# [EM] Strong FBC

Alex Small asmall at physics.ucsb.edu
Tue Feb 18 17:05:28 PST 2003

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
> 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

----