[EM] More 0-info pairwise strategy

[Markus Schulze]

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. The
unique disadvantage 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 C.

Suppose that p(B,A) is the calculated probability that
you change the winner from candidate B to candidate A
when you vote A > B > C > D sincerely. Suppose that
p(B,C) is the calculated probability that you change
the winner from candidate B to candidate C when you
vote A > B > C > D sincerely. Suppose that u(X) is your
von Neumann-Morgenstern utility of candidate X. Then:
If p(B,A)*(u(A)-u(B)) < p(B,C)*(u(B)-u(C)), it is
advantageous for you to vote A = B > C > D insincerely
instead of A > B > C > D sincerely.

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de