Editing Condorcet paradox (section)

=== Empirical studies ===
Many attempts have been made at finding empirical examples of the paradox.<ref>{{Cite journal|last=Kurrild-Klitgaard|first=Peter|date=2014|title=Empirical social choice: An introduction|journal=Public Choice|language=en|volume=158|issue=3–4|pages=297–310|doi=10.1007/s11127-014-0164-4|s2cid=148982833|issn=0048-5829}}</ref>  Empirical identification of a Condorcet paradox presupposes extensive data on the decision-makers' preferences over all alternatives—something that is only very rarely available.

While examples of the paradox seem to occur occasionally in small settings (e.g., parliaments) very few examples have been found in larger groups (e.g. electorates), although some have been identified.<ref>{{Cite journal |last=Kurrild-Klitgaard |first=Peter |date=2001 |title=An empirical example of the Condorcet paradox of voting in a large electorate |journal=Public Choice |language=en |volume=107 |pages=135–145 |doi=10.1023/A:1010304729545 |issn=0048-5829 |s2cid=152300013}}</ref>

A summary of 37 individual studies, covering a total of 265 real-world elections, large and small, found 25 instances of a Condorcet paradox, for a total likelihood of 9.4%<ref name=":0" />{{Rp|325}} (and this may be a high estimate, since cases of the paradox are more likely to be reported on than cases without).<ref name=":1" />{{Rp|47}}

An analysis of 883 three-candidate elections extracted from 84 real-world ranked-ballot elections of the [[Electoral Reform Society]] found a Condorcet cycle likelihood of 0.7%.  These derived elections had between 350 and 1,957 voters.<ref name=":3" /> A similar analysis of data from the 1970–2004 [[American National Election Studies]] [[thermometer scale]] surveys found a Condorcet cycle likelihood of 0.4%. These derived elections had between 759 and 2,521 "voters".<ref name=":3" />

Andrew Myers, who operates the [[online poll|Condorcet Internet Voting Service]], analyzed 10,354 nonpolitical CIVS elections and found cycles in 17% of elections with at least 10 votes, with the figure dropping to 2.1% for elections with at least 100 votes, and 1.2% for ≥300 votes.<ref name="CIVS">{{cite conference |last=Myers |first=A. C. |author-link= |date=March 2024 |title=The Frequency of Condorcet Winners in Real Non-Political Elections |url=https://www.cs.cornell.edu/andru/papers/civs24/ |conference=61st Public Choice Society Conference |pages=5 |quote=83.1% … 97.9% … 98.8% … Figure 2: Frequency of CWs and weak CWs with an increasing number of voters}}</ref>