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

[Kevin Venzke]

Hi Steve, 

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

Steve wrote: 
>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). 

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. 

>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, 
>... 

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

>>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. 

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. 

>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 [...] 

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

> and thus also to choose not to contribute honestly to the discovery of the socially most valued winner? 

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. 

>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. 

"Should" in what sense? If voters don't want the method to violate Arrow/IIA then they "should" decline to rate anybody 
EXCELLENT if there is no EXCELLENT candidate. But the strategic voter "should" not refrain from this, if his concern is to 
get the best outcome for himself. 

>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. 

Is this quote the basis of claims that MJ reduces manipulability? Because most methods don't even have the mechanism 
discussed... Like I've said, I understand this claim as a comparison to Range, but not much else. 

> 
>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’. 

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

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. 

>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. 

I am speaking of something that is either true or false: 

True means: Some voters use the top and bottom grades even if the best/worst candidates do not deserve them 
False means: No voters ever assign grades outside the range that the actual candidates actually merit 

If the case is "True" then the method isn't avoiding Arrow in a practical sense. It will have the same issues with 
irrelevant alternatives that rank methods do. 

>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. 

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. 

>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. 

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’, [...] 

I don't believe this is true. I think the strategic voter can do better than that. I think I've probably done simulations 
on the exact question, I should probably check or make a new one... 

> 
>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’, 

By "know what they are doing" I'm talking about understanding the strategy of a method. 

Regarding "half the scope for manipulation" I would need to understand what that is referring to, if it's the thing quoted 
above, or something else. As someone who has created simulations to measure strategic incentive, I don't feel like much 
can be summarized with that kind of language. The claim could well be true in proper context; for example as I was saying 
above, I see that a strategic voter will have a very hard time making intelligent use of intermediate grades, and by that I 
certainly mean to include the idea of manipulating the outcome with them. On the other hand if "manipulation" includes such 
simple strategies as using only the extreme grades, then I don't think MJ compares that well. 

>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? 

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. 

>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’. 

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. 

>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’? 

Not really. 

>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. 

But I don't view it as a mistake. 

>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? 

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. 

>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. 

I think the "opportunities" are not likely 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:  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. 

Thank you for this summary. 

> 
>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? 

But it would only do that (i.e. "more precisely informing all citizens and candidates about the actual intensities.....") 
if voters use it as intended. I don't think they would. If you want to say that Approval isn't going to produce a lot of 
information on the preferences, I will totally agree, and agree that it's not ideal, but I don't think the conclusion to draw 
is that MJ is better than Approval. 

>>>>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: 

>  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. 

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. 

>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? 

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). 

>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. 

Were those questions related to LNHarm? Are you perhaps implying that if a voter truncates due a LNHarm concern that 
this counts as "manipulation," and would not likely be "successful"? If so, I don't agree with that at all; truncation 
under MJ will have a similar effect as under many other methods. 

>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. 

I grant that MAM is harder to understand, but I think it gets more mileage out of its complexity than MJ gets out of its. 

When it comes to expressiveness, I think that practically speaking MAM is actually better than MJ, due to the scenario that 
MJ turns into Approval and consequently expresses very little. 

>>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. 

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, in this context, if he greatly fears any other candidate winning, rationally he should give his ‘favorite’ an 
>excellent and reject the rest. 

Glad we agree. Note that it is this behavior (rating a sub-par candidate differently based on whether there are any 
better candidates in the race) that raises issues with Arrow. 

Kevin