[EM] (5) MJ -- The easiest method to 'tolerate'
stepjak at yahoo.fr
Mon Sep 12 21:37:42 PDT 2016
>De : steve bosworth <stevebosworth at hotmail.com>
>À : "stepjak at yahoo.fr" <stepjak at yahoo.fr>; "election-methods at lists.electorama.com" <election-methods at lists.electorama.com>
>Envoyé le : Dimanche 11 septembre 2016 18h44
>Objet : Re: [EM] (5) MJ -- The easiest method to 'tolerate'
>K: 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.
>S: I’m not sure what your distinction is between a ‘debate’ and a ‘discussion’.
In a "debate" I would expect to have to respond to every pro-MJ citation you can come up with, and I would not expect you to have any real
curiosity about an alternate view. In a "discussion" I only expect to respond to arguments that you actually find persuasive and can actually
>In any case, I am genuinely searching for the best method for
>electing a president and in hoping to become better informed as a result of our discussions. Given certain clarifications and your arguments, I
>am open to the possibility of being shifted from seeing MJ as the best.
Ok, sounds good.
>K: 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.
>S: Does this mean that you accept B&L’s claim in this regard as valid?
In relation to point-summing methods only. (But you take this back below, so maybe I am being premature.)
>K: 2. You seem to be backing away from IIA/Arrow-related claims, so I will drop that issue too.
>S: In contrast to all the summing and averaging methods, I do accept that only about half of their IIA problems remain with MJ in the (possibly)
>rare cases when a voter dishonestly uses MJ’s ballot to rank rather than grade the candidates.
I probably agree with you here, regarding summing and averaging methods. Regarding other methods as well, this may even be right, but I don't think
the issue is important enough to argue about.
>K: 3. I clarify my points regarding the point of an election in general vs. from the perspective of a voter.
>S: Do you mean by this that while you have not said what the aim of an election should be, you believe that you have accurately described the
>attitude that most citizens have when using any of the available methods: they only wish to maximize the chances of their favorite candidate will
>> S: [….] 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
>> 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….(B&L, Majority Judgment, 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.]
>K: I would answer close to "yes" but I probably would not word it exactly as page 209 does.
>S: Please try to put it in your own words.
I think a utilitarian answer is OK (elect the candidate whose election maximizes some kind of "happiness" or "agreement" among the voters). But of
course it is tricky to measure methods by this standard. In simulations I prefer to seek methods that maximize the rate of electing sincere Condorcet
winners (i.e. given actual preferences, prior to casting any ballots) while reducing strategic incentives.
>K: You are missing most of the meaning in the quotes of mine that you included.
>S: Sorry, I quoted them because I was not sure of your meaning.
>K: The point of an election is not the same thing as what any individual voter [might be] trying to do in that election.
>S: I agree.
>K: 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.
>S: Should not a rational ‘self-interested’ citizen be sufficiently humble to accept that the majority might usually know better than any one voter
>deciding by himself? Is ‘self-interest’ for you always in conflict with altruism?
Well the issue is not necessarily that voters are "self-interested" as that they "confident" in their assessments. A strategic voter confident in
his judgment could still be "altruistic" by preferring candidates with some altruistic quality.
Humility exists at least in that, in the general case, most voters believe we must use majority rule. (Maybe some people would prefer to be
dictators.) But in a specific election where they are participating, they typically believe they know best ("confidence"), and might even deny that
they are "self-interested."
I do not think that casting ballots with subpar effect is a good way to pursue altruism. Suppose that you want to vote for the most altruistic
alternative but don't know what it is, due to not knowing what other voters want. If you have a guess, I think you should vote your guess, because
there's no telling whether the other voters are aiming for an altruistic outcome too. If you can't guess then you can abstain, but I'm not sure
that this counts as altruistic (unless the alternative is to vote in a self-interested way).
>K: I certainly don't say it is NOT valuable to be able to clearly express evaluations. It could be.
>S: Other things being equal, is it not always better? Under what conditions might you think it would not be valuable?
When it isn't strategically advisable to use them. Then it is clutter on the ballot at best, a source of unfairness at worst.
>S: > 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?],
>K: They COULD be more discerning, but whether they practically speaking ARE more discerning would depend on the incentives of the method.
>S: Do you agree that, other things being equal, grades are more ‘discerning’ (i.e. informative with regard to the voter’s values) than ranking?
If other things were equal then sure. Grades also imply rankings, so they could not be worse than rankings, in my view.
>Do you know of any method that would allow voters to evaluate candidates more completely and efficiently than does MJ?
There is that word "allow" again. Any ratings method "allows" this. But if you mean, after considering also the incentives of the method, I would
at least consider James Green-Armytage's Cardinal-Weighted Pairwise (CWP) which is a measure of defeat strength that uses ratings ballots and can
be applied in certain Condorcet methods like Schulze, MAM, and River. (Experimentally I found the approval version (AWP) to be better though.)
I don't have a stronger recommendation because I generally think with ratings/intensities it's difficult to avoid the two extremes: a) the rating
system invites exaggeration and b) the intensities aren't really making a difference to the outcome in comparison to the relative rankings.
>K: "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.
>S: I see that MAM has ‘more mileage’ than Approval (as you say), but in what way does it have more than MJ? For example, if an MAM voter ranks A>B>C,
>this does not allow her to express, e.g. whether this means A is Excellent, B is Very Good (or Good, or Acceptable, or Poor), and C is Good (or
>Acceptable, or Poor, or Rejected), or A is Acceptable, B is Poor, and C is Rejected, etc.
I believe the "more mileage" discussion was related to complexity, not expressiveness. Regarding expressiveness: The MAM voter with A>B>C is not
expressing absolute evaluations, but it's more likely it is strategically wise for him to vote that way. If he cares about that, then MAM is *in
effect* more expressive, if the alternative would be that he can evaluate independently but it is strategically unwise to use the full range.
>S: > 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?].
>K: 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.
>S: Yes we seem to agree on this but do you see any method that more efficiently finds ‘the best winner by reducing the difference between a sincere
>and strategic vote’ than does MJ? You seem to believe that MJ does not ‘making it in the voter's strategic interest to express … honest … opinions’.
>Please try to explain this again if you think you have already done so.
Yes I think MJ is rather poor at this! I will grant it is probably better than all other point-summing methods. But I mostly don't advocate those.
I'm not sure I have the energy to explain this from scratch, when bits and pieces are throughout each email? It all starts with the difficulty of
using middle grades as a strategic voter under MJ. I believe this uncertainty will push strategic voters to use mostly the extreme grades. I think
this is clearer when you expect that elections will continue to have frontrunners, and it will seem unsafe to assign them middle grades. I think
even voters who want to be sincere, and think of themselves as sincere, will have their strategic decisions influenced by the media and political
If I can't convince you of the likelihood of this phenomenon, that is fine. I am happy if you can at least understand the issue I'm talking
>>> 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’.
>This is partly because 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 may correctly 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. For example, in a French Presidential election where between 10 and 20 candidates may be running, many
>voters may see at least 2 to 6 candidates that would be at least acceptable and that their honest evaluations of these will help at least one of them
>to be elected rather than any of the other candidate they evaluate as Poor or to Reject. Such honest voting would 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.
It seems to me if there are candidates that only some voters know about, we probably will not be considering them for the win. I think we have
basically agreed that the goal was just to find the best winner.
I don't know what is the basis of your "many of them may correctly see..." sentence. Suppose that you think candidate A is poor and candidate B is
acceptable. If your ballot has any effect under MJ at all, it will most likely be that you have the opportunity to adjust the median rating of
a single candidate, up or down one grade. Let's say you have the ability to adjust the median rating of B. MJ doesn't care that you think B is better
than A. What if A's median rating is higher than acceptable and your B rating is pulling B down to make him lose? Certainly that could go either way,
and maybe you did actually make the strategically best vote possible, but this isn't obvious.
Suppose that you had reason to believe that A would end up with a median grade of "good;" surely you (as a strategic voter confident in your
assessments) would then want to rate B as better than "good," even though he's only acceptable?
>K: 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: Probably not but as a citizen believing in democracy, he might accept that the majority is more likely to be wise that any one citizen deciding
>on his own.
I think people accept that in general, but it falls apart when we know the specific options in a given election.
>> 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’ (Belinski & Laraki, Majority Judgment, pp.14, 15, 189-198,
>212, 245, 282-292)? [….]
>> K: Is this quote the basis of the claims that MJ reduces manipulability? Because most methods don't even have the mechanism discussed...
>S: Which ‘mechanism’ do you have in mind? Is MJ’s winner winning only by having the highest majority-grade?
Not specifically that I suppose, but just the general "structure" of accepting a bunch of grades from the voters and then evaluating each candidate,
using these grades, completely independently. To make a manipulability claim (as a mathematical proof) in comparison to all methods of this type, is
something I would find plausible.
>K: Like I've said, I understand this claim as a comparison to Range, but not much else.
>S: No, instead of ‘point-summing’ I should have said that B&L include all the ‘traditional methods’ in this ‘comparisons’ with MJ.
Ok, so the scope is still unclear.
>> 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: 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.
>S: If MJ is less vulnerable to IIA than all other methods, would not this make us prefer MJ to all the methods that are more vulnerable, i.e. other
>things being equal?
All things being equal, sure. My feeling is that people don't usually compare methods in terms of IIA except when people bring up how ratings methods
can dodge it on a technicality. It's kind of a given that IIA is a problem in voting systems. If people accept that there's no getting around IIA (at
least in practice) I don't feel a need to argue.
>In fact, as I understand it, B&L explains how MJ does at least pass a weaker IIA test, and this is also confirmed by Jameson in
>his 2 recent informative posts: 1): ‘there is the failure of the later-no-harm (LNH) criterion. But note: MJ actually does pass a weaker version of
>LNH: rating additional candidates at above bottom will not harm the winner as long as those candidates are ranked below the winning median. My claim
>is that over time, the winning median grade will mostly fall in a given band of grades; for instance, using letter grades, between B- and D+. In that
>case, making distinctions between A and B at the top or D and F at the bottom are strategically safe.’
But LNH isn't IIA and B&L's argument about LNH (that you shared) was nothing like this. This is why I don't feel you should ask me to respond to a
Jameson post when you haven't said why you thought his post was valid. It makes it seem like Jameson could have written absolutely anything and
you would use it as an MJ argument. As it happens I was very tempted to ask Jameson whether he thinks that weakened form of LNHarm is valuable, given
that a) he doesn't value LNHarm anyway and b) surely many methods that fail LNHarm can satisfy a weakened version of it. It seems to me you have
endorsed B&L's argument (via copying it for my benefit) that LNHarm doesn't even matter. In any case how does it advance any argument, that MJ
requires a criterion to be weakened, when there are other methods that don't require it to be weakened?
>2): ‘Note that this strategy will almost
>certainly not affect the medians, and thus will not change the winner. Though technically it breaks IIA, it only does so in bizarre cases where both
>voter and candidate distributions differ severely from historical norms.’
I would be interested if you can develop this point and arrive at a comparison to other methods. I don't think that was the original purpose of this
>K: 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: He is ‘wrong’ if and when by doing so he is not minimizing the chances that one of the candidates he honestly evaluates as Rejected will win.
>For example, he might do this by grading his 1st choice candidate as Excellent but also Rejects all the other candidates he honestly values as either
>Excellent, Very Good, Good, or Acceptable.
That situation is possible.
>>> 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: 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. …
>S: Correctly you say, ‘If’. Do you have any method in mind that offers any greater incentive for each voter to evaluate each candidate than that
>offered by MJ?
Actually I guess that many *rank* methods would do better at collecting intensities than MJ, purely by using a graded ballot, without even using the
grades in the calculation of the winner.
>S: B&L and I assume that, as believers in democracy, most voters want the winner to be the candidate most highly valued by a majority of all the
Ok. The issue comes into play when the method could elect A or could elect B, and the outcome is selected by using some ballots in a way that those
voters would not have wanted, making those voters wish they had voted slightly differently. I believe such voters will tend to feel cheated when
this happens: Their preferred candidate could have won, but lost due to their own ballots.
(This came up due to the discussion on Later-no-harm, in case you don't understand what issue I'm talking about.)
>> 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 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: MAM has a disincentive against degrading into Approval because it counts relative preferences that the strategic-minded voter would want to use.
>S: Yes, and why do you not see MJ as containing this same ‘disincentive against degrading into Approval’, and perhaps even to a greater degree?
I thought my answer to that question would be clear by including the term "relative preferences," which are not used by MJ. I think we have agreed
that both sincere and strategic MJ voters should be rating candidates independently, without concern for whether their ballot specifies relative
Why did you say "and perhaps even to a greater degree"? Do you have a specific doubt about MAM?
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