Editing Condorcet paradox (section)

=== Real world instances ===
A database of 189 ranked United States elections from 2004 to 2022 contained only one Condorcet cycle: the [[2021 Minneapolis City Council election#Ward 2|2021 Minneapolis City Council election in Ward 2]], with a narrow circular tie between candidates of the [[Green Party of Minnesota|Green Party]] ([[Cam Gordon]]), the [[Minnesota Democratic–Farmer–Labor Party]] (Yusra Arab), and an independent [[Democratic socialism|democratic socialist]] ([[Robin Wonsley]]).<ref name="GSM2023">{{cite arXiv | last1=Graham-Squire | first1=Adam | last2=McCune | first2=David | title=An Examination of Ranked Choice Voting in the United States, 2004-2022 |eprint=2301.12075v2 | date=2023-01-28 | class=econ.GN}}</ref> Voters' preferences were non-transitive: Arab was preferred over Gordon, Gordon over Wonsley, and Wonsley over Arab, creating a cyclical pattern with no clear winner. Additionally, the election exhibited a [[Negative responsiveness |downward monotonicity]] paradox, as well as a paradox akin to [[Simpson’s paradox]].

A second instance of a Condorcet cycle was found in the 2022 District 4 School Director election in Oakland, CA. Manigo was preferred to Hutchinson, Hutchinson to Resnick, and Resnick to Manigo. Like in Minneapolis, the margins were quite narrow: for instance, 11370 voters preferred Manigo to Hutchinson while 11322 preferred Hutchinson to Manigo.<ref name="g816">{{cite arXiv | last=McCune | first=David | title=Ranked Choice Bedlam in a 2022 Oakland School Director Election | date=2023-03-10 | eprint=2303.05985 | class=econ.GN}}</ref>

Another instance of a Condorcet cycle was with the seat of [[Results of the 2014 Victorian state election (Legislative Assembly)#Prahran|Prahran in the 2014 Victorian state election]], with a narrow circular tie between the [[Australian Greens|Greens]], [[Liberal Party of Australia|Liberal]], and [[Australian Labor Party|Labor]] candidates. The Greens candidate, who was initially third on primary votes, defeated the Liberal candidate by less than 300 votes. However, if the contest had been between Labor and Liberal, the Liberal candidate would have won by 25 votes. While a Greens vs Labor count was not conducted, Liberal preferences tend to flow more towards Labor than Greens in other cases ([[Electoral results for the district of Richmond (Victoria)|including in the seat of Richmond in the same election]]), meaning that Labor would have very likely been preferred to the Greens. This means there was a circular pattern, with the Greens preferred over Liberal, who were preferred over Labor, who were preferred over the Greens.