Forest Simmons said: > It seems to me that any neutral method that gives a three way tie to a > reverse order pair (like the following ballot pair) cannot satisfy both > Pareto and the strong FBC: > > 1 A>B>C > 1 C>B>A . > > Here's my reasoning. Suppose that there are only two voters and one has > already voted A>B>C. Suppose further that your utilities for candidates > A, B, and C are zero, 80, and 100, respectively. > > If you vote sincerely, then a tie results <snip> > How about just staying home from the polls or voting a spoiled ballot? > > The result will be a win by B with utility 80, which is greater than 60.
If somebody has already voted A>B>C, and I stay home, the outcome is A winning with utility zero. So not voting is a non-option (assuming that we count staying home as favorite betrayal). Why do you say B wins? If I betray C by voting B in first place then C cannot win according to Pareto, since everybody prefers B to C. It's an A-B tie with expected utility 40. And if I betray C by putting A in first place then A wins and my utility is zero. Now say I vote C>A>B. According to Pareto B canot win since everybody prefers A to B, so it's an A-C tie. The expected utility is 50. Seems like the best option is the 3-way tie with expected utility 60. Where did I go wrong? Alex ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
