[Election-Methods] A "sincere" ballot is suboptimal in Range Voting.

[Abd ul-Rahman Lomax]

my post was garbled in a few places. Busy, too busy, I am.

I wrote:
>That is, suppose the voter could vote on the question, should this 
>election, we are going to have after this vote, be Range 2 (0,1,2) 
>or Approval (0,1), and the voter maximizes expected return by voting 
>for Range 2 and then voting either sincere or Approval strategy, as 
>appropriate -- it seems to depend on the utility pattern -- in the election.

I meant to say this:

If the voter could choose which method to use for an upcoming 
election, what method should the voter choose to maximize personal 
utility? Range 2 or Approval? The voter is free not to use the 
intermediate ratings in the ensuing election.

And I wrote:
>The election has three candidates, and our voter has utilities for 
>ABC of 210. We have no knowledge of how the other voters, and, with 
>many voters, and restricting our examination to situations where the 
>vote of the voter has no effect on the outcome, and excluding 
>certain situations where there is a three-way tie or near-tie before 
>our voter votes, there are 27 possible presenting votes.


Decoded by inversion:

The election has three candidates, our voter has utilities for them 
of 2, 1, 0. We have no knowledge of how the other voters will vote 
and, with many voters, we can restrict our examination to situations 
where the vote of the voter could possibly, if properly designed, 
affect the outcome, and excluding 'vanishingly rare situations], 
there are 27 possible presenting vote patterns.

And we determine the winner and utility for each of these presenting 
patterns and possible vote. I only looked at votes of 200, 210, and 
220, it being clear that the optimal vote (for maximizing personal 
utility) is one of these. Ties are resolved by lot, so if there is a 
tie, the expected utility is the average of the tied candidates' utilities.