Independence of Smith-dominated alternatives

Independence of Smith-dominated alternatives (ISDA, also known as Smith-IIA) is a voting system criterion which says that the winner of an election should not be affected by candidates who are not in the Smith set.^[1]

Say we classify all candidates in an election into two categories, Frontrunners and non-Frontrunners, where every candidate in the group of Frontrunners defeats every candidate in the group of non-Frontrunners. Then, independence of Smith-dominated alternatives says it is always possible to eliminate all candidates in the group of non-Frontrunners without changing the outcome of the election.

Another way of defining ISDA is to say that adding a new candidate should not change the winner of an election, unless that new candidate beats the original winner, either directly or indirectly (by beating a candidate who beats a candidate who... who beats the winner).

Complying methods

Schulze and Ranked Pairs are independent of Smith-dominated alternatives. Any voting system can be forced to satisfy ISDA by first eliminating all candidates outside the Smith set, then running the full algorithm.

Ambiguity

Smith-IIA can sometimes be taken to mean independence of non-Smith irrelevant alternatives, i.e. that no losing candidate outside the Smith set can affect the result.^{[citation needed]} This differs slightly from the above definition, in that methods passing independence of irrelevant alternatives (but not the Smith criterion) also satisfy this definition of Smith-IIA.

If the criterion is taken to mean independence of non-Smith alternatives, regardless of whether they are relevant (i.e. winners) or not, Smith-independence requires passing the Smith criterion.

References

1. Green-Armytage, J. (2011). "Four Condorcet-Hare hybrid methods for single-winner elections" (PDF). Voting Matters (29): 1–14. S2CID 15220771. Smith-IIA [ISDA] Definition: Removing a candidate from the ballot who is not a member of the Smith set will not change the result of the election. ('IIA' here stands for 'independence of irrelevant alternatives'.)