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.

Voting systems

Part of the Politics and Election series

Single-winner voting system	Approval voting Borda count Bucklin voting Contingent vote Coombs' method Copeland's method Exhaustive ballot First-past-the-post voting Instant-runoff voting Kemeny–Young method Simple majoritarianism Minimax Condorcet Nanson's method Plurality Positional voting system Range voting Ranked pairs Schulze method Two-round system

Proportional representation	Mixed-member Party-list Single transferable vote Schulze STV CPO-STV Highest averages method Sainte-Laguë D'Hondt Largest remainder method Alternative vote Plus Closed list Open list Overhang seat Underhang seat

Semi-proportional representation	Parallel voting Single non-transferable vote Cumulative voting Limited voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting

Usage	Table of voting systems by country

Voting system criterion	Condorcet criterion Condorcet loser criterion Consistency criterion Independence of clones Independence of irrelevant alternatives Independence of Smith-dominated alternatives Later-no-harm criterion Majority criterion Majority loser criterion Monotonicity criterion Mutual majority criterion Pareto efficiency Participation criterion Plurality criterion Resolvability criterion Reversal symmetry Smith criterion

Voting system quotas	Droop quota Hagenbach-Bischoff quota Hare quota Imperiali quota

Other	Ballot Election threshold First-preference votes Spoilt vote Sortition

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