Independence of Smith-dominated alternatives

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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]

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 would beats the original winner, either directly or indirectly (by beating a candidate who beats a candidate who... who beats the winner).^{[citation needed]}

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.

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.