[EM] (2) MJ -- The easiest method to 'tolerate'

[Kevin Venzke]

Hi Steve, 

_______________________________ 
De : steve bosworth <stevebosworth at hotmail.com> 
À : "election-methods at lists.electorama.com" <election-methods at lists.electorama.com>; "stepjak at yahoo.fr" <stepjak at yahoo.fr> 
Envoyé le : Mardi 2 août 2016 21h12 
Objet : Re: [EM] (2) MJ -- The easiest method to 'tolerate' 
>> 
>>My main distaste for median rating comes from my feeling that in most scenarios (i.e. availability of information on 
>>others' rating intentions) strategic-minded voters would only use the top and bottom ratings. This is because (as we 
>>see from the Later-no-harm example) median rating doesn't really offer guarantees about how your ratings will be used 
>>in relation to each other. 
>> 
>S:  As I understand it, MJ does guarantee exactly how all the gradings will be counted but not how every voter will 
>use them. 

Yes but I'm talking about the sort of feature as in IRV where one is guaranteed that if one's favorite candidate A is 
the winner, you (or a group of voters like you) will not accidentally make A lose by adding a new lower preference B. 

>   Belinski claims that MJ has the advantage of allowing each voter clearly to express his or her evaluation 
>of each candidate.  MJ invites each voter to ‘grade’ each candidate as being either EXCELLENT, VERY GOOD, GOOD, 
>ACCEPTABLE, POOR, or REJECTED -- each candidate being graded according to each voter’s concept of an EXCELLENT 
>candidate.  Thus each candidate would receive the same grade, independently of which other candidates are available, 
> i.e. each grade (‘rating’) can be given not ‘in relation to’ the other candidates. 

The notion that the voter should rate 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. 

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. 

> He says that this also allows 
> MJ’s not to violate either the Arrow or Condorcet paradoxes.  Do you disagree? 

It doesn't "violate Arrow," in that Arrow doesn't apply to rated methods. 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. The alternative is that many voters will choose not to rate *any* candidate 
"excellent" or "rejected." But I think even sincere-minded voters will be inclined to make sure somebody is getting 
those ratings. 

"Condorcet paradox" is not really something you can violate. If you don't elect Condorcet winners in the first place, it 
is true that you don't have to consider what happens when there is no Condorcet winner. That might be a marketability advantage. 

> 
>At the same time, in contrast to the use of any of the ‘traditional methods’ which still must violate these paradoxes, 
>Belinski argues that a MJ voter can only be up to half as successful strategically if she focusses instead on voting 
> to maximize the chance that her favorite candidate will win. 
> 

That claim makes some sense to me in comparison to Range (not sure what the actual comparison is), although Range 
does not "violate Arrow" or consider Condorcet cycles either. 

I don't think it's easy to compare MJ to other methods here. Under MAM if I vote A>B>C it is clear that there are 
several effects that might arise from that vote. I may have a strategy that involves voting in some different way, but as 
long as I actually have the preferences A>B>C, there is a plausible motivation for me to vote that way. But under MJ all 
the ratings 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. 


>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: 
> 

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. That transforms the method into Approval. You are right, that I not certain that 
Approval (be it actual Approval or MJ that turned into Approval) is the best method for electing a president. 

>>K:  The rating/grade values have no independent, practical meaning. If [MJ] voters have this perception and respond 
>>with this behavior, then the method is just an overly complicated form of approval voting. In that case I'd rather 
>>just use approval, because it's clearer what's going on. (There are arguments about whether median rating voters 
>>would actually try to be so strategic, and about whether it would be bad if they did, but I will skip over that.) 
> 
>S: Given the above, it seems that MJ voters would be much less likely to ‘actually try to be so strategic’ and this 
>conclusion seems to be supported by the ‘Orsay experiment’. 

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. 

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 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. 

> 
>>[….] 
> 
>>K:  I find a lot of methods tolerable, and I've designed a lot of methods too (most of them tolerable). I care about 
>>certain properties more than others, but the ones I like aren't even all compatible with each other. 
> 
>>S:  Which ‘properties’ do you most care about?  How are they ‘incompatible’ with each other?  Still, which method do 
>>you see as superior to MJ, all things considered? 

Some properties I like are: 
Favorite betrayal (MJ satisfies, IRV doesn't, MAM doesn't but is probably pretty good). This criterion is about 
being able to safely rank/rate your favorite candidate at least equal-top with a compromise choice. 

Minimal defense (MJ and MAM satisfy, IRV doesn't). This is about the ability of a full majority of voters who prefer 
candidate A to candidate B, to ensure that B loses, without any of them having to vote that A is their favorite. 
(Normally they will do this by ranking A sincerely, and not ranking B over anybody.) 

Later-no-harm (IRV satisfies, MJ and MAM don't). 
Later-no-help or "burial resistance" (IRV and MJ satisfy, MAM doesn't). 
Condorcet (MAM satisfies). I guess you know about these last three. 

Plurality (all of IRV, MAM, and MJ satisfy). This is a fairly easy criterion that says we can't elect a candidate 
who has fewer "votes in total" than some other candidate already has in first place votes. 

The (seeming) incompatibility that frustrates me the most is that between minimal defense and LNHarm. 

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. If voters will have good information and use good strategy, I would 
definitely pick Approval over IRV. Maybe over MAM too. 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. 
> 
>>S:  Why would you not see MJ as ‘plausible’ in this sense? 

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. 

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. 

(I'm not assuming the MJ voters have an incentive or ability to use strategy, in this analysis. I want to assume 
that the voters are sincere, and that the method itself will handle the translation of the sincere preferences into 
the strategic, informed behavior you would expect of a legislator.) 

Kevin