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{{Short description|Electoral system criterion}}
'''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]].
{{Refimprove|article|date=August 2019}}
'''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>
 
ASay simplewe wayclassify toall describecandidates isin thatan ifelection ainto votingtwo system is LIIAcategories, then whenever you can partition the candidates into group ''AFrontrunners'' and group ''Bnon-Frontrunners'', suchwhere that eachevery candidate in the group of ''AFrontrunners'' is preferred overdefeats eachevery candidate in the group of ''Bnon-Frontrunners.'' Then, youindependence canof Smith-dominated alternatives says it is always possible to eliminate all candidates ofin the group of ''Bnon-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).
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]] 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==
{{Uncategorized|date=July 2007}}
<references />
{{voting systems}}
[[Category:Electoral system criteria]]
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