It seems to me that the Smith set can be defined simply as the smallest group of candidates such that they have a beatpath to all other candidates, but no other candidates have a beatpath back to them? Why is the beat-or-tie path concept necessary? Edit: Figured it out, if A beats B beats C, with C tying A, then A has a beatpath to C, but C doesn't have a beatpath back, yet C is still in the Smith set. BetterVotingAdvocacy (talk) 05:57, 18 March 2020 (UTC)