[EM] More 0-info pairwise strategy

[Blake Cretney]

Dear Markus,
> Dear Blake,
> 
> this is an example where it is advantageous to vote
> insincerely in a zero information situation:
> 
> Suppose that MinMax(margins) is used. Suppose that there
> are four candidates. Suppose that your sincere opinion
> is A > B > C > D.
> 
> Where is the problem? The problem is: It is possible that
> the worst defeat of candidate B is against candidate A
> and that the worst defeat of candidate C is against
> candidate D and that -by going to the polls and voting
> sincerely- you simultaneously increase the worst
> defeat of candidate B and decrease the worst defeat
> of candidate C and therefore change the winner from
> candidate B to candidate C.
> 
> Now suppose that you have zero information. One possible
> strategy is that you presume that the other voters vote
> randomly. Of course, this is certainly not the best
> strategy. But it is a plausible one.
> 
> The unique advantage of voting A > B > C > D sincerely
> instead of A = B > C > D insincerely is that you could
> change the winner from candidate B to candidate A. 

This is where I disagree.  It is also possible that you could change the 
winner from C to A.  For example, using my base rule for constructing examples:

B>A b+12 (this is a margin, of course)
C>B b+20
A>C b+11
A,B,C>D b+21
 
One vote of the form A>B>C>D will decrease A's largest victory, and 
cause A to win.  A=B>C>D only takes you half way there, and in this 
case causes a tie.

The important point, which distinguishes margins, is that a vote of A>B 
is just as likely to decrease the largest loss of A as it is to increase the 
largest loss of B, unless we know which is already winning.  
So, p(C,A)=p(B,C).

As a result, the change in expected utility by voting insincerely is negative,
independent of candidate utilities.

---
Blake Cretney