On 09/30/2012 08:16 AM, robert bristow-johnson wrote:
i dunno exactly how they do their ordering at Wikipedia (to get 2nd, 3rd
place winners using Schulze), but would you say if the Condorcet
criterion was met for each subset, would it be unfair to just identify
the top CW, then kick him/her out of the set of candidates and do it
again to identify the CW in the remaining set? it seems logical to me to
say that after the top CW is removed from the candidate set, that if a
CW exists in the remaining set, wouldn't that be fair to call the
"2nd-most popular" candidate?
The problem with this is that it amplifies a (bare) majority into
unanimity. Say you have an election like:
51: R1 > R2 > R3 > D1 > D2 > D3
49: D1 > D2 > D3 > R1 > R2 > R3
then R1 is the Condorcet winner. Remove R1, and R2 is the Condorcet
winner. Remove both R1 and R2, and R3 is the CW. So if you pick three
winners, the bare majority's R-preference gets amplified into an
unanimity of every choice elected.
For a similar reason, a runoff between the first two candidates in a
Condorcet social ordering could easily be uninteresting. However, at
least in the situation above, the social ordering would make a good line
of succession order; it could also be used for picking president and
vice president.
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