Independence of Smith-dominated alternatives
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Independence of Smith-dominated alternatives (ISDA, also known as Weak independence of irrelevant alternatives) is a voting system criterion defined such that its satisfaction by a voting system occurs when the selection of the winner is independent of candidates who are not within the Smith set.
A simple way to describe it is that if a voting system is ISDA, then whenever you can partition the candidates into group A and group B such that each candidate in group A is preferred over each candidate in group B, you can eliminate all candidates of group B without changing the outcome of the election.
Any election method that is independent of Smith-dominated alternatives automatically satisfies the Smith criterion, and all criteria implied by it, notably the Condorcet criterion and the mutual majority criterion.
If P is separable and neutral, then the relative standing of A and B depends only on the ranks each voter gives A and B (i.e., not on how he assigns the remaining candidates to the remaining ranks).