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

Wed Aug 31 18:16:47 PDT 2016

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 at yahoo.fr>
Sent: Sunday, August 7, 2016 3:08 AM
To: steve bosworth; election-methods at lists.electorama.com
Subject: Re: [EM] (2) MJ -- The easiest method to 'tolerate'

Hi Steve,

_______________________________
De : steve bosworth <stevebosworth at hotmail.com>
À : "election-methods at lists.electorama.com" <election-methods at lists.electorama.com>; "stepjak at yahoo.fr" <stepjak at 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:

‘The later-no-harm criterion is a voting system criterion<https://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:  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.

Kevin

Steve

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