Talk:Independence of Worst Alternatives
This seems related to:
Local independence A criterion weaker than IIA proposed by H. Peyton Young and A. Levenglick is called local independence from irrelevant alternatives (LIIA). LIIA requires that both of the following conditions always hold:
If the option that finished in last place is deleted from all the votes, then the order of finish of the remaining options must not change. (The winner must not change.) If the winning option is deleted from all the votes, the order of finish of the remaining options must not change. (The option that finished in second place must become the winner.) An equivalent way to express LIIA is that if a subset of the options are in consecutive positions in the order of finish, then their relative order of finish must not change if all other options are deleted from the votes. For example, if all options except those in 3rd, 4th and 5th place are deleted, the option that finished 3rd must win, the 4th must finish second, and 5th must finish 3rd.
Another equivalent way to express LIIA is that if two options are consecutive in the order of finish, the one that finished higher must win if all options except those two are deleted from the votes.
LIIA is weaker than IIA because satisfaction of IIA implies satisfaction of LIIA, but not vice versa.
Despite being a weaker criterion (i.e. easier to satisfy) than IIA, LIIA is satisfied by very few voting methods. These include Kemeny-Young and ranked pairs, but not Schulze.
- In my opinion, this criterion is problematic because, even though most single-winner election methods can be generalized in a natural manner to a method to calculate a collective ranking, people who propose a new single-winner election method usually don't claim that the resulting collective ranking has some meaning whatsoever. When someone proposes a new single-winner election method, you would have to put into his mouth this claim (that this single-winner election method should be generalized in a certain manner to calculate a collective ranking) to be able to check whether this method satisfies this criterion. To circumvent this problem (that the same single-winner election method can be generalized in different manners to calculate a collective ranking), I propose the "Increasing Sequential Independence" criterion in my paper. The "Increasing Sequential Independence" criterion says that when candidate A is a winner, then there must be a (not necessarily unique) candidate B such that, when candidate B is deleted, then candidate A is still a winner. The "Increasing Sequential Independence" criterion is identical to the "Independence of Worst Alternatives" criterion except for the fact that the "Increasing Sequential Independence" criterion makes no presumptions on how the proposed single-winner election method has to be generalized to calculate a collective ranking. MarkusSchulze (talk) 17:33, 30 May 2020 (UTC)