Editing Condorcet paradox (section)

{{About|results that can arise in a collective choice among three or more alternatives|the contention that an individual's vote will probably not affect the outcome|Paradox of voting}}
{{Short description|Self-contradiction of majority rule}}
{{Electoral systems}}

In [[social choice theory]], '''Condorcet's voting paradox''' is a fundamental discovery by the [[Marquis de Condorcet]] that [[majority rule]] is inherently [[contradiction|self-contradictory]]. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters; for example, there can be rock-paper-scissors scenarios where a majority of voters will prefer A to B, B to C, and also C to A, even if every voter's individual preferences are rational and avoid self-contradiction. Examples of Condorcet's paradox are called '''Condorcet cycles''' or '''cyclic ties'''.

In such a cycle, every possible choice is rejected by the electorate in favor of another alternative, who is preferred by more than half of all voters. Thus, any attempt to ground social decision-making in [[majoritarianism]] must accept such self-contradictions (commonly called [[spoiler effect]]s). Systems that attempt to do so, while minimizing the rate of such self-contradictions, are called [[Condorcet method]]s.

Condorcet's paradox is a special case of [[Arrow's impossibility theorem|Arrow's paradox]], which shows that ''any'' kind of social decision-making process is either self-contradictory, a [[dictatorship mechanism|dictatorship]], or incorporates information about the strength of different voters' preferences (e.g. [[cardinal utility]] or [[rated voting]]).