# Talk:Uncovered set

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Does it make any difference if i pairwise beats j? I seem to be missing something... --James Green-Armytage 03:39, 25 Jun 2005 (PDT)

I removed the following: ", while the Banks set requires a beatpath of at most all candidates.[1] ", as that statement would imply that everybody in the Smith set (one-step beatpath) is in the Banks set (at most (c-1)-step beatpath).

The Banks set is instead more sophisticated. For X to win in a sequential elimination rule, there must exist at least one beatpath of some length originating in X that isn't the suffix of any longer beatpath starting in Y.

That the beatpath originates in X means that X can become champion in a sequential elimination rule. That this beatpath is not the suffix (the end) of some beatpath originating in Y means that Y can't take the win from X by rearranging the order of the remaining candidates, once X has become champion. Kristomun (talk) 22:42, 14 March 2020 (UTC)

Or differently put, X is in the Banks set if there's a beatpath originating in X with the additional requirement that every candidate in the beatpath beats every candidate after it (not just the candidate immediately after), and it's impossible to put some other candidate in front of the beatpath while keeping that invariant.[2] As far as I understand it, at least; I could, of course, be wrong. Kristomun (talk) 23:01, 14 March 2020 (UTC)
1. Nurmi, Hannu (1999). Voting Paradoxes and How to Deal with Them. Berlin, Heidelberg: Springer Berlin Heidelberg. p. 106. ISBN 3-662-03782-3. OCLC 851380375.
2. Miller, Nicholas (2001). Committees, agendas and voting. Abingdon, Oxon: Routledge. p. 68. ISBN 1-136-46060-8. OCLC 1082241178.