[EM] Approval satisfies CC

Alex Small asmall at physics.ucsb.edu
Tue Jan 27 23:42:13 PST 2004

Adam Tarr said:
>> > Condorcet Criterion (CC)
>> > If all votes are sincere, the Ideal Democratic Winner should win if
>> one exists.
>>Under Approval, if one candidate is preferred / voted higher / approved
>> more than each of the other candidates, then that candidate will win.
> You're drawing a parallel between "preferred" and "voted higher" that
> was  never stated or implied, and that does not exist.

He may be thinking of a result proven by Brams and Fishburn:  If all
voters only have dichotomous preferences (i.e. each voter's SINCERE
preferences sort the candidates into two groups, and the voter is
indifferent among candidates in the same group) then there is always a
Condorcet Winner, and approval voting always picks that candidate if all
voters vote sincerely.

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