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
- ^ 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'.)
- v
- t
- e
- Approval voting
- Combined approval voting
- Unified primary
- Borda count
- Bucklin voting
- Condorcet methods
- Copeland's method
- Dodgson's method
- Kemeny–Young method
- Minimax Condorcet method
- Nanson's method
- Ranked pairs
- Schulze method
- Exhaustive ballot
- First-past-the-post voting
- Instant-runoff voting
- Simple majoritarianism
- Plurality
- Positional voting system
- Score voting
- STAR voting
- Two-round system
- Graduated majority judgment
Systems | |
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Allocation | |
Quotas |
- Condorcet winner 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
- Participation criterion
- Plurality criterion
- Resolvability criterion
- Reversal symmetry
- Smith criterion
- Seats-to-votes ratio