# Independence of Smith-dominated alternatives

**Independence of Smith-dominated alternatives** (ISDA) 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.

## 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

- J. H. Smith, "Aggregation of preferences with variable electorate",
*Econometrica*, vol. 41, pp. 1027–1041, 1973.