Re: [EM] (6) To Kristofer and everyone: MJ best to ‘tolerate’
Arguably a problem with Majority Judgement is that most voters make no difference to the overall "score" for a candidate. Because it uses the median rather than mean, it is a fairly "robust" measure, and a single vote is unlikely to shift the median. People can use that to argue in its favour - if you like or dislike a candidate you can rate them highly or lowly (above or below their current median), and it doesn't matter whether you use the extreme ratings or not. If a candidate's median is C, then I can give an honest B or an exaggerated A - the candidate's overall median won't be affected by my exaggeration.
But the flipside of being resistant to strategy in this way is that arguably it is only this way because it's resistant to voting itself! It just has much more "inertia" than other systems. In normal score voting every vote has an effect on a candidate's average. And because of this there is arguably a sense of "power" for a voter. But this isn't the case for median voting. Well, each vote would provide some sort of shift that could make a difference in a tie-break, but it's not the same.
One slightly crazy idea to ameliorate this would be to use a measure somewhere between the mean and median. The mean of a data set is the number that minimises the sum of the squared differences to the data points. The median is the number that minimises the sum of the absolute differences (so the differences^1). So maybe you could instead minimise the differences^1.1 or something. This would still be close to a median method but presumably each vote would make a difference to a candidate's "average" score using this measure. But then arguably it doesn't make sense to use letter grades with a verbal description in a system like this. It becomes about numbers again. It might also be difficult to calculate and hard for voters to understand what's going on.
On Sat, 17/9/16, C.Benham cbenham@adam.com.au wrote:
Subject: Re: [EM] (6) To Kristofer and everyone: MJ best to ‘tolerate’
To: "steve bosworth" stevebosworth@hotmail.com, "election-methods@lists.electorama.com" election-methods@lists.electorama.com
Date: Saturday, 17 September, 2016, 5:42
On 9/16/2016
4:22 AM, steve bosworth
wrote:
MJ simply asks each voter to grade
each candidate when judged against each
voter’s own criteria
of what an EXCELLENT candidate would look
like.
Any candidate judged to be less than
EXCELLENT must
be graded either as VERRY GOOD, GOOD,
ACCEPTABLE, POOR, or
REJECTED.
Balinski and Laraki refer to each voters
own criteria
for grading candidates as being ‘absolute’
(but this is only
in the sense that these criteria should be
independent of
any one set of candidates that might be seeking
election).
C: To begin with superficial aesthetics, the grades
should have
simple neutral names (like A B C D E F) and the ballot
"request"
should be something like:
"Give your favourite candidate or candidates an A
and and your
least preferred candidate or candidates an F and any
intermediate
candidates whatever
grade you see fit. Default rating is F."
As it is if in a given election A , by my
"criteria that should
be independent of any one set of candidates that might
be seeking
election" , such as those doing so in election
A,
I rate my favourite candidate as being merely
"Acceptable" I
would resent having to either (a) accept that my
vote will have
less influence on the result than voters who rate
their favourite as "Excellent" or (b)
"lie" and falsely indicate
that I rate my favourite as "Excellent".
MJ poses as being somewhat like a jury in a trial,
or a panel
that judges say a competitive performance of
Gymnastics or Diving.
But elections for powerful public political elections
are very
different. In those cases the jurors/judges are
more-or-less
"disinterested", i.e. it doesn't really
make any
possible difference to their lives who wins the
competition or
whether the accused is jailed or set free. In
elections who wins
the election could have a big effect on the
lives of voters.
Also in those other cases there is usually general
agreement what
an excellent sporting performance looks like and what
a terrible
sporting performance looks like and
what constitutes clear proof of guilt or innocence.
In elections
voters often have opposing ideologies, i.e. very
different ideas
of what policies, priorities, political philosophy,
diplomatic/military strategies the election winner
should have.
Another difference is that in those other cases the
people on the
jury in a trial or the panel judging a sporting
performance base
their decisions the same evidence. The jurors
all hear the same evidence and arguments and base
their verdict on
that. Likewise the judging panel all closely watch the
same
performance and give their scores based purely
on that.
But voters in public elections vary widely in terms of
what
information they get, and the quality and quantity of
that
information. And of course much of the
"information" they
use might be false or misleading, generated by those
with a big
interest in who wins the election.
Leaving aside the strategy incentive for voters to
only use the
very top and very bottom grades, suppose that all the
voters rate
the candidates as sincerely as they can
in the way MJ "invites" them to.
Suppose that that there are
only two candidates with any hope of winning, A and
B. Suppose I
think that A is clearly better than B
and you think the opposite. Suppose my rating of A
is Good and
B is Poor, and your rating of B is Excellent and
A is Rejected.
Your pairwise preference will have greater weight than
mine. Is
that fair? According to the MJ philosophy your
vote should have
greater weight because you are more
"enthusiastic" in your support for B over
A. Does this greater
enthusiasm mean that your opinion that B is better
than A is more
likely to be correct than my opposite
opinion?
Also, MJ seems to
offer less scope for manipulative
voting than any other method.
C: As Kevin has pointed out, sincere voters are less
likely to be
at a disadvantage than with Range (aka Average
Ratings) but in
both the voter's best strategy is to only
use the two most extreme ratings. If all the voters do
that the
method is just Approval.
What exactly is your definition of
"manipulative"?
I still favor MJ
even though it is theoretically
vulnerable to ‘Later-no-harm’
(LNH).
C: I don't particularly care about
Later-no-Harm. It encourages
the expression of preferences that may be very weak,
and to the
extent that they are decisive they
would tend to lower the "Social Utility"
(SU) of the winner. And
the expressed preferences are also more likely to be
the result of
unprincipled mutual back-scratching
deals between candidates.
I put a greater value on Later-no-Help (which MJ,
along with MTA
and MCA meets). Ideally there should be weak zero-info
truncation
incentive.
But MJ has a very strong truncation incentive.
It's compliance
with LNHelp is in practice useless if the voters
should all
truncate.
IRV meets both of Later-no-Help and Later-no-Harm, and
in my
opinion it is the best of the methods that meet
Later-no-Help.
Other methods I like fail both. That is better than
only meeting
LNHarm and so having a random-fill incentive, or only
meeting
LNHelp and having a very
strong truncation incentive.
For reasons I might give in another post, I don't
much like MAM.
A simpler Condorcet method I like is
Smith//Approval:
Voters ignore candidates they don't approve and
rank the rest.
Equal-ranking allowed. Elect the most approved
member of the
Smith set.
The "Smith set" is the smallest set of
candidate/s who all
pairwise beat all (if any) outside-the-set members.
A
single-member "Smith set" is the
Condorcet winner.
Compliance with both FBC and Condorcet is
impossible. MJ meets
FBC.
A MJ-like method that is simpler and in my view better
is
Majority Top Approval (MTA).
It uses 3-slot ratings ballots. Default rating is
Bottom. If any
candidate is rated above bottom on more than half the
ballots,
elect (if there is more than one) the
one of those with the highest number of top ratings.
Otherwise
elect the candidate with the highest number of
above-bottom
ratings.
The voters' best strategy is to normally use only
the top and
bottom ratings slots, but the middle slot is handy if
there is one
or more candidate the voter is
unsure how should rate on a 2-slot ratings ballot, or
if the voter
is prepared to maybe take a small strategic risk for
the sake of
being more expressive.
But a more complex method I much prefer is IBIFA.
http://wiki.electorama.com/wiki/IBIFA
Chris Benham
On 09/17/2016 03:25 PM, Toby Pereira wrote:
Arguably a problem with Majority Judgement is that most voters make
no difference to the overall "score" for a candidate. Because it uses
the median rather than mean, it is a fairly "robust" measure, and a
single vote is unlikely to shift the median. People can use that to
argue in its favour - if you like or dislike a candidate you can rate
them highly or lowly (above or below their current median), and it
doesn't matter whether you use the extreme ratings or not. If a
candidate's median is C, then I can give an honest B or an
exaggerated A - the candidate's overall median won't be affected by
my exaggeration.
But the flipside of being resistant to strategy in this way is that
arguably it is only this way because it's resistant to voting itself!
It just has much more "inertia" than other systems. In normal score
voting every vote has an effect on a candidate's average. And because
of this there is arguably a sense of "power" for a voter. But this
isn't the case for median voting. Well, each vote would provide some
sort of shift that could make a difference in a tie-break, but it's
not the same.
In a way, that's true for ranked methods as well. Suppose that X is the
Condorcet winner. A vote that ranks X in some place has no effect unless
it creates a cycle. If the contest is close, then this may easily
happen, but if it's not, then the vote has no effect except as a way of
moving the contests closer for some other ballot to change the result.
On the other hand, if you'd generalize usually ranked methods to provide
scores rather than rankings as their outputs, then a single vote might
have an effect. So too with MJ: you could have the method return not
just the median grades of the candidates, but how many votes they're
away from getting a higher grade. Any vote that grades a candidate
higher than the MJ result would decrease this counter, and any vote that
grades the candidate lower would increase it.
One slightly crazy idea to ameliorate this would be to use a measure
somewhere between the mean and median. The mean of a data set is the
number that minimises the sum of the squared differences to the data
points. The median is the number that minimises the sum of the
absolute differences (so the differences^1). So maybe you could
instead minimise the differences^1.1 or something. This would still
be close to a median method but presumably each vote would make a
difference to a candidate's "average" score using this measure. But
then arguably it doesn't make sense to use letter grades with a
verbal description in a system like this. It becomes about numbers
again. It might also be difficult to calculate and hard for voters to
understand what's going on.
A more intuitive middle road, I think, would be to use a trimmed mean.
For each candidate, take the ratings and throw out the k% lowest and
highest of them, then that candidate's score is the mean of what's left.
If you let k be 50%-1, then you get MJ (since you throw away everything
but the middle rating). If you let k be 0, then it's Range.
The problem, however, is that if you set k less than the median point,
the method can fail the majority criterion. Furthermore, the method only
gets more vulnerable to Approval-style voting the closer to Range you
get. So if MJ's strategy resistance isn't good enough to keep the voters
from all voting Approval style, then no lesser-k method will be good
enough either.
Kristofer suggests using the trimmed mean to have a useful number to report
in MJ. That's exactly the point of GMJ (graduated majority judgment): for
each candidate, you essentially use the trimmed mean using the widest trim
that does not include grades on both sides of the median. So if somebody
got 10% A (4.0), 25% B (3.0), 35% C (2.0), 20% D (1.0), and 10% F (0.0),
then you would see that the median is C, the A+B tally (35%) is more than
D+F (30%), so you trim 30% from each side, leaving (2.035 + 3.05)/40 =
2.125.
This is very, very similar to MJ in outcome; though it's possible to
construct cases where they disagree, it involves two candidates with the
same median but where one is "more polarizing" (has significantly fewer
grades at that median, thus presumably more at the extremes). Even then it
happens less than half the time (half at the extreme). I think that kind of
situation would be negligibly rare in practice; I'd guess, even less common
than honest Condorcet cycles.
Jameson
2016-09-17 13:20 GMT-04:00 Kristofer Munsterhjelm km_elmet@t-online.de:
On 09/17/2016 03:25 PM, Toby Pereira wrote:
Arguably a problem with Majority Judgement is that most voters make
no difference to the overall "score" for a candidate. Because it uses
the median rather than mean, it is a fairly "robust" measure, and a
single vote is unlikely to shift the median. People can use that to
argue in its favour - if you like or dislike a candidate you can rate
them highly or lowly (above or below their current median), and it
doesn't matter whether you use the extreme ratings or not. If a
candidate's median is C, then I can give an honest B or an
exaggerated A - the candidate's overall median won't be affected by
my exaggeration.
But the flipside of being resistant to strategy in this way is that
arguably it is only this way because it's resistant to voting itself!
It just has much more "inertia" than other systems. In normal score
voting every vote has an effect on a candidate's average. And because
of this there is arguably a sense of "power" for a voter. But this
isn't the case for median voting. Well, each vote would provide some
sort of shift that could make a difference in a tie-break, but it's
not the same.
In a way, that's true for ranked methods as well. Suppose that X is the
Condorcet winner. A vote that ranks X in some place has no effect unless
it creates a cycle. If the contest is close, then this may easily
happen, but if it's not, then the vote has no effect except as a way of
moving the contests closer for some other ballot to change the result.
On the other hand, if you'd generalize usually ranked methods to provide
scores rather than rankings as their outputs, then a single vote might
have an effect. So too with MJ: you could have the method return not
just the median grades of the candidates, but how many votes they're
away from getting a higher grade. Any vote that grades a candidate
higher than the MJ result would decrease this counter, and any vote that
grades the candidate lower would increase it.
One slightly crazy idea to ameliorate this would be to use a measure
somewhere between the mean and median. The mean of a data set is the
number that minimises the sum of the squared differences to the data
points. The median is the number that minimises the sum of the
absolute differences (so the differences^1). So maybe you could
instead minimise the differences^1.1 or something. This would still
be close to a median method but presumably each vote would make a
difference to a candidate's "average" score using this measure. But
then arguably it doesn't make sense to use letter grades with a
verbal description in a system like this. It becomes about numbers
again. It might also be difficult to calculate and hard for voters to
understand what's going on.
A more intuitive middle road, I think, would be to use a trimmed mean.
For each candidate, take the ratings and throw out the k% lowest and
highest of them, then that candidate's score is the mean of what's left.
If you let k be 50%-1, then you get MJ (since you throw away everything
but the middle rating). If you let k be 0, then it's Range.
The problem, however, is that if you set k less than the median point,
the method can fail the majority criterion. Furthermore, the method only
gets more vulnerable to Approval-style voting the closer to Range you
get. So if MJ's strategy resistance isn't good enough to keep the voters
from all voting Approval style, then no lesser-k method will be good
enough either.
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