Editing Smith set (section)

{{Short description|Set preferred to any other by a majority}}
{{Electoral systems sidebar|expanded=Paradox}}
The '''Smith''' '''set''',{{notetag|Many authors reserve the term "Schwartz set" for the strict Smith set described below.}} sometimes called the '''top-cycle''' or '''Condorcet winning set''',<ref>{{Cite journal |last=Elkind |first=Edith |last2=Lang |first2=Jérôme |last3=Saffidine |first3=Abdallah |date=2015-03-01 |title=Condorcet winning sets |url=https://link.springer.com/article/10.1007/s00355-014-0853-4 |journal=Social Choice and Welfare |language=en |volume=44 |issue=3 |pages=493–517 |doi=10.1007/s00355-014-0853-4 |issn=1432-217X}}</ref> generalizes the idea of a [[Condorcet winner]] to cases where [[Condorcet paradox|no such winner exists]]. It does so by allowing cycles of candidates to be treated jointly, as if they were a single Condorcet winner.<ref>{{cite web|last=Soh|first=Leen-Kiat|title=Voting: Preference Aggregating & Social Choice [CSCE475/875 class handout]|date=2017-10-04|url=http://cse.unl.edu/~lksoh/Classes/CSCE475_875_Fall17/handouts/10VotingSocialChoice.pdf}}</ref> Voting systems that always elect a candidate from the Smith set pass the '''Smith criterion'''. The Smith set and Smith criterion are both named for mathematician [[John H. Smith (mathematician)|John H. Smith]]. 

The Smith set provides one standard of optimal choice for an election outcome. An alternative, stricter criterion is given by the [[Landau set]].