Difference between revisions of "Independence of Smith-dominated alternatives"
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(Removed redirect to Independence of irrelevant alternatives)
'''Independence of Smith-dominated alternatives''' (ISDA), also sometimes called '''Smith-IIA''' (Smith-Independence of Irrelevant Alternatives), says that if one option (X) wins an election, and a new alternative (Y) is added, X will still win the election if Y is not in the [[Smith set]]. ISDA implies [[Smith criterion|Smith]] and thus [[Condorcet criterion|Condorcet]], since logically speaking, if an ISDA-passing method's winner were not in the Smith set, eliminating everyone outside of the Smith set would have to change the winner. Some Condorcet methods (e.g. [[Schulze method|Schulze]]) satisfy ISDA.
Any voting method that starts by eliminating everyone outside the Smith set passes ISDA. Satisfaction of ISDA can sometimes make understanding a voting method or finding the winner easier; see the [[Schulze method#The Schwartz set heuristic|Schwartz set heuristic]] for Schulze for an example.
ISDA is incompatible with IIA, since ISDA implies [[Majority criterion|majority]] and majority is incompatible with IIA.
Given Schulze's multi-winner generalization of the Smith set (see the "Multi-winner generalizations" section of the [[Smith criterion]] article), an analogous extension of ISDA for the multi-winner case might be "if candidates not in any groups of candidates guaranteed seats by Schulze's multi winner Smith criterion drop out or enter the race, this shouldn't change the seat guarantees given to those same groups."