[EM] Symmetry and Condorcet--Correction
asmall at physics.ucsb.edu
Thu Jan 16 15:51:36 PST 2003
Rob LeGrand said:
>> If we do the cancellations we get
>> n1 A>B>C
>> n2 B>C>A
>> n3 C>A>B
>> and without loss of generality we can assume n1>n2>n3, eliminate C,
>> and A wins.
> Please forgive me if I've missed something obvious, but isn't n1>n3>n2 a
> fundamentally different case? There's no way to rename candidates to
> equate the two cases that I can see.
Well, without loss of generality we can assume that (barring the case of
ties) one of the numbers will be larger than the others and one will be
smaller than the others. We "cancel out" the smallest faction, the
largest faction from before is still the largest faction, and we're left
with the conclusion that the largest single faction picks the winner
("tyranny of the not-necessarily-even-a-plurality"). We lose nothing by
assuming that A>B>C happens to be the largest faction.
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