[Election-Methods] [EM] Is "sincere" voting in Range suboptimal?

[Abd ul-Rahman Lomax]

At 01:38 AM 7/25/2007, Chris Benham wrote:
Here is my analysis again of  Abd's suggested 0-info 2-voter 
3-candidate election, where our voter's sincere ratings ("utilities") 
are A2, B1, CO :

Benham sent an image referenced to some site.... Yes, I could read 
it, but... I can't take it apart to analyze it.

Below are the votes he presents; he starts by explaining:

>Only considering votes that  both max-rate at least one and min-rate 
>at least one, there are only 12 possible opposition ballots
>(3 that max-rate 2, 3 that min-rate 2, 6 that mid-rate 1).

He has eliminated the non-normalized style ballots. Given that we are 
testing optimum strategy, and know nothing about the strategy of the 
other voter, this is why he comes up with a different result than I. 
I considered all opposing ballots to be equally likely.

Apparently, Benham believes that such votes would be rare. He may be 
right. But this is not zero-knowledge, in fact, it is making 
assumptions about voter behavior that actually does not match reality 
*in some elections.* Further, we are *really* interested in the 
many-voter case, which we can reduce to, effectively, a two-voter 
case if our voter is coordinating and voting identically to exactly 
half of the other voters. In this case, the opposing voters are 
voting, effectively, with very high resolution Range, with our voter 
block having only three choices: 0, 1, 2. (But multiplied so that the 
voting power of the two groups is equal.)

In the many-voter case, any vote combination, among the votes which 
can affect the result, is possible. And, in particular, they are 
equally possible, if we take care to include every case evenly (which 
is why 000 and 222 are both listed, though they have the same effect) 
whereas Benham can argue in the two-voter case that 000 and 222 are 
unlikely. That's debatable. What if the other voter is interested in 
overall social utility and thus votes sincerely, without 
normalization, which is known to maxmize utility better than 
normalization? (Though, in this case, we really would want higher 
resolution Range.)

The other voter may think, all these candidates are really middling, 
so I'll vote 1, 1, 1. Yes, I'm abstaining from the result, but in a 
more informative way than by not voting. We should also remember that 
votes are usually taken in more than one election at a time, and 
blank votes are *common* here, and there is some incidence of 
overvotes where all candidates are marked. These are real 
possibilities, and in some elections, might be equally common. (A 
voter votes 000, it means, "I like none of these enough to vote 
anything for them." Where such a vote is not moot, where, for 
example, some further process would occur, this would be a not 
uncommon result when there are only three candidates.

All this is really about the simple two-voter case; but those votes 
that Benham does not consider here become very important in the 
many-voter case, and they are, clearly, equally as likely, there, as 
the other vote patterns.


>>There are, in the two-voter case, 27 possible ballots, being all 
>>the base-3 numbers from 000 to 222. All are considered equally 
>>likely, which simplifies the calculations by assigning the same 
>>probability to each. In the many-voter, ballot-could-shift-result 
>>election,  the virtual ballots of 000 and 222 are, in fact and in 
>>real elections equally probable with the others.
>
>I find that statement ridiculous, but of course including such 
>essentially blank ballots can't change the ranking of  the our three 
>considered votes

I said "many-voter," i.e., there are 27 possible vote combinations, 
also, with many voters, but they are presented a little differently, 
and *very rare* other combinations are excluded. That is, for 
example, the combination 000 is excluded because it's an exact 
three-way tie with many voters, we might as well consider zero 
probability for that. All of the vote combinations where there are 
three candidates whose election the voter might effect with some vote 
and some luck can be excluded, leaving us only with 3 pairwise sets 
of 9 combinations each. And these are equally likely.

I'd suggest Benham look at this.