But doesn't that wikipedia definition define the Smith set in terms of sincere preferences? The Smith set is defined in terms of actual pairwise-defeats based on votes. The _sincere_ Smith set is the one that is based on sincere preferences.
We discussed Smith set algorithms on EM some years ago. I don't remember them. But why not just use the BeatpathWinner algorithm to find the winner, which will always be a member of the Smith set? That meets not only the Smith Criterion, but a number of other criteria that are more important.
It seems to me that at least one Smith algorithm went something like this:
Find the candidate who has the fewest pairwise defeats. He must be in the Smith set.
Everyone who beats or ties him is in the Smith set.
Everyone who beats or ties anyone who is in the Smith set is in the Smith set.
So, for each Smith set member who has been found so far, find everyone who beats or ties him, and designate them Smith set members too.
[end of Smith set procedure outline]
I'd said, "It goes something like this:". Earl Scruggs introduced one of his songs with an explanation about it or its origin, and then said, "It goes something like this. In fact it goes exactly like this."
Mike Ossipoff
_________________________________________________________________
Express yourself instantly with MSN Messenger! Download today - it's FREE! http://messenger.msn.click-url.com/go/onm00200471ave/direct/01/
---- Election-methods mailing list - see http://electorama.com/em for list info
