[Election-Methods] [EM] Juho--Schudy's statement is correct.

[Steve Eppley]

I have time only for a few quick comments about Mr. Lomax' message (below).

First, he appears to have misunderstood what I meant about altruistic 
voters.  I asked what would happen if they voted sincerely (and selfish 
voters extremize).  Somehow he misinterpreted that as if I'd asked what 
would happen if they misrepresented their preferences.

Second, about optimal Range Voting strategy.   It looks to me from my 
own analysis and that of others that, from the individual voter's point 
of view, the vote most effective at maximizing that voter's expected 
utility is one that extremizes (except in some unimportant rare cases 
where another vote can be as good.)  I haven't had time to hunt for Mr. 
Lomax' definition of optimality to check whether he defines it from the 
perspective of the (social utilitarian) voting system designer, rather 
than from the perspective of the voter who seeks to maximize his/her own 
utility.

Are we all agreed that extremizing is the (game-theoretically) optimal 
Range Vote in the case where there are only two candidates? 

--Steve
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Abd ul-Rahman Lomax wrote:
> At 04:24 PM 7/22/2007, Steve Eppley wrote:
>> I think Warren Schudy could have written a stronger negative comment
>> about Range Voting.  Comparing it to Approval in his paper, he said it
>> offers "little or no gain" (see below).  That suggests outcomes with
>> Range Voting would tend to be at least as good as with Approval.
>> Outcomes with Range Voting could be much worse.
>
> Yes. But they can also be much better. Which effect prevails?
>
>>   What happens if many
>> altruistic voters tend to try to vote sincerely and selfish voters tend
>> to use the optimal strategy of extremizing to the limits of the 
>> range?  Ugh.
>
> But this *assumes* that optimal strategy is voting the extremes! 
> Further, most of us assume that the vast majority of voters will max 
> rate at least one candidate and min rate at least one. This is, 
> already, "extremizing to the limits of the range." Further, it is 
> clear that voting "altruistically" in Range, unless one really 
> understands the consequences, is feeding Range distorted information. 
> Voters should actually vote their own preferences, not what they think 
> are the preferences of others, unless they *know* these and prefer to 
> accept those.
>
> What we are discussing is intermediate ratings for others than the 
> favorite and least favorite. This is where the controversy is. Not 
> about the max and min candidates.
>
> The "selfish" thing is a red herring. If voters vote as sincerely as 
> possible, all of them, we actually do maximize overall utility. If 
> some don't, for some reason, there is loss of overall utility, but it 
> does not follow that the rational counterstrategy is to also vote in 
> that way.
>
> So far, the simulations are indicating that intermediate ratings 
> remain optimal even in the presence of a largest minority of voters 
> (less than half, but only 1 less) voting "Approval style."
>
> Unless we know what those votes are, in which case only one candidate, 
> typically, must be extreme rated in response, and the others are moot, 
> so might as well vote sincerely!
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