I wrote:
>B is the SU winner over A by 275 (av. 69) to 217 (av. 54). 90% of voters
prefer B to A.
Correction. A = 5680 (av. 57) B = 8600 (av. 86), so the utility margin is
v. significant.
>"Reasonable strategy" is a fairly loose term. In an electorate with very
innacurate polling >information, reasonable strategy could result in a
pretty bad outcome. I can give you an >example with zero info strategy;
>
>10 A>B>C>D : 100>30>1>0 Approval vote A
>40 B>D>A>C : 100>52>51>0 Approval vote BDA
>40 C>B>A>D : 100>95>66>0 Approval vote CBA
>10 D>C>B>A : 100>60>50>0 Approval vote DC
In this scenario, given accurate polling information, a basic reasonable
strategy for each group would probably be;
10 A
40 B
40 CB
10 DC
And the rightful king would inherit the throne (candidate B would win).
Although, with a simple change in the sincere utility value for candidate B
in the C faction from 95 to 70, it would be reasonable for the C faction to
approve only C, and C would win the election. The SU scores for the
candidates are: C 4610 (av. 46); A 5680 (av. 57); B 7600 (av. 76). This is
an even worse result than for zero info.
I think this example represents "reasonable strategy". Arguably, the A
faction should for B as well, but even this would only result in a tie
between B and C (of course, I can just tranfer 1 voter from the A faction to
the C faction and C will definately win, even with the A voters approving
B).
Sorry if that was all a bit muddled. The moral of the story is, Approval
can skip the Condorcet winner to find lower utility alternatives, with good
strategy, and with or without accurate polling information.
