[EM] Logic/Jargon question

[Kevin Venzke]

Paul,

 --- Paul Kislanko <kislanko at airmail.net> a écrit : 
> >From Wikipedia:
> 
> In  <http://en.wikipedia.org/wiki/Voting_system> voting systems, the Smith
> set is the smallest set of candidates in a particular election who, when
> paired off in pairwise elections, can beat all other candidates outside the
> set. Ideally, this set consists of only one candidate, the
> <http://en.wikipedia.org/wiki/Condorcet_winner> Condorcet winner. However,
> when the electorate is conflicted (as in
> <http://en.wikipedia.org/wiki/Voting_paradox> Condorcet's paradox), the set
> has at least one cycle of candidates for whom A beats B, B beats C, and C
> beats A. See also  <http://en.wikipedia.org/wiki/Schwartz_set> Schwartz set.

> If there are N candidates, how can the size of the Smith set be smaller than
> N-1 if it is not exactly 1 (i.e. there is a Condorcet winner)?
>  
> If there's no CW, then disregarding ties there can be only one candidate who
> pairwise-loses to all of the others, so candidates for the Smith set are all
> who pairwise defeat that one. 

Yes, so the definition calls for the "smallest" such set. You shed
candidates (or sets of candidates) who are beaten by all of the other
not-shed candidates, until you can't shed anyone else. Ideally this
leaves you with the Condorcet winner.

Kevin Venzke



	

	
		
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