[EM] (4) MJ -- The easiest method to 'tolerate'

steve bosworth stevebosworth at hotmail.com
Tue Sep 6 19:31:22 PDT 2016

Re: [EM] (4) MJ -- The easiest method to 'tolerate'

To Kevin and everyone from Steve,


From: Kevin Venzke <stepjak at yahoo.fr>
Sent: Saturday, September 3, 2016 7:05 PM
To: steve bosworth; election-methods at lists.electorama.com
Subject: Re: [EM] (3) MJ -- The easiest method to 'tolerate'

Hi Kevin,
After reading the rest of your last post, I think I may have initially misunderstand the following response you made to the quotation in the next paragraph:

K: 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.

S: > 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).

S:  At first I read your response to mean that you fully agree with B&L that MJ’s structure has the advantage that it would most likely lead voters to adopt ‘honesty’, rather than manipulation as their ‘dominant strategy’.  By ‘manipulation’, B&L and I mean the gaining of an electoral advantage over other voters by a voter who ranks or grades at least one candidate ‘dishonestly’, i.e. a vote that is not a straight forward expression of that voter’s own degree of preference or honest evaluation of that candidate.

However, correct me if I am mistaken but some of your later phrases suggest to me that you would actually answer NO, to each of the follow questions:

  1.  Do you agree 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)?    For example, you say: 1): ‘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’; 2): ‘ … 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 ….’.  [If you answer is NO, please try to explain what you think the main ‘object’ of an election should be.]

  2.   Do you agree that ‘majorities of grades are … considerably more discerning decisions than are majorities of preferences’ (p.283)?  For example, you say, 1): ‘my criticism is not that MJ is bad, it's that it is needlessly complicated’; 2):  ‘MAM is harder to understand, but I think it gets more mileage out of its complexity than MJ gets out of its’ [Is this ‘more mileage’ more honest evaluation or something else?],

  3.   Do you agree that the ideal voting ‘method should elicit the honest expression of voters’ opinions as inputs, for the aim of an election is to produce … the true wishes of societies ….’ (p.352)  For example, you say, 1): ‘I do not care about "preferences" vs "evaluations"’; 2):  ‘… 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’; 3): ‘… sincere voters … interested in maximizing the effect …  should only use the two extreme ratings’; 4):’… the strategic voter can do better than …. simply to grade the candidates ‘honestly’ [Do you want a method that maximizes the chances that a society will discover the winner closest to being excellent, or one that especially helps the most savvy voters manipulatively to get their way?].

S: > 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…...

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

S:  What else do you require?

>> 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’.  You will see that I agree with you regarding the special case you outline later.  However, this is a long way from showing that all voters should ‘usually’ see ‘that only the two extreme ratings can maximize the effect of their vote’.  MJ also invites all the other voters who may have a greater knowledge of the many different qualities of the candidates, appropriately from their point of view, to use all 6 grades accurately to evaluate each candidate.  Many of them should see that the most efficient way they can help to prevent any of the candidates they evaluate as Poor or want to Reject from winning is honestly to grade the rest of the candidates from EXCELLENT to ACCEPTABLE.  This will both maximize the chance that one of these candidates will win and will best help the process to discover the socially most valued candidate for the office.

K: 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.

S: I would like to understand how you can say that the exact ‘effect’ a voter wants to ‘maximize’ is not also determined by that voter’s own scale of values?

K: 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.

 S: I would like to understand how you can conclude that a voter’s ‘preferred candidates’ as not identified by that voter without reference to her concept of a most excellent candidate.

> 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:  MJ seems to me to be the method that is most likely to enable each voter to see that it is in her ‘strategic interest’ to give these ‘clear evaluations’.
> S:  Surely, to the extent that citizens might evaluate all the candidates honestly, this would also 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’ (rank) each in relation to one another.

S: In any case, whether a voter rationally or irrationally tries to manipulate their MJ ballot, B&L argue that MJ’s structure cuts the probabilities of being successful in this regard by almost ‘half’, i.e. it is still only ‘partially strategy-proof-in ranking’ while being entirely strategy-proof with regard to ‘grading’.  Again, have you found any flaws in B&L’s MAHEMATICL PROOF that MJ’s structure does ‘‘cut in almost ‘half’ the probability of such manipulation being successful’ ((Belinski & Laraki, Majority Judgment, pp.14, 15, 189-198, 212, 245, 282-292)?

> 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).

K: Is this quote the basis of the 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:  No, B&L includes all the ‘point-summing methods’ in their ‘comparisons’.

S: > 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: 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.

S:  I see B&L as accepting this but still arguing that this use of MJ ballot is still almost half as like to ‘run afoul of Arrow/IIA’.  Do you have a reason to disagree with this claim?

 > 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: 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

S:  Yes, it is ‘true’, MJ allows any voter to do this and I expect some will do this as was illustrated by B&L’s analysis of the Orsay experiment.

K: …. 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.

S: Yes, but only about almost half as likely to arise in practice in MJ.

> 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: 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.

S:  Yes, some ‘sincere-minded voters’.

> 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 likely 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.

K: 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’, [...]

S: Yes.

K: I don't believe this is true. I think the strategic voter can do better than that.

S:  If you mean only that any such voters are only half as likely to do better than that, we are not disagreeing.

K: I think I've probably done simulations on the exact question, I should probably check or make a new one...

S: Look forward to the results of your ‘new simulation’ which I assume will take account of B&L’s ‘half’ as likely claim.  Of course, you may also wish to consider Jameson Quin’s recent post which suggested that:  ‘… the chances of an arbitrary ballot being non-optimal [would be the] 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 [worst] 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".’

> S: > Currently, these features incline me to see MJ as the best method for electing a President.  [….]
> 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’,

K: [….] 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?

K: 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.

S:  So far, we seem to agree only that some voters could and would use their MJ ballots simply in an Approval or Range way.  At the same time, are you forgetting that these strategies are half as likely to be successful, presumably partly because other voters have used MJ fully as intended, and because MJ only ranks candidates according to their median grades?

S: > 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: 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.

S:  I have agreed that MJ can allow something like half as much of the manipulation that might be attempt to be successful as contrasted with other methods.  I do not yet see that you have made the case that it does not encourage or at least allow voters ideally (from their own point of view,  to attempt dishonestly) to vote strategically.  If you can, I would be very interested if you could counter B&L’s claim that MJ is structured in practice to lead most votes to adopt ‘honesty’ as their ‘dominant strategy’.

> 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’?

K:  Not really.

S: How do you then explain the actual behavior of voters in the Orsay and other experiments analyzed in B&L’s book?  These shows that many voters used many of the grades?

S: > 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: But I don't view it as a mistake.

S:  In this context, you may again wish to consider Jameson’s post.

S:  You seem to disagree with the belief that the primary aim of a democratic election of one winner should be to discover the candidate who is most fit for the office.  Does this mean you do not want a method to be used that would cut manipulations in the election by half?  Instead, you want methods to be used that will allow the most savvy voters to have the weightiest influence in determining which candidate will win?

> 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?

K: 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.

S: > 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.

K: I think the "opportunities" are not likely [to be] 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: Do you see these instructions as adequately answering your ‘curiosity’?

>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: Thank you for this summary.

S:  Does it not tell against your previous expectations?

> 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:  But it would only do that (i.e. "more precisely informing all citizens and candidates about the actual intensities.....") [only] 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.

S:  Please explain why not.

K: >>>> 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:

S: >   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.

K: 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.

S: By saying this, you seem to have not yet taken into account either of B&L’ analyses of their Orsay and other experiments in which most voters used many of the available grades, or Jameson’s recent EM post that argued that the chances of successfully manipulating MJ would be something like 2.5%.  If so, would not most people see that the best strategy is usually to simply grade the candidates honestly?

S:> At the same time, do you disagree with Belinski’s claims both
>     1. that MJ’s discovery of the winner only by his median grade makes it only half as likely 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: 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).

S:  In your usage, is it possible for a ‘voter to truncate’ his ballot even when every candidate not marked will by default be counted either as an equal bottom or as rejected?

By ‘manipulation’, B&L and I mean the gaining of an electoral advantage over other voters by a voter who ranks or grades at least one candidate ‘dishonestly’, i.e. a vote that is not a straight forward expression of that voter’s own degree of preference or evaluation for that candidate.  Do you agree that MJ offers less scope for manipulation than all ‘point-summing’ methods.

S: As yet, have you had the occasion to read B&L’s book, Majority Judgment?

> 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:  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.

S:  Please explain what ‘more mileage’ is given by MAM as compared to MJ.

K: 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.

S:  Please explain how MAM is more ‘expressive’ (or ‘discerning’) than MJ.  Also, it seems to me that almost any method could be impoverished by some voters so they would be are making only Approval votes, including MAM.  It seems to me that MJ is least likely to be impoverished in this way by many voters.

>> 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.  What do you think?
> 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 the 2 candidates to be equally qualified, the winner would be the one ‘preferred’ by the majority for whatever reason.

K: 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, I agree that in this extreme context, if he greatly fears any other candidate winning, rationally he should give his ‘favorite’ (whom he honestly rates only as acceptable) as excellent and reject the rest.

K: 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.

S:  Yes, but both B&L and Jameson explain that such extreme cases are likely to be very rare. MJ not only allows voters appropriately to vote strategically in special and possibly rare such special cases, it encourages all the other voters who honestly see some of the candidates respectively as EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, POOR, or to REJECT, to express these evaluations honestly as their equal contribution to the welfare decision for their society which aims to elect the most fit candidate for the office.  MJ’s design also makes it usually probable that such honest grading will be in the best interest of the voter.



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