S: For B&L, the grades used are not ‘magically standardized’ but > culturally determined by human definitions and practices, e.g. at > least from our school days we all are prompted to develop our own > understanding of such common words as EXCELLENT, VERY GOOD, etc., i.e. > as used in the various contexts in which we are called upon to > evaluate proposals, decisions, performances, etc.Do we disagree about > this? C: Yes. Candidates for political office are in a different category. Suppose there are several candidates and in your sincere opinion they are all very bad and deserve the lowest possible grade but one is significantly even worse than the others. Would you (a) abstain from voting, or (b) turn up and give all the candidates the lowest rating or (c) give the bottom-most rating only to the worst candidate and "insincerely" give the other bad candidates a higher rating? Chris Benham > > > ------------------------------------------------------------------------ > > *From:*C.Benham <cbenham@adam.com.au> > *Sent:* Saturday, September 3, 2016 10:13 PM > *To:* Kevin Venzke; steve bosworth; election-methods@lists.electorama.com > *Subject:* Re: [EM] (3) MJ -- The easiest method to 'tolerate' > > Hi C. Benham and everyone, > > C: [C. Benham wrote:] An election for a powerful political office > isn't a jury-like > collaboration among voters to select the best winner. Rather it is > competition between factions of voters who are trying to elect their > favourites and/or prevent the election of some candidate > they consider relatively bad. > > S:Perhaps we do not entirely disagree as you also want the ‘best > winner’ to be elected.However, we would seem to disagree if, as a > democrat, you are really saying that you do not want the winner to be > the one who is most highly valued by a majority of the voters.Of > course, different citizens will have different ideas about what an > EXCELLENT candidate would look like and MJ allows each voter honestly > (or dishonestly) to ‘evaluate’ each candidate using a rich common > language, i.e. to ‘grade’ each to the extent that each does or does > not come close to being EXCELLENT.By discovering the one candidate > whose majority ‘median-grade’ is highest, MJ most efficiently allows a > society to discover that most highly valued winner. This is partly > because ‘majorities of grades are … considerably more discerning > decisions than are majorities of preferences’ (Belinski & Laraki, > /Majority Judgment/, p.283). Do we disagree? > > Also, to the extent that I understand your IBIFA method as contrasted > to MJ, IBIFA 1): is more likely to prompt voters to ‘rank’ rather than > to ‘evaluate’ the competing candidates, and 2): its reasons for its > different stages of rules for discovering its winner are more complex > and less obvious than the reasons for MJ’s count.’ 3): Also, as > explained by B&L, IBIFA (as a ‘point-summing method’) is more > vulnerable to strategic ‘manipulation’, as well as to Condorcet ties > and Arrow’s paradoxes. In this last regard, do you see any flaws in > B&L’s argument that MJ is entirely strategy-proof with regard to > grading?Also, in contrast to the many ways that all the ‘point-summing > methods’ offer opportunities for voters to ‘manipulate’ the results, > do you see any flaws in their mathematical proof that MJ is almost > ‘half’ as vulnerable in this regard, i.e. if and when MJ ballots might > be used to ‘rank’ rather than to ‘grade’ the candidates (see pp.14, > 15, 189-198, 282-292)? > > S:With regard to your example (below), I also see X as winning by > MJ.X’s median grade is ‘b’ [or Very Good’] while Y’s is ‘c’ [or Good], > i.e. 51% of the ‘grades’ evaluated X as Very Good, while 51% of the > grades evaluated Y only as Good.What is the problem with this? > > You suggest below:‘The 11 who voted Ya,Xb and the 11 who voted Yc, Xf > might wish they had "lied" and voted like the rest of Y's > supporters.’However, please also note that the 11 who voted Ya,Xb’ > also agreed that X is Very Good, and thus it is only ‘the 11 who voted > Yc, Xf’ who presumably will be less satisfied with X’s win. > > > C: But suppose that MJ is used and the voters give their sincere absolute > ratings (on some magically standardised scale, independent > of the actual candidates). > > S: For B&L, the grades used are not ‘magically standardized’ but > culturally determined by human definitions and practices, e.g. at > least from our school days we all are prompted to develop our own > understanding of such common words as EXCELLENT, VERY GOOD, etc., i.e. > as used in the various contexts in which we are called upon to > evaluate proposals, decisions, performances, etc.Do we disagree about > this? > > C: Say there are candidates X and Y and voters rate them on A-B-C-D-E-F > grading ballots. > > 40: X a, Yf > 11: Ya, Xb > 38: Ya, Xf > 11: Yc, Xf > > 60% of these voters prefer Y to X but MJ elects X. Is this really the > best result? The 11 who voted Ya,Xb and the 11 who voted Yc, Xf > might wish they had "lied" and voted like the rest of Y's supporters. > > I like expressive ballots and there's no reason why IBIFA can't also use > 6-slot ratings ballots. Here it elects Y. Whenever the winners of > IBIFA and MJ (or Bucklin or MCA or Range) differ the IBIFA winner will > pairwise-beat the other. > > http://wiki.electorama.com/wiki/IBIFA > > Chris Benham > > http://wiki.electorama.com/wiki/IBIFA > > > > > > > ------------------------------------------------------------------------ > *From:* C.Benham <cbenham@adam.com.au> > *Sent:* Saturday, September 3, 2016 10:13 PM > *To:* Kevin Venzke; steve bosworth; election-methods@lists.electorama.com > *Subject:* Re: [EM] (3) MJ -- The easiest method to 'tolerate' > Steve, > > An election for a powerful political office isn't a jury-like > collaboration among voters to select the best winner. Rather it is > competition between factions of voters who are trying to elect their > favourites and/or prevent the election of some candidate > they consider relatively bad. > > But suppose that MJ is used and the voters give their sincere absolute > ratings (on some magically standardised scale, independent > of the actual candidates). > > Say there are candidates X and Y and voters rate them on A-B-C-D-E-F > grading ballots. > > 40: X a, Yf > 11: Ya, Xb > 38: Ya, Xf > 11: Yc, Xf > > 60% of these voters prefer Y to X but MJ elects X. Is this really the > best result? The 11 who voted Ya,Xb and the 11 who voted Yc, Xf > might wish they had "lied" and voted like the rest of Y's supporters. > > I like expressive ballots and there's no reason why IBIFA can't also use > 6-slot ratings ballots. Here it elects Y. Whenever the winners of > IBIFA and MJ (or Bucklin or MCA or Range) differ the IBIFA winner will > pairwise-beat the other. > > http://wiki.electorama.com/wiki/IBIFA > > Chris Benham > > http://wiki.electorama.com/wiki/IBIFA > > > > > > > On 9/4/2016 4:35 AM, Kevin Venzke wrote: > > Hi Steve, > > > > I wrote a full response but then trimmed sections to reduce > redundancy. There is still a fair amount. > > > > Steve wrote: > >> At the same time, I see B&L as correctly assuming (with E. J. > Nanson ) that the ‘object of … an election is to select … > >> some candidate who shall, in the opinion of a majority of the > electors, be most fit for the post….(p.209). I also find > >> it hard to disagree with B&L’s following 2 assertions: ‘Clearly …. > majorities of grades are … considerably more discerning > >> decisions than are majorities of preferences’ (p.283); Therefore, > ‘A method [of voting] should elicit the honest expression of > >> voters’ opinions as inputs, for the aim of an election is to > produce outputs which represent as [well] as possible the true > >> wishes of societies and of juries’ (p.352). > > I agree that a method should elicit the honest expression of > opinions as inputs, but I believe they should do that by making > > it in the voter's strategic interest to express them. > > > >> Consequently, I see MJ as always having the advantage over > competing methods by allowing each voter clearly to express his > >> or her evaluation of each candidate. MJ invites each voter to > ‘grade’ each candidate as being either EXCELLENT, VERY GOOD, > >> ... > > And I will say again that I don't feel it is sufficient to simply > "allow" and "invite" these things. > > > >>> K: The notion that the voter should rate [evaluate] candidates > independently of how they rated other candidates is basically > >>> true. But this applies both to sincere voters and to voters > interested in maximizing the effect of their vote. If the latter > >>> voters conclude (as I believe they usually should) that only the > two extreme ratings can maximize the effect of their vote, > >>> then they should only use the two extreme ratings. > >> S: Depending on their own scale of values, I accept that some voter > may validly choose to use only these two ‘extreme > >> ratings’. However, MJ also allows other voters who may have a > greater knowledge of the different qualities of the candidates, > >> appropriately from their point of view, to use all 6 grades > accurately to evaluate each candidate. > > Well, strategic voters don't have different scales of values or > inferior knowledge of the different candidates. They are simply > > trying to maximize the effect of their vote given the method's rules. > > > >> If a voter sees 6 candidates > >> as EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, and to REJECT, > respectively, she may see that to reject all except her excellent > >> candidate might allow her rejected candidate to win, rather than > her very good, good, or acceptable candidate. Why should she > >> take this risk [...] > > But this risk is exactly what strategic voting aims to reduce. > > > >> and thus also to choose not to contribute honestly to the discovery > of the socially most valued winner? > > If I could disagree with only one thing it would be this notion, > that voters care about discovering the best winner, as opposed > > to trying to get their preferred candidates elected. > > > >> K: Relatedly, I don't see it as an inherently valuable feature of a > method for voters to be able to "clearly express his > >> or her evaluation" of a candidate, without it actually being in > their strategic interest to do that. > >> > >> S: Surely, to the extent that citizens might evaluate all the > candidates honestly, this would help greatly to inform all > >> candidates and the public both about the real values held by > citizens and the perceived value of each candidate. Perhaps > >> most importantly, it would also have the best chance of electing > the candidate with the qualities needed successfully to > >> face her official challenges. > >> If so, contrary to what you say several paragraphs below, this > inclines me to say that each voter usually *should* grade > >> each candidate on their own merits, not ‘rate’ or rank each in > relation to one another. > > "Should" in what sense? If voters don't want the method to violate > Arrow/IIA then they "should" decline to rate anybody > > EXCELLENT if there is no EXCELLENT candidate. But the strategic > voter "should" not refrain from this, if his concern is to > > get the best outcome for himself. > > > >> On the other hand, if a voter or a group > >> of voters wish to manipulate the MJ ballot to maximize the chances > of their favorite candidate winning (i.e. by attempting to > >> translate the ‘grades’ into ‘rankings’), MJ’s method of electing a > winner only by his highest median-grade minimizes ‘cheating’, > >> ‘minimizes the probability that a judge may be found who can > effectively raise or lower the grade in the worst case’ (p.212). > >> MJ reduces such opportunities almost by ‘half’ (pp. 15, 197, 282), > i.e. it is still only ‘partially strategy-proof-in ranking’ > >> (pp.15, 245). Do you see any errors in B&L’s mathematical proofs > of the above claims. > > Is this quote the basis of claims that MJ reduces manipulability? > Because most methods don't even have the mechanism > > discussed... Like I've said, I understand this claim as a comparison > to Range, but not much else. > > > >> S: MJ avoids Arrow’s paradoxes. Do you disagree? > >> > >> K: [….] This is not a particularly impressive way to evade Arrow > because practically speaking voters under rated methods > >> *should* be expected to rate candidates differently based on which > other candidates are in the race. > >> S: Up until now, I thought you were using ‘rate’ as equivalent to > ‘grade’ but now you seem to be using it as equivalent > >> to ‘rank’. > > No, rate means grade. I am not using it here to mean rank. > > > >> As I understand it, MJ’s design prompts each citizen to ‘grade’ > each candidate with respect only to her own concept of > >> what her EXCELLENT candidate would be. Each candidate can be > judged on their own merits in the light of each voter’s own > >> criteria, not in the light of who else is running. Thus, while > rankings can be deduced from grades, grading is not ranking. > >> The MJ winner is intended not to be decided by ranking. > > Yes, that is MJ's intention, and if people do that (rate in > comparison to a hypothetical candidate that might not be in > > the race), then it does not run afoul of Arrow/IIA. However, if > voters do the strategically obvious thing of rating their > > favorite candidate EXCELLENT even if he is not exactly excellent, > then in effect the method will not be independent of > > irrelevant alternatives, and the method isn't dodging Arrow in any > meaningful way. > > > >> K: The alternative is that many voters will choose not to rate > *any* candidate "excellent" or "rejected." > >> S: I agree that this is one ‘option’ among many but I do not see > why you say it is ‘the alternative’, as if this option > >> is the only option or the one that should be preferred. > > I am speaking of something that is either true or false: > > > > True means: Some voters use the top and bottom grades even if the > best/worst candidates do not deserve them > > False means: No voters ever assign grades outside the range that the > actual candidates actually merit > > > > If the case is "True" then the method isn't avoiding Arrow in a > practical sense. It will have the same issues with > > irrelevant alternatives that rank methods do. > > > >> K: But I think even sincere-minded voters will be inclined to make > sure somebody is getting those ratings. > >> S: Yes, especially if they see them as deserving these different > grades. > > Yes, that is obvious ("those ratings" referring to the top and > bottom ones). I'm saying I think sincere-minded voters > > will probably use the top and bottom ratings even when no candidate > actually deserves them. > > > >> K: But under MJ all the ratings [gradings] are independent. The > only reason for a strategic-minded MJ voter to rate B > >> between A and C is if he has peculiarly good information about what > (final) score for B will be good enough to beat C but > >> not so good that it creates a problem for A. > >> > >> S: Yes, but with MJ he is less like to have such ‘peculiarly good > information’. MJ makes it less likely that this > >> ‘strategic-minded voter’ will be able to make this calculation with > confidence. > > Completely agree. However, while I am saying that this means the > strategic voter cannot calculate any good way to use the > > intermediate ratings, you want to take it further: > > > >> Therefore, he is more likely simply to grade the candidates > ‘honestly’, [...] > > I don't believe this is true. I think the strategic voter can do > better than that. I think I've probably done simulations > > on the exact question, I should probably check or make a new one... > > > >> S: > Currently, these features incline me to see MJ as the best > method for electing a President. However, you do not seem > >> to agree, given your next sentence, even though ‘approval voting’ > does not allow each voter to express the deferent > >> intensities with which > >> they might approve of the different candidates: > >> > >> K: >This is because in the scenario I discuss below, MJ would offer > different intensities, but nobody (who knew what they > >> were doing) would use them. > >> S: Given that MJ offers something like half the scope for > manipulation, I would like to understand why you still think a > >> knowing MJ voter would choose not to use the different intensities > it offers. > >> At the same time, no method allows a voter to ‘know what they are > doing’, > > By "know what they are doing" I'm talking about understanding the > strategy of a method. > > > > Regarding "half the scope for manipulation" I would need to > understand what that is referring to, if it's the thing quoted > > above, or something else. As someone who has created simulations to > measure strategic incentive, I don't feel like much > > can be summarized with that kind of language. The claim could well > be true in proper context; for example as I was saying > > above, I see that a strategic voter will have a very hard time > making intelligent use of intermediate grades, and by that I > > certainly mean to include the idea of manipulating the outcome with > them. On the other hand if "manipulation" includes such > > simple strategies as using only the extreme grades, then I don't > think MJ compares that well. > > > >> K: That transforms the method into Approval. You are right, that > I’m not certain that Approval (be it actual Approval or > >> MJ that turned into Approval) is the best method for electing a > president. > >> S: Again, am I correct in believing that whenever MJ might be > ‘turned into Approval’, this use could still allow only > >> half the manipulation offered by actual Approval? > > Well, two-slot MJ, two-slot Range, and Approval are exactly the same > method, so the answer must be no, no matter what the > > manipulability claim is. > > > >> Also, given that Approval does not allow any voter to express different > >> intensities of approval, I would like to understand why you might > still consider it to be the ‘best’. > > I might but probably wouldn't deem it best. I've already explained > why I prefer it to MJ: MJ "allows" and "invites" voters > > to fill out the ballot in a way that is probably not strategically > ideal. That feels deceptive to me, in that less savvy > > voters could be at a disadvantage. > > > >> K: If [MJ] voters have this perception and respond with this > behavior, then the method is just an overly complicated form > >> of approval voting. > >> S: But do you agree that this is a largely mistaken ‘perception’? > > Not really. > > > >> In any case, if some citizens make this mistake, they > >> could only blame themselves for failing both to take advantage of > the opportunity to help elect the most valued candidate > >> by honestly evaluating all of them, and perhaps to have partly > wasted their vote by voting strategically but only with > >> half a chance of being successful in their own eyes. Consequently, > we could argue that MJ at least has the clear virtue > >> over the ‘traditional’ methods of most certainly offering these > democratic advantages most completely to citizens. > > But I don't view it as a mistake. > > > >> K: In that case, I'd rather just use approval, because it's > clearer what's going on. > >> S: As I see it, no method allows us to know exactly the motives or > calculations which each voter is making when they > >> vote. However, is it not true that citizens are more like to > ‘evaluate’ the candidates, given that MJ’s ballots alone > >> asks for these grades? > > Once again, just because you ask for the grades doesn't mean you're > going to get them or that the voter should (per his > > own interests) want to give them to you. It is trivially true that > if the grades aren't present on the ballot then > > nobody gets to submit them, of course. > > > >> At the same time, I would like to understand why you might ‘rather’ > use an ‘impoverished’ method like APPROVAL rather > >> than MJ which is ‘rich’ with the above opportunities. > > I think the "opportunities" are not likely an advantage for those > who take them. > > > >> K: If I understand correctly, Orsay was a poll with no stakes. I > would be curious to know whether/how the voters were > >> told how the ballots would be counted. > >> S: In this regard, you may wish to consider Belinski’s following > report on page 255 in his book with Laraki (B&L: > >> Majority Judgment): ‘The experiment—the ballot and the method of > ranking—was explained to potential participants well > >> before election day in individual letters, an article in the town’s > quarterly magazine, posters, and an evening presentation > >> open to all.’ Also, on page 17, B&L report their following > instructions to the participants in their different October 2008 > >> experiment conducted on the Web: ‘You will be asked to evaluate in > a language of grades. A candidate’s majority-grade is > >> the middlemost of her/his grades… The candidates are ranked > according to their majority-grades.’ > >> S: While B&L openly accept that a binding election was not at > ‘stake’, I see that experiment as surely providing some > >> empirical evidence that goes some why to suggesting how people > would use the MJ ballot in an actual election. Of course, > >> better empirical evidence would be provided, at least by a ‘trial’ > adoption of MJ for some actual elections. > > Thank you for this summary. > > > >> K: In any case, don't think I am saying that under MJ, voters would > all become strategic and this would make the outcomes > >> worse. I actually think it would make the outcomes better. (As in > "more plausible," if the voters had been a legislature.) > >> The downside of the voters being strategic is just that the > different rating [grading] options become pointless. So my > >> criticism is not that MJ is bad, it's that it is needlessly > complicated for what it might and *hopefully would* turn into. > >> S: Yes, MJ offers ‘different rating [grading] options’, and much > less scope for manipulation. Admittedly, the counting > >> of MJ is slightly more complicated than simply summing approvals or > scores. However, is not MJ’s potential for periodically > >> and more precisely informing all citizens and candidates about the > actual intensities with which the many different scales of > >> values and concerns that actually exist within one’s society an > additional benefit well worth this slight additional > >> complication, e.g. a complication which is also much less than any > Condorcet methods or IRV? > > But it would only do that (i.e. "more precisely informing all > citizens and candidates about the actual intensities.....") > > if voters use it as intended. I don't think they would. If you want > to say that Approval isn't going to produce a lot of > > information on the preferences, I will totally agree, and agree that > it's not ideal, but I don't think the conclusion to draw > > is that MJ is better than Approval. > > > >>>>> Later-no-harm (IRV satisfies, MJ and MAM don't). > > I am going to trim your argument from B&L because the point of > disagreement becomes quickly obvious and has little to > > do with LNHarm itself: > > > >> B&L admit and address this theoretical failure and explain > >> why it is unimportant in practice (pp.285-287). I will try to > explain why. > > [...] > >> Thus, by the 1st voter now ‘giving a more ‘positive rating [than > before (i.e. Good rather than > >> Poor) to her] less-preferred candidate’, this has caused her > ‘more-preferred candidate to lose. This criterion presumes > >> that this result would not have been 1st voter’s intention. It > assumes that each voter is only interested in maximizing > >> the chances that the candidate she personally most favors will be > the winner. B&L see this as the flawed assumption made > >> by advocates of the ‘traditional methods’. > >> Instead, B&L assume that voters want the winner to be the candidate > most highly valued by a majority of all the voters. > > I think this is bizarre and unrealistic. It's hard for me to believe > that somebody thinks this is what motivates voters. > > The premise would render moot all concerns, not just about LNHarm, > but about probably *all* strategy criteria and > > guarantees. This is such an unbridgeable gap that I guess we may > soon be able to wrap up this discussion. > > > >> At the same time, do you disagree with Belinski’s claims both > >> 1. that MJ discovery of the winner only by his median grade > makes it only half as like that one voter changing her > >> grade for one candidate will change who is the winner, and > >> 2. that with many candidates and millions of voters, it is > ‘almost certain’ that any manipulation sought by such > >> changes would not be successful? > > 1. compared to Range? maybe. Otherwise the question is not clear > > 2. Depends what you mean by manipulation. With some limited > definition I might agree (see earlier thoughts in this post). > > > >> The (seeming) incompatibility that frustrates me the most is that > between minimal defense and LNHarm. > >> S: In practice, there should be no need for such ‘frustration’ if > you answers ‘yes’ to both questions posed by the last > >> sentence in my immediately above paragraph. > > Were those questions related to LNHarm? Are you perhaps implying > that if a voter truncates due a LNHarm concern that > > this counts as "manipulation," and would not likely be "successful"? > If so, I don't agree with that at all; truncation > > under MJ will have a similar effect as under many other methods. > > > >> K: Of the three methods (MAM, IRV, MJ) I would pick MAM. I'm not > sure if I prefer MJ to IRV. Even if we replace MJ in the > >> question with Approval, I am not sure. > >> S: Given my above points plus the fact that MAM gives each voter > less opportunity to express the different intensities of > >> support they might have for the different candidates, and the much > greater difficulty that ordinary citizens would have in > >> understanding exactly how MAM is counted, I would like to > understand why you would ‘prefer’ MAM over MJ. > > I grant that MAM is harder to understand, but I think it gets more > mileage out of its complexity than MJ gets out of its. > > > > When it comes to expressiveness, I think that practically speaking > MAM is actually better than MJ, due to the scenario that > > MJ turns into Approval and consequently expresses very little. > > > >>> K: [….] Otherwise, I'm afraid of Approval's potential to produce > results that appear arbitrary and inconclusive (fragmented > >>> electorate, unconvincing winner). > >>>> K: In general I feel that election methods should produce an > outcome that would be plausible if the voters had been able > >>>> to gather and vote in person, just as a legislature. > >>> K: For example, MJ violates Condorcet Loser. In theory it can > elect a candidate who could not win head-to-head against any > >>> of the other candidates. It is not likely that a legislature would > settle on an outcome that could not survive a one-on-one > >>> vote against any of the other options. > >> S: Contrary to B&L’s belief, your worry here regarding Condorcet > seems to assume that ‘preferences’ are more important > >> than ‘evaluations’. However, if all MJ voters equally distributed > their EXCELLENTs between all the candidates except the > >> one candidate to which they all gave VERY GOOD, why would you (or a > legislature) be justified in not seeing the one with > >> all these VERY GOODs as the appropriate winner? This is an example > of the fact that MJ seems naturally to discover the > >> most valued candidate unless every voter grades all the candidates > exactly in the same way. > >> > >> S: Why would you not see MJ as ‘plausible’ in this sense? For > example, a legislature could elect its prime minister > >> in a parliamentary system using MJ. In the extremely unlikely > event that this might result in an MJ tie, it could be > >> quickly resolved by electing one winner by a head to head vote. > I.e. after discovering to 2 candidates to be equally > >> qualified, the winner would be the one ‘preferred’ by the majority > for whatever reason. > > Let me clarify my thought experiment. I'm not saying to imagine > using MJ (or another method) being used in a legislature. > > Legislators talk to each other, gauge support for positions, and > vote yea or nay on specific proposals (or they delay > > and don't vote at all), usually ending up with a majority approving > a single outcome. I'm saying take the cast ballots > > for an electorate, and the method's outcome, and ask whether a > traditional legislature could have realistically arrived > > at the same outcome using the same proportions of voters. If it > doesn't make sense, then somebody probably has a basis > > to complain about the method and undermine the legitimacy of the winner. > > > > Now why do I say to do this, and why I do not care about > "preferences" vs "evaluations": > > Legislatures normally function according to majority rule. The > electorate is basically a legislature that can't fit in > > a single room, so they have to record their voting instructions on a > ballot paper. If majority rule is violated in a > > legislature, people will cry foul. It shouldn't be expected to be > different for an electorate (this is my opinion). So I > > say that a good way to minimize strategy complaints/concerns is to > make sure the interpretation of the ballots produces > > an outcome that would be plausible if the electorate had actually > met in a room. > > > >> K: Also, suppose that an MJ voter doesn't like any candidate and > his best rating awarded is "acceptable." In so doing he > >> can actually cause his "favorite" candidate to lose to somebody > else. I would expect a legislator to understand the risk > >> of this happening > >> and not cast votes that could have such an effect. > >> S: Yes, in this context, if he greatly fears any other candidate > winning, rationally he should give his ‘favorite’ an > >> excellent and reject the rest. > > Glad we agree. Note that it is this behavior (rating a sub-par > candidate differently based on whether there are any > > better candidates in the race) that raises issues with Arrow. > > > > Kevin > > ---- > > Election-Methods mailing list - see http://electorama.com/em for > list info > > > > > > ----- > > No virus found in this message. > > Checked by AVG - www.avg.com <http://www.avg.com> > > Version: 2016.0.7752 / Virus Database: 4649/12936 - Release Date: > 09/03/16 > > > No virus found in this message. > Checked by AVG - www.avg.com <http://www.avg.com> > Version: 2016.0.7752 / Virus Database: 4649/12952 - Release Date: 09/05/16 >

Kevin Venzke

Wed, Sep 7, 2016 4:08 AM

  De : Jameson Quinn <jameson.quinn@gmail.com>

À : steve bosworth stevebosworth@hotmail.com
Cc : "election-methods@lists.electorama.com" election-methods@lists.electorama.com; "stepjak@yahoo.fr" stepjak@yahoo.fr
Envoyé le : Lundi 5 septembre 2016 15h30
Objet : Re: [EM] (3) MJ -- The easiest method to 'tolerate'

It's really hard to respond point-by-point as a third party in a discussion like this. However, I'd like to say in general that I believe that Majority Judgment, and more-generally, the class of "median" or "graded Bucklin" systems which includes MJ, MCA, GMJ, ERB, DA, etc., are the best non-delegated single-winner systems for a potentially-strategic electorate, in terms of outcome.
(I'll include a glossary at bottom. All of these systems are basically similar in that candidates are graded independently into grade classes and the winner is one of those with the highest median. Until I get there, I'll just use "MJ" as a representative stand-in for an arbitrary member of this class of systems.)
Why do I believe this? Because I think these systems would allow a large supermajority of voters to vote "unstrategically" in a large supermajority of elections. That is, they could arrive at a iterated-strategically-optimal ballot by simply comparing each of the candidates to some universal scale which was calibrated using simple summary statistics of historical data about elections for the same office (or, if no such historical data is available, using polling and/or historical data for comparable elections).
In order to argue the above, I think it will work best to refute the objections commonly raised against MJ.
First, there is the failure of the later-no-harm (LNH) criterion. But note: MJ actually does pass a weaker version of LNH: rating additional candidates at above bottom will not harm the winner as long as those candidates are ranked below the winning median. My claim is that over time, the winning median grade will mostly fall in a given band of grades; for instance, using letter grades, between B- and D+. In that case, making distinctions between A and B at the top or D and F at the bottom are strategically safe.
Even the rare cases where the winning median might be outside this band, it is unlikely that an honest ballot will violate LNH in practice. Consider the possibilities. If the winner has an unusually high median, they are an unusually good candidate, and it is unlikely that any strategic voting by their opponents would be enough to unseat them. (And that's a good thing). If the winner has an unusually low median, that is usually an indicator that the electorate is unusually fragmented into 3 or more distinct factions. If those factions can be located along a 1D spectrum, then the voters who might cast strategically non-optimal votes are the centrists, whose favored candidate is probably the honest Condorcet winner. But centrists are likely to honestly view both extremes as equally bad, and thus to honestly vote both at F.
Thus, the chances of an arbitrary ballot being non-optimal are product of the minority fraction of elections with such extreme division, multiplied by the minority fraction of the electorate who are centrists, multiplied by the minority fraction of centrists who would honestly rate a given non-centrist winner above F. I'd argue that each of these fractions are almost certain to be below 1/3, making the overall "zero-information strategic incentive" equal to 1/27 times the possible advantage from a strategic ballot. If that last factor is, say, 2/3 of the distance between the optimal and the pessimal candidate, the overall ZISI is around 2.5% of that distance. As a statistician, I have a name I'd use for that kind of number in most contexts: "insignificant".
A similar argument can be used against the charge that MJ can elect a Condorcet loser (or even a majority loser in a two-way election). Any such scenario where this happens involves at least two critical portions of the electorate badly misjudging what the likely winning median will be, and doing so in opposite directions. Note that the winning median is much easier to roughly guess ahead of time than the specific winner or frontrunners; guessing the former can be done using historical data, while, in the absence of two-party domination, the latter probably takes current polling data, likely to be harder to come by. But even if people guess the winning median poorly... how likely is it that there will be significant fractions misjudging in both directions in favor of a given Condorcet loser, while none misjudge the median against that candidate?
...
To me, the toughest realistic election scenario is the chicken dilemma. For instance, consider the following 900-voter scenario300: A>B>>C200: B>>A>C400: C>>B>A
(where ">>" indicates universal agreement, and ">" at bottom indicates 90% agreement and 10% reversal)
The "correct" winner here is pretty clearly B; they'll win an honest election under Condorcet, score, or MJ. How would this play out in different systems? I'll distinguish "first time", with a mix of honesty and naive strategy, and "later", with something approaching evolutionarily stable strategy.
In plurality, C would win the first time. Eventually, the A and B factions would manage to coordinate strategy, probably electing A in the long term. That sub-optimal result would then mean that B voters would be more-or-less permanently disenfranchised.
In IRV, A would win the first time, leaving the C voters very unhappy. If enough of them were ready to strategically compromise, they might be able to elect B; but I think that's unlikely. More likely, they'd just complain until IRV was reverted to plurality, as happened in Burlington.
In Borda with truncation, C would win the first time, then later A, as in plurality. Eventually that might transition to a win for B as the C voters stopped truncating.
In approval, B would probably win the first time and stably going forward. However, if naive strategy was too uncompromising, or if later strategy was too inclined towards brinksmanship, either of the other two might win occasionally.
In score, B would win the first time, and then later it would come to behave as approval; that is, B with a risk of brinksmanship pathologies.
In MJ, B would win the first time and stably going forward. It would take extreme brinksmanship for C to win; frankly, I find that implausible. A might win occasionally, motivating the C voters to rate B above zero in the long term.
(The only system I know of that would be more certain to elect B than MJ would be SODA.)
...
As promised, here's my glossary of graded Bucklin systems:
ERB: Equal Ratings Bucklin. "Equal ratings" just means that ballots are graded, not forced to be strict rankings. 4 or more grade levels, highest median, tiebreaker is number of votes at or above median.MCA: Majority Choice Approval. As above, but 3 grade levels (preferred, approved, unapproved)GMJ: Graduated Majority Judgment. 4 or more grade levels, highest median, tiebreaker is average between number of votes at or above median and number of votes above median.DA: "Double Approval" or "Disqualify/Approve" voting. Voters can rate each candidate preferred, neutral, or disqualified. (Both preferred and disqualified is also legal and counted, though it's strategically nonsensical.) Winner is the most-preferred among those not majority disqualified. If all candidates are majority-disqualified, winner is simply most-preferred. Any candidate who is majority-disqualified is prohibited from appearing on the ballot for the same office in the following election.

Lately, I favor DA, as being the simplest to explain and the most intuitive to reason about for most people. I expect that the majority of voters would prefer a single candidate, and use a rough approval strategy for disqualification (that is, disqualify one frontrunner and anybody worse.) The good thing is that cooperation is stable in DA in an iterated chicken dilemma scenario; the prospect of tit for tat retaliation is enough to discourage brinksmanship strategy.
2016-08-31 21:16 GMT-04:00 steve bosworth stevebosworth@hotmail.com:

To Kevin and everyone,Sorry for the late reply but travel and a family reunion intervened. I look forward to your response.SteveFrom: Kevin Venzke stepjak@yahoo.fr
Sent: Sunday, August 7, 2016 3:08 AM
To: steve bosworth; election-methods@lists. electorama.com
Subject: Re: [EM] (2) MJ -- The easiest method to 'tolerate' Hi Steve,

De : steve bosworth stevebosworth@hotmail.com
À : "election-methods@lists. electorama.com" <election-methods@lists. electorama.com>; "stepjak@yahoo.fr" stepjak@yahoo.fr
Envoyé le : Mardi 2 août 2016 21h12
Objet : Re: [EM] (2) MJ -- The easiest method to 'tolerate'

K: >> My main distaste for median rating comes from my feeling that in most scenarios (i.e. availability of information on

others' rating intentions) strategic-minded voters would only use the top and bottom ratings. This is because (as we
see from the Later-no-harm example) median rating doesn't really offer guarantees about how your ratings will be used
in relation to each other.

S: As I understand it, MJ does guarantee exactly how all the gradings will be counted but, of course, not how every voter will use them.

K: Yes but I'm talking about the sort of feature as in IRV where one is guaranteed that if one's favorite candidate A is the winner, you (or a group of voters like you) will not accidentally make A lose by adding a new lower preference B. S: I understand Belinski as showing use that this is not a practical danger unless only a few voters are being asked to elect one winner, i.e. it is almost certain of not occurring in an election with many voters (Belinski & Laraki,Majority Judgment, pp.285-292) At the same time, I see B&L as correctly assuming (with E. J. Nanson ) that the ‘object of … an election is to select … some candidate who shall, in the opinion of a majority of the electors, be most fit for the post….(p.209). I also find it hard to disagree with B&L’s following 2 assertions: ‘Clearly …. majorities of grades are … considerably more discerning decisions than are majorities of preferences’ (p.283); Therefore, ‘A method [of voting] should elicit the honest expression of voters’ opinions as inputs, for the aim of an election is to produce outputs which represent as [well] as possible the true wishes of societies and of juries’ (p.352).Consequently, I see MJ as always having the advantage over competing methods by allowing each voter clearly to express his or her evaluation of each candidate. MJ invites each voter to ‘grade’ each candidate as being either EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, POOR, or REJECTED -- each candidate being graded according the extent to which he matches each voter’s concept of an EXCELLENT candidate. Thus each candidate would receive the same grade from a given judge or voter, independently of which other candidates are available, i.e. each grade (‘rating’) can be given not ‘in relation to’ the other candidates. In this limited sense, B&L say that these judgments are not ‘relative’ but ‘absolute’: ‘Judges … have a collective absolute sense of the excellence of the performances or the qualities of the competing entities’. At the same time, ‘however competent voters may be, they can have very different evaluations of the candidates because of fundamentally different conceptions of how society should be run and organized’ (pp.251-2).
K: The notion that the voter should rate [evaluate] candidates independently of how they rated other candidates is basically true. But this applies both to sincere voters and to voters interested in maximizing the effect of their vote. If the latter voters conclude (as I believe they usually should) that only the two extreme ratings can maximize the effect of their vote, then they should only use the two extreme ratings.S: Depending on their own scale of values, I accept that some voter may validly choose to use only these two ‘extreme ratings’. However, MJ also allows other voters who may have a greater knowledge of the different qualities of the candidates, appropriately from their point of view, to use all 6 grades accurately to evaluate each candidate. If a voter sees 6 candidates as EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, and to REJECT, respectively, she may see that to reject all except her excellent candidate might allow her rejected candidate to win, rather than her very good, good, or acceptable candidate. Why should she take this risk and thus also to choose not to contribute honestly to the discovery of the socially most valued winner? I see this as one of the reasons Belinski & Laraki (B&L) argue that grading ‘honestly’ in a large election is most likely to be seen as the ‘dominant strategy’ (pp.190,193,220,230).

K: Relatedly, I don't see it as an inherently valuable feature of a method for voters to be able to "clearly express his or her evaluation" of a candidate, without it actually being in their strategic interest to do that.

S: Surely, to the extent that citizens might evaluate all the candidates honestly, this would help greatly to inform all candidates and the public both about the real values held by citizens and the perceived value of each candidate. Perhaps most importantly, it would also have the best chance of electing the candidate with the qualities needed successfully to face her official challenges.If so, contrary to what you say several paragraphs below, this inclines me to say that each voter usually should grade each candidate on their own merits, not ‘rate’ or rank each in relation to one another.At the same time, MJ does not deny any voter the attempt to vote strategically if she thinks this will ‘maximize’ the achievement of her own agenda. B&L only argue that MJ has the advantage both of being completely ‘strategy-proof-in-grading’ (pp.14, 189-198), i.e. if the voters wish honestly only to evaluate each candidate. On the other hand, if a voter or a group of voters wish to manipulate the MJ ballot to maximize the chances of their favorite candidate winning (i.e. by attempting to translate the ‘grades’ into ‘rankings’), MJ’s method of electing a winner only by his highest median-grade minimizes ‘cheating’, ‘minimizes the probability that a judge may be found who can effectively raise or lower the grade in the worst case’ (p.212). MJ reduces such opportunities almost by ‘half’ (pp. 15, 197, 282), i.e. it is still only ‘partially strategy-proof-in ranking’ (pp.15, 245). Do you see any errors in B&L’s mathematical proofs of the above claims.
S: MJ avoids Arrow’s paradoxes. Do you disagree?

K: [….] This is not a particularly impressive way to evade Arrow because practically speaking voters under rated methods should be expected to rate candidates differently based on which other candidates are in the race.S: Up until now, I thought you were using ‘rate’ as equivalent to ‘grade’ but now you seem to be using it as equivalent to ‘rank’. As I understand it, MJ’s design prompts each citizen to ‘grade’ each candidate with respect only to her own concept of what her EXCELLENT candidate would be. Each candidate can be judged on their own merits in the light of each voter’s own criteria, not in the light of who else is running. Thus, while rankings can be deduced from grades, grading is not ranking. The MJ winner is intended not to be decided by ranking.K: The alternative is that many voters will choose not to rate any candidate "excellent" or "rejected."S: I agree that this is one ‘option’ among many but I do not see why you say it is ‘the alternative’, as if this option is the only option or the one that should be preferred.K: But I think even sincere-minded voters will be inclined to make sure somebody is getting those ratings.S: Yes, especially if they see them as deserving these different grades.

K: "Condorcet paradox" is not really something you can violate. If you don't elect Condorcet winners in the first place, it is true that [with MJ] you don't have to consider what happens when there is no Condorcet winner. That might be a marketability advantage.S: I agree that MJ offers a ‘marketability advantage’ if you mean here that MJ has an advantage over Condorcet counts. This is because almost certainly in a large MJ election, any temporary MJ tie would be naturally resolve by calculating the relevant ‘majority-value’ of each candidate when their relevant ‘majority-grades’ or ‘majority –gauges’ are not sufficiently precise.

S: > At the same time, in contrast to the use of any of the ‘traditional methods’ which still can suffer from these paradoxes, again, Belinski argues that an MJ voter can only be up to half as successful strategically if she focusses not on grading but instead on voting to maximize the chance that her favorite candidate will win. K: That claim makes some sense to me in comparison to Range (not sure what the actual comparison is), although Range does not "violate Arrow" or consider Condorcet cycles either.

I don't think it's easy to compare MJ to other methods here. S: I accept that Range is not vulnerable to Arrow paradoxes but Range is more easily manipulated than MJ because Range uses total or average scores not medians. Also, range like the other traditional methods which are subject to Arrow’s paradoxes can be easily ‘contrasted’ with MJ: none of them allow voters as clearly to express their ‘evaluation’ of each candidate and all ‘are by far the most manipulatable’ (pp.280, 302, 312. 314).K: Under MAM, if I vote A>B>C it is clear that there are several [unpredicted] effects that might arise from that vote. I may have a strategy that involves voting in some different way, but as long as I actually have the preferences A>B>C, there is a plausible motivation for me to vote that way.S: Yes.K: But under MJ all the ratings [gradings] are independent. The only reason for a strategic-minded MJ voter to rate B between A and C is if he has peculiarly good information about what (final) score for B will be good enough to beat C but not so good that it creates a problem for A.

S: Yes, but with MJ he is less like to have such ‘peculiarly good information’. MJ makes it less likely that this ‘strategic-minded voter’ will be able to make this calculation with confidence. Therefore, he is more likely simply to grade the candidates ‘honestly’, i.e. to adopt what Belinski calls MJ’s ‘dominant strategy’. Honesty provides the greater social choice benefit of electing the one candidate who is most valued by all voting citizens given the grades awarded by each voter to each candidate.

S: > Currently, these features incline me to see MJ as the best method for electing a President. However, you do not seem to agree, given your next sentence, even though ‘approval voting’ does not allow each voter to express the deferent intensities with which they might approve of the different candidates:
K: >This is because in the scenario I discuss below, MJ would offer different intensities, but nobody (who knew what they were doing) would use them.S: Given that MJ offers something like half the scope for manipulation, I would like to understand why you still think a knowing MJ voter would choose not to use the different intensities it offers.At the same time, no method allows a voter to ‘know what they are doing’, i.e. beforehand, the outcome of every election is uncertain. The results of all the ‘traditional methods’ are even more uncertain both because they may display one of Arrow’s paradoxes, and they make manipulation of the outcomes easier. In contrast, the rational and socially minded MJ voter will again know that by grading all the candidates honestly, she is playing her part in helping to elect the candidate most valued by the electorate.K: That transforms the method into Approval. You are right, that I’m not certain that Approval (be it actual Approval or MJ that turned into Approval) is the best method for electing a president.S: Again, am I correct in believing that whenever MJ might be ‘turned into Approval’, this use could still allow only half the manipulation offered by actual Approval? Also, given that Approval does not allow any voter to express different intensities of approval, I would like to understand why you might still consider it to be the ‘best’.

K: The rating/grade values have no independent, practical meaning.S: All the honest grades are ‘independent’ of each other by being only dependent on each voter’s idea of an EXCELLENT candidate. Yes, if a voter merely treats the ‘grades’ as ‘rankings’, then they would lose their ‘independence’ from each other. At the same time, any attempts to manipulate the results using these ‘rankings’ would be half as likely to succeed. Again, please correct me if I am mistaken that B&L have successfully justified this ‘half as likely’ claim.K: If [MJ] voters have this perception and respond with this behavior, then the method is just an overly complicated form of approval voting.S: But do you agree that this is a largely mistaken ‘perception’? In any case, if some citizens make this mistake, they could only blame themselves for failing both to take advantage of the opportunity to help elect the most valued candidate by honestly evaluating all of them, and perhaps to have partly wasted their vote by voting strategically but only with half a chance of being successful in their own eyes. Consequently, we could argue that MJ at least has the clear virtue over the ‘traditional’ methods of most certainly offering these democratic advantages most completely to citizens.K: In that case, I'd rather just use approval, because it's clearer what's going on.S: As I see it, no method allows us to know exactly the motives or calculations which each voter is making when they vote. However, is it not true that citizens are more like to ‘evaluate’ the candidates, given that MJ’s ballots alone asks for these grades?At the same time, I would like to understand why you might ‘rather’ use an ‘impoverished’ method like APPROVAL rather than MJ which is ‘rich’ with the above opportunities. At the same time, perhaps the first part of your next but two paragraphs below actually agree with this point. However, its second part then seems to reverse this again by you saying that MJ would hopefully be changed into Approval.[….]> S: Given the above, it seems that MJ voters would be much less likely ‘actually to try to be so strategic’ and this conclusion seems to be supported by the ‘Orsay experiment’ (pp.9-16. 257-265).

K: If I understand correctly, Orsay was a poll with no stakes. I would be curious to know whether/how the voters were told how the ballots would be counted.S: In this regard, you may wish to consider Belinski’s following report on page 255 in his book with Laraki (B&L: Majority Judgment): ‘The experiment—the ballot and the method of ranking—was explained to potential participants well before election day in individual letters, an article in the town’s quarterly magazine, posters, and an evening presentation open to all.’ Also, on page 17, B&L report their following instructions to the participants in their different October 2008 experiment conducted on the Web: ‘You will be asked to evaluate in a language of grades. A candidate’s majority-grade is the middlemost of her/his grades… The candidates are ranked according to their majority-grades.’S: While B&L openly accept that a binding election was not at ‘stake’, I see that experiment as surely providing some empirical evidence that goes some why to suggesting how people would use the MJ ballot in an actual election. Of course, better empirical evidence would be provided, at least by a ‘trial’ adoption of MJ for some actual elections.

K: In any case, don't think I am saying that under MJ, voters would all become strategic and this would make the outcomes worse. I actually think it would make the outcomes better. (As in "more plausible," if the voters had been a legislature.)
The downside of the voters being strategic is just that the different rating [grading] options become pointless. So my criticism is not that MJ is bad, it's that it is needlessly complicated for what it might and hopefully would turn into.S: Yes, MJ offers ‘different rating [grading] options’, and much less scope for manipulation. Admittedly, the counting of MJ is slightly more complicated than simply summing approvals or scores. However, is not MJ’s potential for periodically and more precisely informing all citizens and candidates about the actual intensities with which the many different scales of values and concerns that actually exist within one’s society an additional benefit well worth this slight additional complication, e.g. a complication which is also much less than any Condorcet methods or IRV?

[….]

K: I find a lot of methods tolerable, and I've designed a lot of methods too (most of them tolerable). I care about
certain properties more than others, but the ones I like aren't even all compatible with each other.

S: Which ‘properties’ do you most care about? How are they ‘incompatible’ with each other? Still, which method do you see as superior to MJ, all things considered?

K: Some properties I like are:
Favorite betrayal (MJ satisfies, IRV doesn't, MAM doesn't but is probably pretty good). This criterion is about being able to safely rank/rate your favorite candidate at least equal-top with a compromise choice.

Minimal defense (MJ and MAM satisfy, IRV doesn't). This is about the ability of a full majority of voters who prefer candidate A to candidate B, to ensure that B loses, without any of them having to vote that A is their favorite.
(Normally they will do this by ranking A sincerely, and not ranking B over anybody.)

Later-no-harm (IRV satisfies, MJ and MAM don't). S: On August 12, Wikipedia defined this criterion as follows:‘Thelater-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate does not cause a more-preferred candidate to lose.’This seems to be the only criteria which MJ fails for you. B&L admit and address this theoretical failure and explain why it is unimportant in practice (pp.285-287). I will try to explain why. Below, the following Wikipedia example illustrates how MJ can violate the ‘later-no-harm’ criterion. In scenario 1, the 1st voter explicitly gives only candidate A a grade, i.e. Excellent. Thus, by default, she gives candidate B a grade of Poor and consequently B has a median grade of Poor from the 1st voter. Thus, A is elected with a median grade of Fair.
| MJ SCENARIO 1 |
| Candidates:VOTERS | A | B |
| 1st | E | (P) |
| 2nd | P | E |
| 3rd | F | P |
| | Median-grade:Fair | |
| | Winner | |

| MJ SCENARIO 2 |
| Candidates:VOTERS | A | B |
| 1st | E | G |
| 2nd | P | E |
| 3rd | F | P |
| | | Median-grade:Good |
| | | Winner |

In scenario 2, the 1st voter instead gives B a more ‘positive rating’ (i.e. Good). Now, B has a median grade of Good and thus B would be elected. Thus, by the 1st voter now ‘giving a more ‘positive rating [than before (i.e. Good rather than Poor) to her] less-preferred candidate’, this has caused her ‘more-preferred candidate to lose. This criterion presumes that this result would not have been 1st voter’s intention. It assumes that each voter is only interested in maximizing the chances that the candidate she personally most favors will be the winner. B&L see this as the flawed assumption made by advocates of the ‘traditional methods’.Instead, B&L assume that voters want the winner to be the candidate most highly valued by a majority of all the voters. They see MJ as offering a method by which such a winner is best discovered. It gives each citizen the opportunity to grade each and every candidate honestly according to each citizen’s own concept of the characteristics that an EXCELLENT winner would have. MJ discovers which candidate comes closest to being EXCELLENT as judged by the largest majority. MJ assumes that each voter should accept that this majority is more likely to identify the winner who is truly most qualified for the office than if any one voter could decide this on their own.Consequently, rather than an example of a flaw in MJ, the above 2 scenarios illustrate to me how MJ should work. If the 1st voter in scenario 1 honestly sees no reason to give a grade higher than POOR to candidate B, then clearly A should be elected as he has the higher median grade FAIR. However, if the 1st voter instead honesty grades B as GOOD in scenario 2, scenario 2 shows that B should be elected instead because B now has the higher median grade of GOOD.At the same time, do you disagree with Belinski’s claims both

that MJ discovery of the winner only by his median grade makes it only half as like that one voter changing her grade for one candidate will change who is the winner, and
that with many candidates and millions of voters, it is ‘almost certain’ that any manipulation sought by such changes would not be successful?

K: Later-no-help or "burial resistance" (IRV and MJ satisfy, MAM doesn't).
Condorcet (MAM satisfies). I guess you know about these last three.

Plurality (all of IRV, MAM, and MJ satisfy). This is a fairly easy criterion that says we can't elect a candidate
who has fewer "votes in total" than some other candidate already has in first place votes.

The (seeming) incompatibility that frustrates me the most is that between minimal defense and LNHarm.S: In practice, there should be no need for such ‘frustration’ if you answers ‘yes’ to both questions posed by the last sentence in my immediately above paragraph.

K: Of the three methods (MAM, IRV, MJ) I would pick MAM. I'm not sure if I prefer MJ to IRV. Even if we replace MJ in the question with Approval, I am not sure.S: Given my above points plus the fact that MAM gives each voter less opportunity to express the different intensities of support they might have for the different candidates, and the much greater difficulty that ordinary citizens would have in understanding exactly how MAM is counted, I would like to understand why you would ‘prefer’ MAM over MJ.K: [….] Otherwise, I'm afraid of Approval's potential to produce results that appear arbitrary and inconclusive (fragmented electorate, unconvincing winner).

K: In general I feel that election methods should produce an outcome that would be plausible if the voters had been able to gather and vote in person, just as a legislature.

K: For example, MJ violates Condorcet Loser. In theory it can elect a candidate who could not win head-to-head against any of the other candidates. It is not likely that a legislature would settle on an outcome that could not survive a one-on-one vote against any of the other options.

S: Contrary to B&L’s belief, your worry here regarding Condorcet seems to assume that ‘preferences’ are more important than ‘evaluations’. However, if all MJ voters equally distributed their EXCELLENTs between all the candidates except the one candidate to which they all gave VERY GOOD, why would you (or a legislature) be justified in not seeing the one with all these VERY GOODs as the appropriate winner? This is an example of the fact that MJ seems naturally to discover the most valued candidate unless every voter grades all the candidates exactly in the same way.

S: Why would you not see MJ as ‘plausible’ in this sense? For example, a legislature could elect its prime minister in a parliamentary system using MJ. In the extremely unlikely event that this might result in an MJ tie, it could be quickly resolved by electing one winner by a head to head vote. I.e. after discovering to 2 candidates to be equally qualified, the winner would be the one ‘preferred’ by the majority for whatever reason.

K: Also, suppose that an MJ voter doesn't like any candidate and his best rating awarded is "acceptable." In so doing he can actually cause his "favorite" candidate to lose to somebody else. I would expect a legislator to understand the risk of this happening and not cast votes that could have such an effect. S: Yes, in this context, if he greatly fears any other candidate winning, rationally he should give his ‘favorite’ an excellent and reject the rest.

K: (I'm not assuming the MJ voters have an incentive or ability to use strategy, in this analysis. I want to assume that the voters are sincere, and that the method itself will handle the translation of the sincere preferences into the strategic, informed behavior you would expect of a legislator.) S: Yes, I do not see how MJ could be any worse than any of the alternative methods. At the same time, its design seems to make it most probably better that any of the others I know for electing one winner.KevinSteve

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Hi Jameson, I don't follow some of your arguments, e.g. the parts where centrists would give other candidates an F and do so sincerely. It seems to me that if a race comes down to candidate A with median score 6 (/10) vs. candidate B with a 5, this will provide immediate and obvious feedback to the voters who chose to dabble in those scores, and to assign them no less to the (de facto) frontrunners of the race. Suppose though that MJ debuts and the very initial status quo is that most everyone is using min and max ratings only. They are disregarding B&L's "properly phrased ballot"; maybe they are getting advice from somebody else. What do you say, does MJ contain a mechanism to moderate this situation and make people vote more sincerely? Kevin De : Jameson Quinn <jameson.quinn@gmail.com> À : steve bosworth <stevebosworth@hotmail.com> Cc : "election-methods@lists.electorama.com" <election-methods@lists.electorama.com>; "stepjak@yahoo.fr" <stepjak@yahoo.fr> Envoyé le : Lundi 5 septembre 2016 15h30 Objet : Re: [EM] (3) MJ -- The easiest method to 'tolerate' It's really hard to respond point-by-point as a third party in a discussion like this. However, I'd like to say in general that I believe that Majority Judgment, and more-generally, the class of "median" or "graded Bucklin" systems which includes MJ, MCA, GMJ, ERB, DA, etc., are the best non-delegated single-winner systems for a potentially-strategic electorate, in terms of outcome. (I'll include a glossary at bottom. All of these systems are basically similar in that candidates are graded independently into grade classes and the winner is one of those with the highest median. Until I get there, I'll just use "MJ" as a representative stand-in for an arbitrary member of this class of systems.) Why do I believe this? Because I think these systems would allow a large supermajority of voters to vote "unstrategically" in a large supermajority of elections. That is, they could arrive at a iterated-strategically-optimal ballot by simply comparing each of the candidates to some universal scale which was calibrated using simple summary statistics of historical data about elections for the same office (or, if no such historical data is available, using polling and/or historical data for comparable elections). In order to argue the above, I think it will work best to refute the objections commonly raised against MJ. First, there is the failure of the later-no-harm (LNH) criterion. But note: MJ actually does pass a weaker version of LNH: rating additional candidates at above bottom will not harm the winner as long as those candidates are ranked below the winning median. My claim is that over time, the winning median grade will mostly fall in a given band of grades; for instance, using letter grades, between B- and D+. In that case, making distinctions between A and B at the top or D and F at the bottom are strategically safe. Even the rare cases where the winning median might be outside this band, it is unlikely that an honest ballot will violate LNH in practice. Consider the possibilities. If the winner has an unusually high median, they are an unusually good candidate, and it is unlikely that any strategic voting by their opponents would be enough to unseat them. (And that's a good thing). If the winner has an unusually low median, that is usually an indicator that the electorate is unusually fragmented into 3 or more distinct factions. If those factions can be located along a 1D spectrum, then the voters who might cast strategically non-optimal votes are the centrists, whose favored candidate is probably the honest Condorcet winner. But centrists are likely to honestly view both extremes as equally bad, and thus to honestly vote both at F. Thus, the chances of an arbitrary ballot being non-optimal are product of the minority fraction of elections with such extreme division, multiplied by the minority fraction of the electorate who are centrists, multiplied by the minority fraction of centrists who would honestly rate a given non-centrist winner above F. I'd argue that each of these fractions are almost certain to be below 1/3, making the overall "zero-information strategic incentive" equal to 1/27 times the possible advantage from a strategic ballot. If that last factor is, say, 2/3 of the distance between the optimal and the pessimal candidate, the overall ZISI is around 2.5% of that distance. As a statistician, I have a name I'd use for that kind of number in most contexts: "insignificant". A similar argument can be used against the charge that MJ can elect a Condorcet loser (or even a majority loser in a two-way election). Any such scenario where this happens involves at least two critical portions of the electorate badly misjudging what the likely winning median will be, and doing so in opposite directions. Note that the winning median is much easier to roughly guess ahead of time than the specific winner or frontrunners; guessing the former can be done using historical data, while, in the absence of two-party domination, the latter probably takes current polling data, likely to be harder to come by. But even if people guess the winning median poorly... how likely is it that there will be significant fractions misjudging in both directions in favor of a given Condorcet loser, while none misjudge the median against that candidate? ... To me, the toughest realistic election scenario is the chicken dilemma. For instance, consider the following 900-voter scenario300: A>B>>C200: B>>A>C400: C>>B>A (where ">>" indicates universal agreement, and ">" at bottom indicates 90% agreement and 10% reversal) The "correct" winner here is pretty clearly B; they'll win an honest election under Condorcet, score, or MJ. How would this play out in different systems? I'll distinguish "first time", with a mix of honesty and naive strategy, and "later", with something approaching evolutionarily stable strategy. In plurality, C would win the first time. Eventually, the A and B factions would manage to coordinate strategy, probably electing A in the long term. That sub-optimal result would then mean that B voters would be more-or-less permanently disenfranchised. In IRV, A would win the first time, leaving the C voters very unhappy. If enough of them were ready to strategically compromise, they might be able to elect B; but I think that's unlikely. More likely, they'd just complain until IRV was reverted to plurality, as happened in Burlington. In Borda with truncation, C would win the first time, then later A, as in plurality. Eventually that might transition to a win for B as the C voters stopped truncating. In approval, B would probably win the first time and stably going forward. However, if naive strategy was too uncompromising, or if later strategy was too inclined towards brinksmanship, either of the other two might win occasionally. In score, B would win the first time, and then later it would come to behave as approval; that is, B with a risk of brinksmanship pathologies. In MJ, B would win the first time and stably going forward. It would take extreme brinksmanship for C to win; frankly, I find that implausible. A might win occasionally, motivating the C voters to rate B above zero in the long term. (The only system I know of that would be more certain to elect B than MJ would be SODA.) ... As promised, here's my glossary of graded Bucklin systems: ERB: Equal Ratings Bucklin. "Equal ratings" just means that ballots are graded, not forced to be strict rankings. 4 or more grade levels, highest median, tiebreaker is number of votes at or above median.MCA: Majority Choice Approval. As above, but 3 grade levels (preferred, approved, unapproved)GMJ: Graduated Majority Judgment. 4 or more grade levels, highest median, tiebreaker is average between number of votes at or above median and number of votes above median.DA: "Double Approval" or "Disqualify/Approve" voting. Voters can rate each candidate preferred, neutral, or disqualified. (Both preferred and disqualified is also legal and counted, though it's strategically nonsensical.) Winner is the most-preferred among those not majority disqualified. If all candidates are majority-disqualified, winner is simply most-preferred. Any candidate who is majority-disqualified is prohibited from appearing on the ballot for the same office in the following election. Lately, I favor DA, as being the simplest to explain and the most intuitive to reason about for most people. I expect that the majority of voters would prefer a single candidate, and use a rough approval strategy for disqualification (that is, disqualify one frontrunner and anybody worse.) The good thing is that cooperation is stable in DA in an iterated chicken dilemma scenario; the prospect of tit for tat retaliation is enough to discourage brinksmanship strategy. 2016-08-31 21:16 GMT-04:00 steve bosworth <stevebosworth@hotmail.com>: To Kevin and everyone,Sorry for the late reply but travel and a family reunion intervened. I look forward to your response.SteveFrom: Kevin Venzke <stepjak@yahoo.fr> Sent: Sunday, August 7, 2016 3:08 AM To: steve bosworth; election-methods@lists. electorama.com Subject: Re: [EM] (2) MJ -- The easiest method to 'tolerate' Hi Steve, ______________________________ _ De : steve bosworth <stevebosworth@hotmail.com> À : "election-methods@lists. electorama.com" <election-methods@lists. electorama.com>; "stepjak@yahoo.fr" <stepjak@yahoo.fr> Envoyé le : Mardi 2 août 2016 21h12 Objet : Re: [EM] (2) MJ -- The easiest method to 'tolerate' >> K: >> My main distaste for median rating comes from my feeling that in most scenarios (i.e. availability of information on >> others' rating intentions) strategic-minded voters would only use the top and bottom ratings. This is because (as we >> see from the Later-no-harm example) median rating doesn't really offer guarantees about how your ratings will be used >> in relation to each other. >> > S: As I understand it, MJ does guarantee exactly how all the gradings will be counted but, of course, not how every voter will use them. K: Yes but I'm talking about the sort of feature as in IRV where one is guaranteed that if one's favorite candidate A is the winner, you (or a group of voters like you) will not accidentally make A lose by adding a new lower preference B. S: I understand Belinski as showing use that this is not a practical danger unless only a few voters are being asked to elect one winner, i.e. it is almost certain of not occurring in an election with many voters (Belinski & Laraki,Majority Judgment, pp.285-292) At the same time, I see B&L as correctly assuming (with E. J. Nanson ) that the ‘object of … an election is to select … some candidate who shall, in the opinion of a majority of the electors, be most fit for the post….(p.209). I also find it hard to disagree with B&L’s following 2 assertions: ‘Clearly …. majorities of grades are … considerably more discerning decisions than are majorities of preferences’ (p.283); Therefore, ‘A method [of voting] should elicit the honest expression of voters’ opinions as inputs, for the aim of an election is to produce outputs which represent as [well] as possible the true wishes of societies and of juries’ (p.352).Consequently, I see MJ as always having the advantage over competing methods by allowing each voter clearly to express his or her evaluation of each candidate. MJ invites each voter to ‘grade’ each candidate as being either EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, POOR, or REJECTED -- each candidate being graded according the extent to which he matches each voter’s concept of an EXCELLENT candidate. Thus each candidate would receive the same grade from a given judge or voter, independently of which other candidates are available, i.e. each grade (‘rating’) can be given not ‘in relation to’ the other candidates. In this limited sense, B&L say that these judgments are not ‘relative’ but ‘absolute’: ‘Judges … have a collective absolute sense of the excellence of the performances or the qualities of the competing entities’. At the same time, ‘however competent voters may be, they can have very different evaluations of the candidates because of fundamentally different conceptions of how society should be run and organized’ (pp.251-2). K: The notion that the voter should rate [evaluate] candidates independently of how they rated other candidates is basically true. But this applies both to sincere voters and to voters interested in maximizing the effect of their vote. If the latter voters conclude (as I believe they usually should) that only the two extreme ratings can maximize the effect of their vote, then they should only use the two extreme ratings.S: Depending on their own scale of values, I accept that some voter may validly choose to use only these two ‘extreme ratings’. However, MJ also allows other voters who may have a greater knowledge of the different qualities of the candidates, appropriately from their point of view, to use all 6 grades accurately to evaluate each candidate. If a voter sees 6 candidates as EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, and to REJECT, respectively, she may see that to reject all except her excellent candidate might allow her rejected candidate to win, rather than her very good, good, or acceptable candidate. Why should she take this risk and thus also to choose not to contribute honestly to the discovery of the socially most valued winner? I see this as one of the reasons Belinski & Laraki (B&L) argue that grading ‘honestly’ in a large election is most likely to be seen as the ‘dominant strategy’ (pp.190,193,220,230). K: Relatedly, I don't see it as an inherently valuable feature of a method for voters to be able to "clearly express his or her evaluation" of a candidate, without it actually being in their strategic interest to do that. S: Surely, to the extent that citizens might evaluate all the candidates honestly, this would help greatly to inform all candidates and the public both about the real values held by citizens and the perceived value of each candidate. Perhaps most importantly, it would also have the best chance of electing the candidate with the qualities needed successfully to face her official challenges.If so, contrary to what you say several paragraphs below, this inclines me to say that each voter usually *should* grade each candidate on their own merits, not ‘rate’ or rank each in relation to one another.At the same time, MJ does not deny any voter the attempt to vote strategically if she thinks this will ‘maximize’ the achievement of her own agenda. B&L only argue that MJ has the advantage both of being completely ‘strategy-proof-in-grading’ (pp.14, 189-198), i.e. if the voters wish honestly only to evaluate each candidate. On the other hand, if a voter or a group of voters wish to manipulate the MJ ballot to maximize the chances of their favorite candidate winning (i.e. by attempting to translate the ‘grades’ into ‘rankings’), MJ’s method of electing a winner only by his highest median-grade minimizes ‘cheating’, ‘minimizes the probability that a judge may be found who can effectively raise or lower the grade in the worst case’ (p.212). MJ reduces such opportunities almost by ‘half’ (pp. 15, 197, 282), i.e. it is still only ‘partially strategy-proof-in ranking’ (pp.15, 245). Do you see any errors in B&L’s mathematical proofs of the above claims. S: MJ avoids Arrow’s paradoxes. Do you disagree? K: [….] This is not a particularly impressive way to evade Arrow because practically speaking voters under rated methods *should* be expected to rate candidates differently based on which other candidates are in the race.S: Up until now, I thought you were using ‘rate’ as equivalent to ‘grade’ but now you seem to be using it as equivalent to ‘rank’. As I understand it, MJ’s design prompts each citizen to ‘grade’ each candidate with respect only to her own concept of what her EXCELLENT candidate would be. Each candidate can be judged on their own merits in the light of each voter’s own criteria, not in the light of who else is running. Thus, while rankings can be deduced from grades, grading is not ranking. The MJ winner is intended not to be decided by ranking.K: The alternative is that many voters will choose not to rate *any* candidate "excellent" or "rejected."S: I agree that this is one ‘option’ among many but I do not see why you say it is ‘the alternative’, as if this option is the only option or the one that should be preferred.K: But I think even sincere-minded voters will be inclined to make sure somebody is getting those ratings.S: Yes, especially if they see them as deserving these different grades. K: "Condorcet paradox" is not really something you can violate. If you don't elect Condorcet winners in the first place, it is true that [with MJ] you don't have to consider what happens when there is no Condorcet winner. That might be a marketability advantage.S: I agree that MJ offers a ‘marketability advantage’ if you mean here that MJ has an advantage over Condorcet counts. This is because almost certainly in a large MJ election, any temporary MJ tie would be naturally resolve by calculating the relevant ‘majority-value’ of each candidate when their relevant ‘majority-grades’ or ‘majority –gauges’ are not sufficiently precise. > S: > At the same time, in contrast to the use of any of the ‘traditional methods’ which still can suffer from these paradoxes, again, Belinski argues that an MJ voter can only be up to half as successful strategically if she focusses not on grading but instead on voting to maximize the chance that her favorite candidate will win. K: That claim makes some sense to me in comparison to Range (not sure what the actual comparison is), although Range does not "violate Arrow" or consider Condorcet cycles either. I don't think it's easy to compare MJ to other methods here. S: I accept that Range is not vulnerable to Arrow paradoxes but Range is more easily manipulated than MJ because Range uses total or average scores not medians. Also, range like the other traditional methods which are subject to Arrow’s paradoxes can be easily ‘contrasted’ with MJ: none of them allow voters as clearly to express their ‘evaluation’ of each candidate and all ‘are by far the most manipulatable’ (pp.280, 302, 312. 314).K: Under MAM, if I vote A>B>C it is clear that there are several [unpredicted] effects that might arise from that vote. I may have a strategy that involves voting in some different way, but as long as I actually have the preferences A>B>C, there is a plausible motivation for me to vote that way.S: Yes.K: But under MJ all the ratings [gradings] are independent. The only reason for a strategic-minded MJ voter to rate B between A and C is if he has peculiarly good information about what (final) score for B will be good enough to beat C but not so good that it creates a problem for A. S: Yes, but with MJ he is less like to have such ‘peculiarly good information’. MJ makes it less likely that this ‘strategic-minded voter’ will be able to make this calculation with confidence. Therefore, he is more likely simply to grade the candidates ‘honestly’, i.e. to adopt what Belinski calls MJ’s ‘dominant strategy’. Honesty provides the greater social choice benefit of electing the one candidate who is most valued by all voting citizens given the grades awarded by each voter to each candidate. S: > Currently, these features incline me to see MJ as the best method for electing a President. However, you do not seem to agree, given your next sentence, even though ‘approval voting’ does not allow each voter to express the deferent intensities with which they might approve of the different candidates: K: >This is because in the scenario I discuss below, MJ would offer different intensities, but nobody (who knew what they were doing) would use them.S: Given that MJ offers something like half the scope for manipulation, I would like to understand why you still think a knowing MJ voter would choose not to use the different intensities it offers.At the same time, no method allows a voter to ‘know what they are doing’, i.e. beforehand, the outcome of every election is uncertain. The results of all the ‘traditional methods’ are even more uncertain both because they may display one of Arrow’s paradoxes, and they make manipulation of the outcomes easier. In contrast, the rational and socially minded MJ voter will again know that by grading all the candidates honestly, she is playing her part in helping to elect the candidate most valued by the electorate.K: That transforms the method into Approval. You are right, that I’m not certain that Approval (be it actual Approval or MJ that turned into Approval) is the best method for electing a president.S: Again, am I correct in believing that whenever MJ might be ‘turned into Approval’, this use could still allow only half the manipulation offered by actual Approval? Also, given that Approval does not allow any voter to express different intensities of approval, I would like to understand why you might still consider it to be the ‘best’. >> K: The rating/grade values have no independent, practical meaning.S: All the honest grades are ‘independent’ of each other by being only dependent on each voter’s idea of an EXCELLENT candidate. Yes, if a voter merely treats the ‘grades’ as ‘rankings’, then they would lose their ‘independence’ from each other. At the same time, any attempts to manipulate the results using these ‘rankings’ would be half as likely to succeed. Again, please correct me if I am mistaken that B&L have successfully justified this ‘half as likely’ claim.K: If [MJ] voters have this perception and respond with this behavior, then the method is just an overly complicated form of approval voting.S: But do you agree that this is a largely mistaken ‘perception’? In any case, if some citizens make this mistake, they could only blame themselves for failing both to take advantage of the opportunity to help elect the most valued candidate by honestly evaluating all of them, and perhaps to have partly wasted their vote by voting strategically but only with half a chance of being successful in their own eyes. Consequently, we could argue that MJ at least has the clear virtue over the ‘traditional’ methods of most certainly offering these democratic advantages most completely to citizens.K: In that case, I'd rather just use approval, because it's clearer what's going on.S: As I see it, no method allows us to know exactly the motives or calculations which each voter is making when they vote. However, is it not true that citizens are more like to ‘evaluate’ the candidates, given that MJ’s ballots alone asks for these grades?At the same time, I would like to understand why you might ‘rather’ use an ‘impoverished’ method like APPROVAL rather than MJ which is ‘rich’ with the above opportunities. At the same time, perhaps the first part of your next but two paragraphs below actually agree with this point. However, its second part then seems to reverse this again by you saying that MJ would *hopefully* be changed into Approval.[….]> S: Given the above, it seems that MJ voters would be much less likely ‘actually to try to be so strategic’ and this conclusion seems to be supported by the ‘Orsay experiment’ (pp.9-16. 257-265). K: If I understand correctly, Orsay was a poll with no stakes. I would be curious to know whether/how the voters were told how the ballots would be counted.S: In this regard, you may wish to consider Belinski’s following report on page 255 in his book with Laraki (B&L: Majority Judgment): ‘The experiment—the ballot and the method of ranking—was explained to potential participants well before election day in individual letters, an article in the town’s quarterly magazine, posters, and an evening presentation open to all.’ Also, on page 17, B&L report their following instructions to the participants in their different October 2008 experiment conducted on the Web: ‘You will be asked to evaluate in a language of grades. A candidate’s majority-grade is the middlemost of her/his grades… The candidates are ranked according to their majority-grades.’S: While B&L openly accept that a binding election was not at ‘stake’, I see that experiment as surely providing some empirical evidence that goes some why to suggesting how people would use the MJ ballot in an actual election. Of course, better empirical evidence would be provided, at least by a ‘trial’ adoption of MJ for some actual elections. K: In any case, don't think I am saying that under MJ, voters would all become strategic and this would make the outcomes worse. I actually think it would make the outcomes better. (As in "more plausible," if the voters had been a legislature.) The downside of the voters being strategic is just that the different rating [grading] options become pointless. So my criticism is not that MJ is bad, it's that it is needlessly complicated for what it might and *hopefully would* turn into.S: Yes, MJ offers ‘different rating [grading] options’, and much less scope for manipulation. Admittedly, the counting of MJ is slightly more complicated than simply summing approvals or scores. However, is not MJ’s potential for periodically and more precisely informing all citizens and candidates about the actual intensities with which the many different scales of values and concerns that actually exist within one’s society an additional benefit well worth this slight additional complication, e.g. a complication which is also much less than any Condorcet methods or IRV? >> [….] > >> K: I find a lot of methods tolerable, and I've designed a lot of methods too (most of them tolerable). I care about >> certain properties more than others, but the ones I like aren't even all compatible with each other. > >> S: Which ‘properties’ do you most care about? How are they ‘incompatible’ with each other? Still, which method do you see as superior to MJ, all things considered? K: Some properties I like are: Favorite betrayal (MJ satisfies, IRV doesn't, MAM doesn't but is probably pretty good). This criterion is about being able to safely rank/rate your favorite candidate at least equal-top with a compromise choice. Minimal defense (MJ and MAM satisfy, IRV doesn't). This is about the ability of a full majority of voters who prefer candidate A to candidate B, to ensure that B loses, without any of them having to vote that A is their favorite. (Normally they will do this by ranking A sincerely, and not ranking B over anybody.) Later-no-harm (IRV satisfies, MJ and MAM don't). S: On August 12, Wikipedia defined this criterion as follows:‘Thelater-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate does not cause a more-preferred candidate to lose.’This seems to be the only criteria which MJ fails for you. B&L admit and address this theoretical failure and explain why it is unimportant in practice (pp.285-287). I will try to explain why. Below, the following Wikipedia example illustrates how MJ can violate the ‘later-no-harm’ criterion. In scenario 1, the 1st voter explicitly gives only candidate A a grade, i.e. Excellent. Thus, by default, she gives candidate B a grade of Poor and consequently B has a median grade of Poor from the 1st voter. Thus, A is elected with a median grade of Fair. | MJ SCENARIO 1 | | Candidates:VOTERS | A | B | | 1st | E | (P) | | 2nd | P | E | | 3rd | F | P | | | Median-grade:Fair | | | | Winner | | | MJ SCENARIO 2 | | Candidates:VOTERS | A | B | | 1st | E | G | | 2nd | P | E | | 3rd | F | P | | | | Median-grade:Good | | | | Winner | In scenario 2, the 1st voter instead gives B a more ‘positive rating’ (i.e. Good). Now, B has a median grade of Good and thus B would be elected. Thus, by the 1st voter now ‘giving a more ‘positive rating [than before (i.e. Good rather than Poor) to her] less-preferred candidate’, this has caused her ‘more-preferred candidate to lose. This criterion presumes that this result would not have been 1st voter’s intention. It assumes that each voter is only interested in maximizing the chances that the candidate she personally most favors will be the winner. B&L see this as the flawed assumption made by advocates of the ‘traditional methods’.Instead, B&L assume that voters want the winner to be the candidate most highly valued by a majority of all the voters. They see MJ as offering a method by which such a winner is best discovered. It gives each citizen the opportunity to grade each and every candidate honestly according to each citizen’s own concept of the characteristics that an EXCELLENT winner would have. MJ discovers which candidate comes closest to being EXCELLENT as judged by the largest majority. MJ assumes that each voter should accept that this majority is more likely to identify the winner who is truly most qualified for the office than if any one voter could decide this on their own.Consequently, rather than an example of a flaw in MJ, the above 2 scenarios illustrate to me how MJ should work. If the 1st voter in scenario 1 honestly sees no reason to give a grade higher than POOR to candidate B, then clearly A should be elected as he has the higher median grade FAIR. However, if the 1st voter instead honesty grades B as GOOD in scenario 2, scenario 2 shows that B should be elected instead because B now has the higher median grade of GOOD.At the same time, do you disagree with Belinski’s claims both - that MJ discovery of the winner only by his median grade makes it only half as like that one voter changing her grade for one candidate will change who is the winner, and - that with many candidates and millions of voters, it is ‘almost certain’ that any manipulation sought by such changes would not be successful? K: Later-no-help or "burial resistance" (IRV and MJ satisfy, MAM doesn't). Condorcet (MAM satisfies). I guess you know about these last three. Plurality (all of IRV, MAM, and MJ satisfy). This is a fairly easy criterion that says we can't elect a candidate who has fewer "votes in total" than some other candidate already has in first place votes. The (seeming) incompatibility that frustrates me the most is that between minimal defense and LNHarm.S: In practice, there should be no need for such ‘frustration’ if you answers ‘yes’ to both questions posed by the last sentence in my immediately above paragraph. K: Of the three methods (MAM, IRV, MJ) I would pick MAM. I'm not sure if I prefer MJ to IRV. Even if we replace MJ in the question with Approval, I am not sure.S: Given my above points plus the fact that MAM gives each voter less opportunity to express the different intensities of support they might have for the different candidates, and the much greater difficulty that ordinary citizens would have in understanding exactly how MAM is counted, I would like to understand why you would ‘prefer’ MAM over MJ.K: [….] Otherwise, I'm afraid of Approval's potential to produce results that appear arbitrary and inconclusive (fragmented electorate, unconvincing winner). > >>K: In general I feel that election methods should produce an outcome that would be plausible if the voters had been able to gather and vote in person, just as a legislature. K: For example, MJ violates Condorcet Loser. In theory it can elect a candidate who could not win head-to-head against any of the other candidates. It is not likely that a legislature would settle on an outcome that could not survive a one-on-one vote against any of the other options. S: Contrary to B&L’s belief, your worry here regarding Condorcet seems to assume that ‘preferences’ are more important than ‘evaluations’. However, if all MJ voters equally distributed their EXCELLENTs between all the candidates except the one candidate to which they all gave VERY GOOD, why would you (or a legislature) be justified in not seeing the one with all these VERY GOODs as the appropriate winner? This is an example of the fact that MJ seems naturally to discover the most valued candidate unless every voter grades all the candidates exactly in the same way. >> S: Why would you not see MJ as ‘plausible’ in this sense? For example, a legislature could elect its prime minister in a parliamentary system using MJ. In the extremely unlikely event that this might result in an MJ tie, it could be quickly resolved by electing one winner by a head to head vote. I.e. after discovering to 2 candidates to be equally qualified, the winner would be the one ‘preferred’ by the majority for whatever reason. K: Also, suppose that an MJ voter doesn't like any candidate and his best rating awarded is "acceptable." In so doing he can actually cause his "favorite" candidate to lose to somebody else. I would expect a legislator to understand the risk of this happening and not cast votes that could have such an effect. S: Yes, in this context, if he greatly fears any other candidate winning, rationally he should give his ‘favorite’ an excellent and reject the rest. K: (I'm not assuming the MJ voters have an incentive or ability to use strategy, in this analysis. I want to assume that the voters are sincere, and that the method itself will handle the translation of the sincere preferences into the strategic, informed behavior you would expect of a legislator.) S: Yes, I do not see how MJ could be any worse than any of the alternative methods. At the same time, its design seems to make it most probably better that any of the others I know for electing one winner.KevinSteve ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info

Jameson Quinn

Wed, Sep 7, 2016 2:32 PM

I think I should be a bit more explicit with my mental models here.

In order to evaluate the quality of a voting system, you need a few things:

A probability model over electorates. This should be able to generate
monte-carlo scenarios involving voters, candidates, and utilities for each
voter-candidate pair. Or, in the reverse direction, it should be able to
take a class of scenarios, and assign it some kind of plausibility score
(that is, non-normalized probability). The process of figuring out how
plausible a given class of scenarios is might be computationally difficult,
but ideally we should be able to approximate it using some short-cuts.
A model for voter information; what does each voter believe about the
rest of the electorate.
A model for voter strategy. This is a function that takes a voter's
candidate utilities, information about other voters, and understanding of
the voting system, and outputs a ballot, "strategic" or "honest".

Once you have the above, you can run a monte-carlo simulation and figure
out VSE, voter satisfaction efficiency; that is, you can understand each
system's expected utility.

Right now, we're not being that rigorous; we're just arguing verbally. But
my arguments are intended to be educated guesses about what the above
procedure would find.

So, in order to be able to make such guesses, I must have some rough idea
of what I'd fill in at steps 1, 2, and 3. The first of those, the
probability model over electorates, is the most crucial.

I'm imagining a model where each candidate has a point location in some
n-dimensional space of issues and inherent qualities. Each voter has a
single-peaked utility function over that space; we can approximate that by
saying that the voter is "at" the peak of that utility function.

Of the n dimensions, one ideological dimension dominates; that is, it
accounts for a majority of the variance of candidates, voters, and
candidate/voter utilities. We can assume that candidates and voters are
each distributed unimodally along this primary dimension. (I would not go
so far as to assume that distributions are unimodal or even multivariate
normal in the full-dimensional space, as that would essentially rule out
Condorcet cycles. But I think that unimodal distributions over the primary
ideological dimension are an unobjectionable assumption.)

Let's imagine that we have 3 candidates (P,Q,R), located at -100, 0
(center), and +70 on the main ideological dimension; and we have voters
(p,q,r) located at -70, 0, and 199. Ignoring for the moment the other
dimensions, we can say that U(x,X) is the negative of the ideological
distance between candidate X and voter x; so U(p,P)=-30, U(r,P)=-300, etc.

What does this mean for the "honest" MJ ballots? Well, if by "honest" you
mean "using a single canonical mapping from utility to grades", it's a
mess. Say the cutoffs for A, B, C, D, and F are -40, -80, -120, -160, and
-200. That would mean the "honest" ballots would be:
p: P:A; Q:B; R:D
q: P:B; Q:A; R:C
r: P:C; Q:D; R:F

To me, that's a broken definition of "honesty". None of our three voters
uses the full range of grades; and for voters q and r, that failure to use
the full range was entirely predictable, and will probably continue in
future elections.

For me, a better definition of "honesty" would be: calibrate an absolute
scale such that the historical and/or plausible winners of similar
elections would cover the range of grades from B to F, and any candidate
better than 95% of historical winners gets an A. If the historical winners
come from the ideological range {-80, 80}, that would mean the "honest"
ballots would be:
p: P:B, Q:C, R:F
q: P:F, Q:A, R:D
r: P:F, Q:C, R:B

Note that these "honest" ballots still don't use the full range of grades,
but they come a lot closer than the "honest" ballots above. And for voter
p, a candidate at -72 would indeed get an A; as would one at 90 for voter
r, even though the absolute utility would still be -109, which would be
worse than an F for voter q.

Note also that this definition of "honesty" still preserves IIA within any
given election.

As this last example shows, one consequence of the model above is that
voters near the center are likely to be much pickier. They're used to being
more or less catered to ideologically, so they can afford to exaggerate
their differences with both sides. That's what I meant when I said that
it's likely that a centrist would give both sides an honest F, which was
one of the factors of 1/3 in my rough calculation that an arbitrary honest
ballot has less than a 1/27 chance of being strategically suboptimal.

And that, to me, is the key number. My information and strategic models
(steps 2 and 3 above) are based on regret; that is, each voter looks at
historical elections they've voted in and perhaps a noisy poll or two of
the current election, and sees if they have any strategic regret. If such
regret happens only 1/27 of the time, and even when it happens it means
that the winner is only slightly worse than the strategically optimal
winner... I think most voters won't bother attempting strategy, except in
the trivial sense of rating at least one favorite candidate at A and at
least one despised one at F. (Note that this strategy will almost certainly
not affect the medians, and thus will not change the winner. Though
technically it breaks IIA, it only does so in bizarre cases where both
voter and candidate distributions differ severely from historical norms.)

I think I should be a bit more explicit with my mental models here. In order to evaluate the quality of a voting system, you need a few things: 1. A probability model over electorates. This should be able to generate monte-carlo scenarios involving voters, candidates, and utilities for each voter-candidate pair. Or, in the reverse direction, it should be able to take a class of scenarios, and assign it some kind of plausibility score (that is, non-normalized probability). The process of figuring out how plausible a given class of scenarios is might be computationally difficult, but ideally we should be able to approximate it using some short-cuts. 2. A model for voter information; what does each voter believe about the rest of the electorate. 3. A model for voter strategy. This is a function that takes a voter's candidate utilities, information about other voters, and understanding of the voting system, and outputs a ballot, "strategic" or "honest". Once you have the above, you can run a monte-carlo simulation and figure out VSE, voter satisfaction efficiency; that is, you can understand each system's expected utility. Right now, we're not being that rigorous; we're just arguing verbally. But my arguments are intended to be educated guesses about what the above procedure would find. So, in order to be able to make such guesses, I must have some rough idea of what I'd fill in at steps 1, 2, and 3. The first of those, the probability model over electorates, is the most crucial. I'm imagining a model where each candidate has a point location in some n-dimensional space of issues and inherent qualities. Each voter has a single-peaked utility function over that space; we can approximate that by saying that the voter is "at" the peak of that utility function. Of the n dimensions, one ideological dimension dominates; that is, it accounts for a majority of the variance of candidates, voters, and candidate/voter utilities. We can assume that candidates and voters are each distributed unimodally along this primary dimension. (I would not go so far as to assume that distributions are unimodal or even multivariate normal in the full-dimensional space, as that would essentially rule out Condorcet cycles. But I think that unimodal distributions over the primary ideological dimension are an unobjectionable assumption.) Let's imagine that we have 3 candidates (P,Q,R), located at -100, 0 (center), and +70 on the main ideological dimension; and we have voters (p,q,r) located at -70, 0, and 199. Ignoring for the moment the other dimensions, we can say that U(x,X) is the negative of the ideological distance between candidate X and voter x; so U(p,P)=-30, U(r,P)=-300, etc. What does this mean for the "honest" MJ ballots? Well, if by "honest" you mean "using a single canonical mapping from utility to grades", it's a mess. Say the cutoffs for A, B, C, D, and F are -40, -80, -120, -160, and -200. That would mean the "honest" ballots would be: p: P:A; Q:B; R:D q: P:B; Q:A; R:C r: P:C; Q:D; R:F To me, that's a broken definition of "honesty". None of our three voters uses the full range of grades; and for voters q and r, that failure to use the full range was entirely predictable, and will probably continue in future elections. For me, a better definition of "honesty" would be: calibrate an absolute scale such that the historical and/or plausible winners of similar elections would cover the range of grades from B to F, and any candidate better than 95% of historical winners gets an A. If the historical winners come from the ideological range {-80, 80}, that would mean the "honest" ballots would be: p: P:B, Q:C, R:F q: P:F, Q:A, R:D r: P:F, Q:C, R:B Note that these "honest" ballots still don't use the full range of grades, but they come a lot closer than the "honest" ballots above. And for voter p, a candidate at -72 would indeed get an A; as would one at 90 for voter r, even though the absolute utility would still be -109, which would be worse than an F for voter q. Note also that this definition of "honesty" still preserves IIA within any given election. As this last example shows, one consequence of the model above is that voters near the center are likely to be much pickier. They're used to being more or less catered to ideologically, so they can afford to exaggerate their differences with both sides. That's what I meant when I said that it's likely that a centrist would give both sides an honest F, which was one of the factors of 1/3 in my rough calculation that an arbitrary honest ballot has less than a 1/27 chance of being strategically suboptimal. And that, to me, is the key number. My information and strategic models (steps 2 and 3 above) are based on regret; that is, each voter looks at historical elections they've voted in and perhaps a noisy poll or two of the current election, and sees if they have any strategic regret. If such regret happens only 1/27 of the time, and even when it happens it means that the winner is only slightly worse than the strategically optimal winner... I think most voters won't bother attempting strategy, except in the trivial sense of rating at least one favorite candidate at A and at least one despised one at F. (Note that this strategy will almost certainly not affect the medians, and thus will not change the winner. Though technically it breaks IIA, it only does so in bizarre cases where both voter and candidate distributions differ severely from historical norms.)

Kevin Venzke

Thu, Sep 8, 2016 1:37 AM

  De : Jameson Quinn <jameson.quinn@gmail.com>

À : Kevin Venzke stepjak@yahoo.fr
Cc : Kristofer Munsterhjelm km_elmet@t-online.de; "election-methods@lists.electorama.com" election-methods@lists.electorama.com
Envoyé le : Mercredi 7 septembre 2016 9h32
Objet : Re: [EM] (3) MJ -- The easiest method to 'tolerate'

I think I should be a bit more explicit with my mental models here.
In order to evaluate the quality of a voting system, you need a few things:

A probability model over electorates. This should be able to generate monte-carlo scenarios involving voters, candidates, and utilities for each voter-candidate pair. Or, in the reverse direction, it should be able to take a class of scenarios, and assign it some kind of plausibility score (that is, non-normalized probability). The process of figuring out how plausible a given class of scenarios is might be computationally difficult, but ideally we should be able to approximate it using some short-cuts.
A model for voter information; what does each voter believe about the rest of the electorate.
A model for voter strategy. This is a function that takes a voter's candidate utilities, information about other voters, and understanding of the voting system, and outputs a ballot, "strategic" or "honest".
Once you have the above, you can run a monte-carlo simulation and figure out VSE, voter satisfaction efficiency; that is, you can understand each system's expected utility.
Right now, we're not being that rigorous; we're just arguing verbally. But my arguments are intended to be educated guesses about what the above procedure would find.
So, in order to be able to make such guesses, I must have some rough idea of what I'd fill in at steps 1, 2, and 3. The first of those, the probability model over electorates, is the most crucial.
I'm imagining a model where each candidate has a point location in some n-dimensional space of issues and inherent qualities. Each voter has a single-peaked utility function over that space; we can approximate that by saying that the voter is "at" the peak of that utility function.
Of the n dimensions, one ideological dimension dominates; that is, it accounts for a majority of the variance of candidates, voters, and candidate/voter utilities. We can assume that candidates and voters are each distributed unimodally along this primary dimension. (I would not go so far as to assume that distributions are unimodal or even multivariate normal in the full-dimensional space, as that would essentially rule out Condorcet cycles. But I think that unimodal distributions over the primary ideological dimension are an unobjectionable assumption.)
Let's imagine that we have 3 candidates (P,Q,R), located at -100, 0 (center), and +70 on the main ideological dimension; and we have voters (p,q,r) located at -70, 0, and 199. Ignoring for the moment the other dimensions, we can say that U(x,X) is the negative of the ideological distance between candidate X and voter x; so U(p,P)=-30, U(r,P)=-300, etc.
What does this mean for the "honest" MJ ballots? Well, if by "honest" you mean "using a single canonical mapping from utility to grades", it's a mess. Say the cutoffs for A, B, C, D, and F are -40, -80, -120, -160, and -200. That would mean the "honest" ballots would be:p: P:A; Q:B; R:Dq: P:B; Q:A; R:Cr: P:C; Q:D; R:F
To me, that's a broken definition of "honesty". None of our three voters uses the full range of grades; and for voters q and r, that failure to use the full range was entirely predictable, and will probably continue in future elections.
For me, a better definition of "honesty" would be: calibrate an absolute scale such that the historical and/or plausible winners of similar elections would cover the range of grades from B to F, and any candidate better than 95% of historical winners gets an A. If the historical winners come from the ideological range {-80, 80}, that would mean the "honest" ballots would be:p: P:B, Q:C, R:Fq: P:F, Q:A, R:Dr: P:F, Q:C, R:B
Note that these "honest" ballots still don't use the full range of grades, but they come a lot closer than the "honest" ballots above. And for voter p, a candidate at -72 would indeed get an A; as would one at 90 for voter r, even though the absolute utility would still be -109, which would be worse than an F for voter q.
Note also that this definition of "honesty" still preserves IIA within any given election.
As this last example shows, one consequence of the model above is that voters near the center are likely to be much pickier. They're used to being more or less catered to ideologically, so they can afford to exaggerate their differences with both sides. That's what I meant when I said that it's likely that a centrist would give both sides an honest F, which was one of the factors of 1/3 in my rough calculation that an arbitrary honest ballot has less than a 1/27 chance of being strategically suboptimal.
And that, to me, is the key number. My information and strategic models (steps 2 and 3 above) are based on regret; that is, each voter looks at historical elections they've voted in and perhaps a noisy poll or two of the current election, and sees if they have any strategic regret. If such regret happens only 1/27 of the time, and even when it happens it means that the winner is only slightly worse than the strategically optimal winner... I think most voters won't bother attempting strategy, except in the trivial sense of rating at least one favorite candidate at A and at least one despised one at F. (Note that this strategy will almost certainly not affect the medians, and thus will not change the winner. Though technically it breaks IIA, it only does so in bizarre cases where both voter and candidate distributions differ severely from historical norms.)

Hi Jameson, I wonder if you might remember that I created some simulations that attempted to determine methods' strategies in an organic way, using voters that don't have a concept of sincerity and just pull the levers (initially randomly) in repeated polls to learn what they do. Maybe you can see, from this concept, why I might find it unnatural to consider whether the strategic voter would make a decision to deviate from honesty in MJ. I tend to think the public dialogue preceding the election would color voters' thinking to the point that they wouldn't even perceive a difference between how they think they should vote, and what the ballot language would suggest is sincere. What I imagine is an occasional letter to the editor commenting on how things would be different if people actually did vote as they were asked to. I'm not sure if the tone would be humorous or critical. In the below post you both suggest a weakening of IIA, and dismiss actual IIA failures as something that will happen only in bizarre scenarios. I wonder to what extent you feel that IIA is an advantage of MJ worth pointing out. Is it an issue you have to raise because other people are raising it? Your concept of calculating the likelihood that a sincere ballot is suboptimal is an interesting one. You seemingly end up with incredibly high numbers, no doubt because you don't require that the voter can actually change the outcome. But that makes me wonder, in theory, how one would accurately measure this likelihood. Kevin De : Jameson Quinn <jameson.quinn@gmail.com> À : Kevin Venzke <stepjak@yahoo.fr> Cc : Kristofer Munsterhjelm <km_elmet@t-online.de>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> Envoyé le : Mercredi 7 septembre 2016 9h32 Objet : Re: [EM] (3) MJ -- The easiest method to 'tolerate' I think I should be a bit more explicit with my mental models here. In order to evaluate the quality of a voting system, you need a few things: 1. A probability model over electorates. This should be able to generate monte-carlo scenarios involving voters, candidates, and utilities for each voter-candidate pair. Or, in the reverse direction, it should be able to take a class of scenarios, and assign it some kind of plausibility score (that is, non-normalized probability). The process of figuring out how plausible a given class of scenarios is might be computationally difficult, but ideally we should be able to approximate it using some short-cuts. 2. A model for voter information; what does each voter believe about the rest of the electorate. 3. A model for voter strategy. This is a function that takes a voter's candidate utilities, information about other voters, and understanding of the voting system, and outputs a ballot, "strategic" or "honest". Once you have the above, you can run a monte-carlo simulation and figure out VSE, voter satisfaction efficiency; that is, you can understand each system's expected utility. Right now, we're not being that rigorous; we're just arguing verbally. But my arguments are intended to be educated guesses about what the above procedure would find. So, in order to be able to make such guesses, I must have some rough idea of what I'd fill in at steps 1, 2, and 3. The first of those, the probability model over electorates, is the most crucial. I'm imagining a model where each candidate has a point location in some n-dimensional space of issues and inherent qualities. Each voter has a single-peaked utility function over that space; we can approximate that by saying that the voter is "at" the peak of that utility function. Of the n dimensions, one ideological dimension dominates; that is, it accounts for a majority of the variance of candidates, voters, and candidate/voter utilities. We can assume that candidates and voters are each distributed unimodally along this primary dimension. (I would not go so far as to assume that distributions are unimodal or even multivariate normal in the full-dimensional space, as that would essentially rule out Condorcet cycles. But I think that unimodal distributions over the primary ideological dimension are an unobjectionable assumption.) Let's imagine that we have 3 candidates (P,Q,R), located at -100, 0 (center), and +70 on the main ideological dimension; and we have voters (p,q,r) located at -70, 0, and 199. Ignoring for the moment the other dimensions, we can say that U(x,X) is the negative of the ideological distance between candidate X and voter x; so U(p,P)=-30, U(r,P)=-300, etc. What does this mean for the "honest" MJ ballots? Well, if by "honest" you mean "using a single canonical mapping from utility to grades", it's a mess. Say the cutoffs for A, B, C, D, and F are -40, -80, -120, -160, and -200. That would mean the "honest" ballots would be:p: P:A; Q:B; R:Dq: P:B; Q:A; R:Cr: P:C; Q:D; R:F To me, that's a broken definition of "honesty". None of our three voters uses the full range of grades; and for voters q and r, that failure to use the full range was entirely predictable, and will probably continue in future elections. For me, a better definition of "honesty" would be: calibrate an absolute scale such that the historical and/or plausible winners of similar elections would cover the range of grades from B to F, and any candidate better than 95% of historical winners gets an A. If the historical winners come from the ideological range {-80, 80}, that would mean the "honest" ballots would be:p: P:B, Q:C, R:Fq: P:F, Q:A, R:Dr: P:F, Q:C, R:B Note that these "honest" ballots still don't use the full range of grades, but they come a lot closer than the "honest" ballots above. And for voter p, a candidate at -72 would indeed get an A; as would one at 90 for voter r, even though the absolute utility would still be -109, which would be worse than an F for voter q. Note also that this definition of "honesty" still preserves IIA within any given election. As this last example shows, one consequence of the model above is that voters near the center are likely to be much pickier. They're used to being more or less catered to ideologically, so they can afford to exaggerate their differences with both sides. That's what I meant when I said that it's likely that a centrist would give both sides an honest F, which was one of the factors of 1/3 in my rough calculation that an arbitrary honest ballot has less than a 1/27 chance of being strategically suboptimal. And that, to me, is the key number. My information and strategic models (steps 2 and 3 above) are based on regret; that is, each voter looks at historical elections they've voted in and perhaps a noisy poll or two of the current election, and sees if they have any strategic regret. If such regret happens only 1/27 of the time, and even when it happens it means that the winner is only slightly worse than the strategically optimal winner... I think most voters won't bother attempting strategy, except in the trivial sense of rating at least one favorite candidate at A and at least one despised one at F. (Note that this strategy will almost certainly not affect the medians, and thus will not change the winner. Though technically it breaks IIA, it only does so in bizarre cases where both voter and candidate distributions differ severely from historical norms.)