To Kevin and everyone,

Sorry for the late reply but travel and a family reunion intervened.  I look forward to your response.

Steve

From: 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

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’.

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.

[….]

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: 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:

‘The later-no-harm criterion is a voting system criterionhttps://en.wikipedia.org/wiki/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

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?

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: 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.

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.

Kevin

Steve

Hi Steve,

I wrote a full response but then trimmed sections to reduce redundancy. There is still a fair amount.

Steve wrote:

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.

And I will say again that I don't feel it is sufficient to simply "allow" and "invite" these things.

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.

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

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.

"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.

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.

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

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.

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.

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.

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:

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...

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.

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.

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.

Not really.

But I don't view it as a mistake.

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.

I think the "opportunities" are not likely an advantage for those who take them.

Thank you for this summary.

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.

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:

[...]

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.

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).

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.

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.

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.

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

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:

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 scenario
300: A>B>>C
200: B>>A>C
400: 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:

On 09/05/2016 10:30 PM, Jameson Quinn wrote:

Quick response: I seem to recall B&L saying that in their polling data,
Approval responses showed sign of many voters using what I've been
calling "scenario 3" reasoning, i.e. relative ranks (where rated/graded
systems would fail IIA). They then argued that this means you have to
have a properly phrased ballot to get the voters to consider grading
against a common standard rather than ranking relatively, and more
specifically, that Approval's two grades were not sufficient to do
permit that kind of mindset.

If that's true, then there's some kind of threshold of number of grades,
below which there aren't enough grades for the ballot format to
encourage grading against a common standard. So three-slot methods would
have to be tested to see if voters would vote grading-style or
relative-rank style with three grades, or if three grades are still too few.

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:

On 9/6/2016 6:00 AM, Jameson Quinn wrote:

C: How are they better than IBIFA?  Or, say, Smith//Approval?

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

C:  How is this a "chicken dilemma" scenario? In this context, I don't
understand what the words "agreement" and "reversal" mean.

C: Why is rating a candidate both approved and "disqualified" "legal and
counted"? What is the default rating?  The rule regarding "the
following election" I consider arbitrary
and very undemocratic.

In all these Bucklin/MJ/MCA methods the strategic incentive for the
voters to just cast approval-type votes (i.e. only use the top and
bottom slots/grades) is in my view
far too strong.  The least bad of them is 3-slot MTA (where if more than
one candidate exceeds the majority threshold in the second round the
winner is the one of those with the
most Top Ratings), which is simple and slightly reduces the truncation
incentive.  It didn't make your list.

All them absurdly fail Irrelevant Ballots independence and (unless you
have a fetish for strict compliance with Later-no-Help) are completely
dominated by IBIFA.
The IBIFA winner will always pairwise beat any different winner that any
of these methods come up with.

Chris Benham