[EM] The Smith set

[MIKE OSSIPOFF]

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

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