Condorcet paradox: a standalone construct

The Marquis de Condorcet described this result in his 1785 Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix: when a group chooses among three or more options by pairwise majority vote, the group's collective ranking can be cyclic even though every individual voter holds a consistent, transitive ranking. In the classic case a majority prefers A to B, another majority prefers B to C, and a further majority prefers C to A, so there is no option that beats all others and no stable majority winner. Duncan Black's 1948 analysis and later formalisations, such as Gehrlein's 1983 survey, reframed the finding in modern terms and studied how often such cycles arise under different assumptions about voter preferences. The construct is distinctive because it shows that a property holding for each individual, transitivity of preference, need not carry over to the group formed by majority rule, and it is the historical seed of the wider impossibility results in social choice theory that concern how individual rankings can be combined into a group ranking.[1][2][3]

Unit

A logical property of a preference profile: whether pairwise majority rule over the options yields a cycle rather than a single undefeated option

Recovery means

Not applicable

Measured by

Identified by tallying every pairwise majority comparison among the options and checking whether the resulting majority relation contains a cycle (no Condorcet winner)