[EM] Range Voting in presence of partial information of a certain character

[Jameson Quinn]

2010/5/20 <fsimmons at pcc.edu>

> Thanks for the comments Kevin and Lomax.
>
> Let me start over in the same vein:
>
> Suppose that candidate X was just announced as the winning candidate, and
> no
> indication was given of how the other candidates fared in the range style
> election.
>
> How would you wish that you had voted your range ballot?
>

I would say: I don't know who is coming in second. All that matters is
whether I like X better than the second-place candidate, and thus vote for
X, or less, and thus against.

If I were a frequentist, I'd say: I'd like to have voted them at the
fraction of other candidates they were better than, or at that value rounded
to top or bottom value, or anything in between.

If I'm a Bayesian, I'd say: I expect the median voter to be somewhere
slightly towards me from the winning candidate. Thus, I expect the
second-place candidate to be either one of the ones I like more than the
winning candidate, or one of the ones I like just a little less. I'll
basically discount the candidates who are too much worse than the winner as
no-hopes. But some fraction of my favorite candidates could be no-hopes too,
on the other side of me from the median. Without trying to figure out how
many dimensions of issue space I have in my prior and discount based on
exactly where the winning candidate is, I'd say my first approximation
strategy would be to want my vote at min(1,n)/sqrt(m), where n is the
candidates I like less than X and m is the number I like more than X. Again,
I also wouldn't regret a vote which rounded that value to the top or bottom,
or any other limited exaggeration of that value.

The Bayesian answer is probably more realistic, but the frequentist answer
gives more stable results.

Hope that helps,
JQ

ps. Condorcet is only range-DSV, as Juho claims, if there is not just a CW,
but a clear second-place CW. If there is a circular tie for second place,
the CW can get buried by the strategic effects of the tie.
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