Condorcet paradox: Difference between revisions
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{{Wikipedia|Condorcet paradox}}[[Image:Condorcetparadox.png|thumb|right|A majority of the dots are closer to B than A, C than B, and A than C.Note that a cycle or circular figure can be drawn pointing from B to C, C to A, and A to B.]]
[[File:Condorcet cycle simple example.png|thumb|1259x1259px|A Condorcet cycle example with ice cream flavors, with reference to the [[Smith set]].]]
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If C is chosen as the winner, it can be argued that B should win instead, since two voters (1 and 2 i.e. the first and second) prefer B to C and only one voter (3) prefers C to B. However, by the same argument A is preferred to B, and C is preferred to A, by a margin of two to one on each occasion.
== Known Condorcet cycles ==
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* The [[2021 Minneapolis Ward 2 city council election]].
* The Norwegian parliamentary vote involving the [[w:Oslo Airport location controversy]].<ref>{{cite web|url=https://www.stortinget.no/Global/pdf/Dokumentserien/2000-2001/dok18-200001.pdf|website=The Norwegian Parliament web site|title=Dokument nr. 18 (in Norwegian)|author=The parliamentary investigation committee for Gardermoen|quote=It's likely that the choice of voting order determined the outcome. In all likelihood there was a cyclical majority ('roterende flertall'). In such a case, the term 'the will of the majority' is meaningless, and one cannot assert that the actual outcome respects the will of the majority...}}</ref>
== Modeling Condorcet cycles ==
Simple mathematical models may under- or overestimate the probability of Condorcet cycles. For instance, the [[impartial culture]] model maximizes the chance of a Condorcet cycle among a very broad range of voting models. Failing to take voter indifference into account can also lead to models that overstate the chance of a cycle.<ref name="Fishburn Gehrlein 1980 pp. 83–94">{{cite journal | last=Fishburn | first=Peter C. | last2=Gehrlein | first2=William V. | title=The paradox of voting. Effects of individual indifference and intransitivity | journal=Journal of Public Economics | publisher=Elsevier BV | volume=14 | issue=1 | year=1980 | issn=0047-2727 | doi=10.1016/0047-2727(80)90006-7 | pages=83–94}}</ref>
== Notes ==
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