At 09:48 AM 7/23/2007, Kevin Venzke wrote:
>Are you going to argue that it should make no difference to the voter
>how likely it is that he will be able to change the outcome given some
>way of voting?
No, for if it is so unlikely as to be impossible, rational voting
strategy is to not bother to vote.
Further, the likelihood of changing the outcome may differ with
respect to the various pairwise elections involved.
What I am arguing is that a voter should properly assume that many
other people will vote as he votes. If the voter knows that
assumption is true, then there is always a reasonable chance that the
voter's vote will shift the outcome, to the point where, if the voter
and those like him are in the majority, the voter's vote, depending
on the method, may be *certain* to affect the outcome.
The case I'm studying is zero-knowledge, Range 2, i.e., CR3. Three
candidates, voter's preference is A>B>C, with midrange sincere rating for B.
We now know that in the two-voter case, the optimal vote is sincere.
This alone would be sufficient to refute the insufficiently qualified
claims made that started this discussion. However, on the face of it,
it is possible that in the large-election case, the advantage of
voting sincerely vanishes. I am in process of examining that possibility.
However, I note that the voter may behave as if a member of a class
of voters with similar preferences, who are distinct from a class of
other voters with unknown preferences, and the two classes are equal
in size. This reduces the situation to a two-voter problem! But
instead, of course, of being Range 2, it is Range V+1, with V being
the number of voters. However, the strategy should be the same with
higher resolution Range.