Editing Spoiler effect (section)

=== Tournament (Condorcet) voting ===
Spoiler effects rarely occur when using [[tournament solution]]s, where candidates are compared in one-on-one matchups to determine relative preference. For each pair of candidates, there is a count for how many voters prefer the first candidate in the pair to the second candidate. The resulting table of pairwise counts eliminates the step-by-step redistribution of votes, which is usually the cause for spoilers in other methods.<ref name="Holliday3"/> This pairwise comparison means that spoilers can only occur when there is a [[Condorcet cycle]], where there is no single candidate preferred to all others.<ref name="Holliday3"/><ref name=":53"/><ref name=":63"/>

Theoretical models suggest that somewhere between 90% and 99% of real-world elections have a Condorcet winner,<ref name=":53">{{Cite journal |last=Gehrlein |first=William V. |date=2002-03-01 |title=Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences* |url=https://doi.org/10.1023/A:1015551010381 |journal=[[Theory and Decision]] |language=en |volume=52 |issue=2 |pages=171–199 |doi=10.1023/A:1015551010381 |issn=1573-7187}}</ref><ref name=":63">{{Cite journal |last=Van Deemen |first=Adrian |date=2014-03-01 |title=On the empirical relevance of Condorcet's paradox |url=https://doi.org/10.1007/s11127-013-0133-3 |journal=[[Public Choice (journal)|Public Choice]] |language=en |volume=158 |issue=3 |pages=311–330 |doi=10.1007/s11127-013-0133-3 |issn=1573-7101}}</ref> and the first Condorcet cycle in a ranked American election was found in 2021.<ref name="s192">{{cite journal | last1=McCune | first1=David | last2=McCune | first2=Lori | title=The Curious Case of the 2021 Minneapolis Ward 2 City Council Election | journal=The College Mathematics Journal | date=2023-05-24 | issn=0746-8342 | doi=10.1080/07468342.2023.2212548 | pages=1–5 |arxiv=2111.09846 |quote=The 2021 Minneapolis election for city council seat in Ward 2 contained three candidates, each of whom has a legitimate claim to be the winner, the first known example of an American political election without a Condorcet winner ...}}</ref> Some systems like the [[Schulze method]] and [[ranked pairs]] have stronger spoiler resistance guarantees that limit which candidates can spoil an election without a [[Condorcet winner]].<ref name="Schulze">{{cite arXiv | last=Schulze | first=Markus | title=The Schulze Method of Voting | eprint=1804.02973 | class=cs.GT| date=2018-03-15 |quote="The Smith criterion and Smith-IIA (where IIA means “independence of irrelevant alternatives”) say that weak alternatives should have no impact on the result of the elections ... the Schulze method, as defined in section 2.2, satisfies Smith-IIA."}}</ref>{{rp|228–229}}