# [EM] Truncation and Strong FBC

Alex Small asmall at physics.ucsb.edu
Mon Oct 7 15:50:17 PDT 2002

> I don't see how this follows.  Say the three types of ballots in a
> given election are A>B>C, B>A>C and C>A>B.  The corresponding triangle
> would look different depending on the method used; in particular,
> plurality would look different from Condorcet.  But Condorcet doesn't
> violate symmetry.  Am I missing something?

Good point.  I was wrong.  Below I'll show a counter-example to my
original assertion.  However, I also need to restate my conditions,
because your example violates my (very poorly worded) conditions.

The symmetry condition is that if candidate A wins, and all voters reverse
their rankings of A and B, then B is the new winner.  The requirement of
three ballot types is that all possible ranked ballots can be placed into
one of three exhaustive and non-overlapping categories.  If all voters
reverse their reverse their rankings of two candidates it should be
possible to still sort the ballots into the same 3 categories.

Your limitation that all ballots have one of 3 particular preference
orders doesn't permit voters to swap candidates A and B because there is
no category for ballots marked C>B>A.

A good counter-example to my assertion that we can derive plurality voting
is negative voting:  Instead of the ballots types {A in first place, B in
first place, C in first place} we could have the exhaustive and
non-overlapping categories {A in last place, B in last place, C in last
place}.

Alex

P.S.  This is off-topic, but if you're getting married in the Catholic
Church, and the archdiocese requires you to attend a church-sanctioned
marriage class, pick a class other than Catholic Engaged Encounter!  Can
you guess where I spent the weekend?

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