Talk:Uncovered set: Difference between revisions
imported>James Green-Armytage No edit summary |
(Banks set) |
||
| Line 1: | Line 1: | ||
Does it make any difference if i pairwise beats j? I seem to be missing something... --[[User:James Green-Armytage|James Green-Armytage]] 03:39, 25 Jun 2005 (PDT) |
Does it make any difference if i pairwise beats j? I seem to be missing something... --[[User:James Green-Armytage|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.<ref name="Nurmi 1999 p. ">{{cite book | last=Nurmi | first=Hannu | title=Voting Paradoxes and How to Deal with Them | publisher=Springer Berlin Heidelberg | publication-place=Berlin, Heidelberg | year=1999 | isbn=3-662-03782-3 | oclc=851380375 | page=106}}</ref> ", 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. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 22:42, 14 March 2020 (UTC) |
|||
Revision as of 22:43, 14 March 2020
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)
- ↑ 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.