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{{Short description|Electoral system criterion}}
{{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>
 
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.
'''Independence of Smith-dominated alternatives''' (ISDA, also known as '''Weak independence of irrelevant alternatives''') 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 simpleAnother way toof describedefining itISDA is to say that ifadding a votingnew system is ISDA, then whenevercandidate youshould cannot partitionchange the candidateswinner intoof groupan ''A'' and groupelection, ''Bunless'' such that eachnew candidate inbeats groupthe ''A''original iswinner, preferredeither overdirectly eachor candidateindirectly in(by groupbeating ''B'',a youcandidate canwho eliminatebeats alla candidatescandidate ofwho... groupwho ''B'' without changingbeats the outcome of the electionwinner).
 
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]].
 
Note that though ISDA is also called "weak independence of irrelevant alternatives", this may be misleading, since [[independence of irrelevant alternatives]] is incompatible with ISDA; this is because all majority criterion-passing methods [[Independence_of_irrelevant_alternatives#Criticism_of_IIA|fail]] IIA and ISDA implies the majority criterion.
 
== Original Definition ==
 
If ''P'' is separable and neutral, then the relative standing of ''A'' and ''B''
depends only on the ranks each voter gives ''A'' and ''B'' (i.e., not on how he assigns the
remaining candidates to the remaining ranks).<ref>Lemma 2 of {{cite journal
| last = Smith
| first = John H.
| date = November 1973
| title = Aggregation of preferences with variable electorate
| journal = Econometrica
| volume = 41
| issue = 6
| pages = 1027–1041
| doi = 10.2307/1914033
| jstor = 1914033
}}</ref>
 
== Complying methods ==
[[Schulze method|Schulze]] and [[Ranked Pairs]] are independent of Smith-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 independent of Smith-dominated 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 independence of Smith-dominated alternatives.
 
==References==
<references />
 
{{voting systems}}
 
[[Category:Electoral system criteria]]
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