# Independence of Smith-dominated alternatives

**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.

## Original Definition

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).[1]

## Complying methods

Schulze and Ranked Pairs are independent of Smith-dominated alternatives. Any voting system can be "forced" to be ISDA by applying the voting system to the Smith set only.

Methods failing the Smith criterion (let alone the Condorcet criterion) never satisfy independence of Smith-dominated alternatives.

## References

- Lemma 2 of Smith, John H. (November 1973). "Aggregation of preferences with variable electorate".
*Econometrica*.**41**(6): 1027–1041. doi:10.2307/1914033. JSTOR 1914033.