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

[Kevin Venzke]

Hi Steve, 

Let me be clear that if you are completely sold on MJ, I'm not interested in trying to change your mind. In 
particular I'm not going to refute Jameson posts solely because they are pro-MJ. That might make sense in a debate 
with fixed positions, but my assumption is that this isn't a debate, only a discussion. 

Major points in this exchange: 
1. You clarified the scope of the "half as manipulable" claim, and I can largely stop responding to those references. 
2. You seem to be backing away from IIA/Arrow-related claims, so I will drop that issue too. 
3. I clarify my points regarding the point of an election in general vs. from the perspective of a voter. 

>________________________________ 
>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 6 septembre 2016 21h31 
>Objet : Re: [EM] (4) MJ -- The easiest method to 'tolerate' 
> 
> 
>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.] 

I would answer close to "yes" but I probably would not word it exactly as page 209 does. You are missing most of the 
meaning in the quotes of mine that you included. The point of an election is not the same thing as what an individual 
voter is trying to do in that election. And when I say it's not "inherently valuable" etc. etc. I am just saying the 
same thing I have said 100 times, that it's not enough to permit it, you should give the voter a self-interested reason to 
do it. I certainly don't say it is NOT valuable to be able to clearly express evaluations. It could 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?], 

They COULD be more discerning, but whether they practically speaking ARE more discerning would depend on the incentives of 
the method. 

"More mileage" regarding MAM means if you try to reduce complexity of MAM you would also hurt its performance. Remember 
that I feel that MJ is too complicated for what it does. "More honest evaluation" for MAM could be true in that MAM counts 
relative rankings, which is a disincentive against trying to turn MAM into Approval. 

>    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?]. 

Quote #2 of mine is the one you should use to answer this question. It is also the answer to the question you ask in 
square brackets. The method should maximize the odds of finding the best winner by reducing the difference between a 
sincere and strategic vote. In principle I think we might actually agree on that. 

> 
>>> 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? 

It is. You said "depending on their own scale of values, I accept that some voter may validly choose" etc. etc. and I 
did not understand how that was a response to what I wrote, so I responded to point out that I'm not talking about a 
voter who has some kind of unusual 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. 

That's not the issue. Suppose that a voter votes for A and detests B and the winner of that election is B. Does the voter 
think "the wrong candidate won" or does he think "I was evidently mistaken to think A was best"? 

>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 voteror 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’. 

This is probably the single-most important point in this email. You said "no," but you are actually agreeing, because 
hardly any proposed methods are "point-summing methods." Range is the main one, just as I've been saying. 

So yes, that is a pretty major limitation of the proof. 

>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? 

Well, if neither you nor B&L are defending the idea that MJ dodges all Arrow issues, then that solves that topic entirely 
as far as I'm concerned. I am not going to quibble about what methods have "more" IIA issues. 

>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. 

All I intend to find is under what circumstances the strategic voter is better off exaggerating under MJ. I don't really 
care how small the advantage is, or even know how I would quantify that. Just whether there is an advantage. 

>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’. 

Simulations would have that goal I think. 

> 
>> 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? 

Whether some people use many of the grades isn't the question here, is it? The question is whether the strategic 
voter is wrong to think he should exaggerate his 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. 

I don't think Jameson even argued it would be a mistake. 

>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. 

No, I disagree that it's the individual voter's goal to do this. The individual voter thinks he has already discovered 
the answer, and his goal is to try to get that answer elected. 

>> 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’? 

Yes. 

>>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? 

Partly, but not regarding the stakes. 

>> 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. 

It should be clear. If MJ doesn't offer the right incentives to entice people to state actual intensities then (in the 
extreme case) it isn't actually better than Approval. In that case a complaint about Approval's expressiveness shouldn't 
lead you to MJ but to something else. 

> 
>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? 

The B&L argument that you shared, regarding LNHarm, had nothing to do with manipulability. It argued that voters won't 
care if they make a costly strategic mistake because what they really care about is that the best candidate wins (according 
to "a majority of all the voters," even if that majority does not include them). That is what I disagree with, to put it 
mildly. 

> 
>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? 

Yes, absolutely. I intended, without stating it, that truncation would imply the bottom rating. 

>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? 

No, you are doing a fine job, especially with the last two replies. 

>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. 

MAM has a disincentive against degrading into Approval because it counts relative preferences that the strategic-minded 
voter would want to use. 

Kevin