Editing Condorcet paradox (section)

=== Spoiler effects ===
Condorcet paradoxes imply that [[Majority rule|majoritarian methods]] fail independence of irrelevant alternatives. Label the three candidates in a race [[Rock paper scissors|''Rock'', ''Paper'', and ''Scissors'']]. In one-on-one races, Rock loses to Paper, Paper loses to Scissors, and Scissors loses to Rock. 

[[Without loss of generality]], say that Rock wins the election with a certain method. Then, Scissors is a spoiler candidate for Paper; if Scissors were to drop out, Paper would win the only one-on-one race (Paper defeats Rock). The same reasoning applies regardless of the winner.

This example also shows why Condorcet elections are rarely (if ever) spoiled; spoilers can ''only'' happen when there is no Condorcet winner. Condorcet cycles are rare in large elections,<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 |language=en |volume=158 |issue=3 |pages=311–330 |doi=10.1007/s11127-013-0133-3 |issn=1573-7101}}</ref> and the [[median voter theorem]] shows cycles are impossible whenever candidates are arrayed on a [[Political spectrum|left-right spectrum]].