[EM] (6) MJ -- The easiest method to 'tolerate'

[Kevin Venzke]

Hi Steve,

Due to your requests I have decided to write out a complete argument that I can refer to. I will 
write some other responses below.

1. Under MJ or other median rating methods, there should still be frontrunners. Frequently two, 
and they will still tend to be known by the voters in advance.
2. The only useful strategy in this setting is to rate the better frontrunner such that his median
score may be increased, and to rate the worse frontrunner such that his median score may be
decreased. (It usually doesn't matter how you rate anybody else.)
3. In order to do this, you have to estimate the range of scores that those candidates might
end up with, and vote (at least) just outside that range. For example, if you estimate that the
winner will get a median rating in the 5-7 range (out of 10), then you should rate the better
candidate at least an 8 and the worse one at most a 4.
4. I claim that voters won't even be able to estimate the range of the winner's score, because
the individual grades don't have any particular meaning outside the whims of the electorate.
(For example, if a pollster asks a strategic MJ voter what ratings he's going to give, the answer
will depend totally on what other voters are saying.) If that's the case, that you cannot guess
the range, then the only safe way to vote is to use the 10 and 1 ratings for the frontrunners.
5. Suppose I am wrong about #4 and the range of scores of the winner can be estimated. Should we
not expect a vicious circle that makes the range less and less clear, anyway? I just suggested
that if the estimated range is 5-7, then you should *not* use this range, and vote outside of it.
If everyone has the same estimate and the same concern about strategy, the result would be that
neither candidate would receive *any* 5s, 6s, or 7s. Ironically it would prove, in retrospect, that
the size of the estimated range should have been *greater* than 5-7, and so it was not actually so
safe to give 8 and 4 ratings. The further you stay away from the estimated range, the safer you 
are.

My conclusions.
6. If the electorate so much as knows who the frontrunners of the election are, the resulting
strategies should be expected to thoroughly corrupt the absolute preference/intensity information
being collected by MJ's ratings ballot. Moving frontrunners around on the ballot for strategic
reasons would likely mean you're moving around all the other candidates too.
7. The MJ voter requires information and strategy simply to ensure that his ballot will contribute
(in a desirable way) to the primary (or only) real decision of importance in the race. This seems
unfair to uninformed or non-strategic voters.
8. Consequently any method that simply counted *relative* preferences between two frontrunners,
without intensities, would be more fair, and also would not necessarily be collecting any less 
information than MJ (due to #6).

Other.
9. Separately we have discussed whether voters actually are inclined to be strategic, or if they
are happy to simply be contributing to a group-determined outcome. I claim that the former is the
case, especially when it is clear which candidates may win, and which ways of voting can increase
one's influence on the outcome.
10. Whether or not I am wrong about #9, I do not think we should advocate methods that will only
work properly under an optimistic scenario. We should assume the worst of the voters. (This means,
it should be said, both the willingness of some to use strategy, as well as others' total 
ignorance of it.) The ideal situation is that a sincere vote would not be different from any
strategic variation of it.


>________________________________
>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 : Jeudi 22 septembre 2016 0h47
>Objet : Re: [EM] (6) MJ -- The easiest method to 'tolerate'
> 
>Hi Kevin and everyone, 
>S: It now seems that the main question between us is whether MJ is, or is not, better than your 
>preferred method at providing each citizen with the two voting incentives we both seem to desire: 
> 1) to express their evaluations of all the candidates honestly (sincerely) on the ballot, and 2) 
>to vote in a way that maximize the chances of their preferred candidate winning? 

Yes, that seems right.

>Again, I see MJ as maximally encouraging each voter to evaluate (‘grade’) all the candidates 
>sincerely while, at the same, allowing each citizen to vote strategically (manipulatively) when 
>they see this as the most likely way to assist their most preferred candidate to win or their most 
>opposed candidate to lose. 
>You seem to see MJ as more likely than the method you prefer to lead less savvy voters effectively 
>to support candidates they would not like if they knew more about how to vote strategically. If 
>this is so, please explain your reasons.

I hope you will find the answer above.

> To explain this, perhaps it would be most helpful to me 
>if you would compare the different strategies you would adopt when using both an MJ ballot and the 
>ballot of the method you most prefer with regard to the following presidential election: 15 
>candidates, 5 of whom you would honestly value above Poor (e.g. 1 Excellent, 2 Very Good, 1 Good, 
>and 1 Acceptable. Perhaps your strategies would change depending on the different degrees of 
>knowledge you might have about how all the other citizens are likely to vote. When using MJ, would 
>your strategy be other than simply to grade each candidate honestly? If not, what would it be and 
>why? In the same conditions, what would your strategies be while using your preferred method 
>instead? What extra ‘mileage’ do see your method providing? Which method is more ‘discerning’ 
>with regard to the values held both by voters and candidates? Which method is more likely to elect 
>the candidate who is most fit for the office? What are the different ‘incentives’ offered by the 
>2 methods? 
>If you would do this, it would help me be clearer about the reasoning behind your position. 

Here too I hope you will find the answer above. You are correct that I would want to use any
available information about the sentiments of other voters. (If no information is available, then
I don't think the scenario is realistic enough to worry about.)

> 
>As you explained in your last post, perhaps your preferred method is MAM, as enhanced by the 
>addition of Cardinal-Weighted-Pairweis (CWP, as proposed by James Armytage-Green in 2004). I can 
>see that CWP could help make the counting of the different intensities of preferences by MAM more 
>exact. Unfortunately, the addition of CWP might make MAM even more complicated for most voters to 
>understand. 
>[….] 

Yes, that's true. But I won't support a ratings method unless I feel that the method makes good use
of its ratings.

Incidentally I think it makes more sense to advocate Schulze than MAM, since Schulze has seen more
use. I also like River better than MAM, since in River you only need to lock (up to) one defeat
per candidate, so it's easier to solve by hand.

>>> S: [….] 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)? [….] 
> 
>> 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. 
>[….] 
>> 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? 
>
>K: If other things were equal then sure. Grades also imply rankings, so they could not be worse 
>than rankings, in my view. 
>[….] 
>> 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. 
>
>K: […] 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: Please explain exactly why you think that ‘MAM is *in effect* more expressive’. 

This too is answered above (#6 and #8).

>Also, how does MAM allow a savvy voter to be ‘more strategically wise’? 

Not savvy but *non*-savvy. MAM allows the non-savvy voter to simply indicate a relative preference
between two candidates, and it will be counted. The MJ voter doing the same thing is not necessarily
voting wisely: He may need to use specific grades to get the same outcome.

>> K: [….]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 a strategic vote’ than does MJ? You seem to
>believe that MJ does not ‘make it in the voter's strategic
>interest to express … honest … opinions’. Please exaplain. 
>[….]
>K: [….] 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. [….] 
>S: Again, your reasoning behind this key claim is one of the elements I hope to understand as a
>result of your next post. 

Ok, hopefully my current effort will help you. I explained the elements of this "uncertainty" more
completely than before.

>[...] 
>> 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. 
>
>K: That situation is possible. 
>
>S: Are you accepting that this strategy would not minimize the chances that his most Rejected
>candidate will win?
>> [….] 

It mostly depends on who the frontrunners are. If the strategic voter rates both of two frontrunners
"Rejected" (or both "Excellent") then he was (almost surely) wrong.

Kevin
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