A Condorcet winner (French: [kɔ̃dɔʁsɛ], English: /kɒndɔːrˈseɪ/) is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the Condorcet winner criterion. The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates.

Named after Nicolas de Condorcet, it is also called a majority winner, a majority-preferred candidate, a beats-all winner, or tournament winner (by analogy with round-robin tournaments). A Condorcet winner may not necessarily always exist in a given electorate: it is possible to have a rock, paper, scissors-style cycle, when multiple candidates defeat each other (Rock < Paper < Scissors < Rock). This is called Condorcet's voting paradox, and is analogous to the counterintuitive intransitive dice phenomenon known in probability. However, the Smith set, a generalization of the Condorcet criteria that is the smallest set of candidates that are pairwise unbeaten by every candidate outside of it, will always exist.

If voters are arranged on a sole 1-dimensional axis, such as the left-right political spectrum for a common example, and always prefer candidates who are more similar to themselves, a majority-rule winner always exists and is the candidate whose ideology is most representative of the electorate, a result known as the median voter theorem. However, in real-life political electorates are inherently multidimensional, and the use of a one- or even two-dimensional model of such electorates would be inaccurate. Previous research has found cycles to be somewhat rare in real elections, with estimates of their prevalence ranging from 1-10% of races.

Systems that guarantee the election of a Condorcet winners (when one exists) include Ranked Pairs, Schulze's method, and the Tideman alternative method. Methods that do not guarantee that the Cordorcet winner will be elected, even when one does exist, include instant-runoff voting (often called ranked-choice in the United States), First-past-the-post voting, and the two-round system. Most rated systems, like score voting and highest median, fail the majority winner criterion.

Condorcet methods were first studied in detail by the Spanish philosopher and theologian Ramon Llull in the 13th century, during his investigations into church governance. Because his manuscript Ars Electionis was lost soon after his death, his ideas were overlooked for the next 500 years.

The first revolution in voting theory coincided with the rediscovery of these ideas during the Age of Enlightenment by Nicolas de Caritat, Marquis de Condorcet, a mathematician and political philosopher.

Suppose the government comes across a windfall source of funds. There are three options for what to do with the money. The government can spend it, use it to cut taxes, or use it to pay off the debt. The government holds a vote where it asks citizens which of two options they would prefer, and tabulates the results as follows:

In this case, the option of paying off the debt is the beats-all winner, because repaying debt is more popular than the other two options. But, it is worth noting that such a winner will not always exist. In this case, tournament solutions search for the candidate who is closest to being an undefeated champion.