# Talk:Uncovered set

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)

- 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),

- ↑ 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. - ↑ Miller, Nicholas (2001).
*Committees, agendas and voting*. Abingdon, Oxon: Routledge. p. 68. ISBN 1-136-46060-8. OCLC 1082241178.