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'''Independence of Smith-dominated alternatives''' ('''ISDA''', also known as '''Smith-[[Independence of irrelevant alternatives|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]].<ref name="Green 2001 four">{{cite journal | last=Green-Armytage |first=J. |title=Four Condorcet-Hare hybrid methods for single-winner elections | journal=Voting Matters | issue=29 | pages=1–14 | year=2011 | url=http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf|quote=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’.) |s2cid=15220771}}</ref>
 
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.
'''Local independence of irrelevant alternatives''' (LIIA), also known as '''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]].
 
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).
A simple way to describe is that if a voting system is LIIA, 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 locally independent of irrelevant alternatives automatically satisfies the [[Smith criterion]], and all criteria implied by it, notably the [[Condorcet criterion]] and the [[Mutual majority criterion]].
 
Contrary to what its name might suggest, it doesn't have much to do with [[Independence of irrelevant alternatives]], which is a criterion that is actually incompatible with the [[Condorcet criterion]].
 
== Complying methods ==
[[Schulze method|Schulze]] and [[Ranked Pairs]] are locally independent of irrelevantSmith-dominated alternatives. Any voting system can be "forced" to besatisfy ISDA by applyingfirst theeliminating votingall systemcandidates tooutside the Smith set, then running the full onlyalgorithm.▼
 
== Ambiguity ==
▲[[Schulze method|Schulze]] and [[Ranked Pairs]] are locally independent of irrelevant alternatives. Any voting system can be "forced" to be ISDA by applying the voting system to the Smith set only.
Smith-[[Independence of irrelevant alternatives|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.{{cn|date=March 2024}} 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]].
Methods failing the [[Smith criterion]] (let alone the [[Condorcet criterion]]) never satisfy local independence of irrelevant alternatives.
 
==References==
[[Category:Voting system criteria]]▼
<references />
{{voting systems}}
▲[[Category:VotingElectoral system criteria]]
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