When a Condorcet winner exists, he does not necessarily win a runoff election due to insufficient support in the first round.

Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (; 17 September 1743 – 28 March 1794 ), known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election.

The paper also outlines a generic Condorcet method, designed to simulate pair-wise elections between all candidates in an election.

A Condorcet method is any election method that elects the candidate that would win by majority rule in all pairings against the other candidates, whenever one of the candidates has that property.

In certain circumstances an election has no Condorcet winner.

As noted above, if there is no Condorcet winner a further method must be used to find the winner of the election, and this mechanism varies from one Condorcet method to another.

Any election method that is independent of Smith-dominated alternatives automatically satisfies the Smith criterion, and all criteria implied by it, notably the Condorcet criterion and the mutual majority criterion.

The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters.

Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates.

In the statement that Condorcet criterion is stronger than the majority criterion, the word criterion must be understood as a criterion that a voting system may or may not satisfy, not as a criterion that a candidate must satisfy in order to win the election.

In voting systems, the Minimax method is one of several Condorcet methods used for tabulating votes and determining a winner when using ranked voting in a single-winner election.

CPO-STV compares every possible outcome of an election to every other possible outcome to find the set of winners with the highest level of support, which is a variation of the Condorcet method.

Most Condorcet methods have a single round of voting, in which each voter ranks the candidates from top to bottom.

Some Condorcet methods allow voters to rank more than one candidate equally, so that, for example, the voter might express two first preferences rather than just one.

If every voter votes for their top two favorites, Candidate B would win ( with 100 % approval ) even though A would be the Condorcet winner.

Currently, the Schulze method is the most widespread Condorcet method ( list ).

Also, in the case of three candidates or less and a robust political equilibrium, the two-round system will pick the Condorcet winner whenever there is one, which is not the case in the Contingent vote model.

Condorcet methods can allow candidates to win who have minimal first-choice support and can win largely on the compromise appeal of being ranked second or third by more voters.

Some Condorcet methods may have other kinds of ties ; for example, it would not be rare for two or more candidates to win the same number of pairings, when there is no Condorcet winner.

Some Condorcet elections permit write-in candidates but, because this can be difficult to implement, software designed for conducting Condorcet elections often does not allow this option.

When all possible pairings of candidates have been considered, if one candidate beats every other candidate in these contests then they are declared the Condorcet winner.

Unlike a plurality voting system, a run-off system meets the Condorcet loser criterion in that the candidate that ultimately wins would not have been beaten in a two-way race with every one of the other candidates.

Copeland's method or Copeland's pairwise aggregation method is a Condorcet method in which candidates are ordered by the number of pairwise victories, minus the number of pairwise defeats.

When voters identify candidates on a left-to-right axis and always prefer candidates closer to themselves, a Condorcet winner always exists.

The Smith criterion ( sometimes generalized Condorcet criterion, but this can have other meanings ) is a voting systems criterion defined such that its satisfaction by a voting system occurs when the system always elects a candidate that is in the Smith set, which is the smallest non-empty subset of the candidates such that every candidate in the subset is majority-preferred over every candidate not in the subset.

When there is a Condorcet winner -- a candidate that is majority-preferred over all other candidates -- the Smith set consists of only that candidate.

( Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in different head-to-head competitions.

For most Condorcet methods, those counts usually suffice to determine the complete order of finish.

Runoff advocates counter that voters first preference is more important than lower preferences because that's where voters are putting the most effort of decision and that, unlike Condorcet methods, runoffs require a high showing among the full field of choices in addition to a strong showing in the final head-to-head competition.

The Robert's Rules method for voting on motions and amendments is also a Condorcet method even though the voters do not vote by expressing their orders of preference.

; Condorcet winner: Given a preference ν on the outcome space, an outcome a is a condorcet winner if all non-dummy players prefer a to all other outcomes.

The French tradition included Rousseau, Condorcet, the Encyclopedists and the Physiocrats.

Many countries have growing electoral reform movements, which advocate systems such as approval voting, single transferable vote, instant runoff voting or a Condorcet method ; these methods are also gaining popularity for lesser elections in some countries where more important elections still use more traditional counting methods.

Nicolas de Condorcet was especially noted for his advocacy, in his articles published in the Journal de la Société de 1789, and by publishing De l ' admission des femmes au droit de cité (" For the Admission to the Rights of Citizenship For Women ") in 1790.

Born in Paris, Cesbron attended what is now known as Lycée Condorcet.

In Toulon, where he was serving on the Condorcet, Cousteau carried out his first underwater experiments, thanks to his friend Philippe Tailliez who in 1936 lent him some Fernez underwater goggles, predecessors of modern swimming goggles.

Given civilian status, he recovered his teaching position at Lycée Pasteur near Paris, settled at the Hotel Misgiven a new position at Lycée Condorcet, replacing a Jewish teacher who had been forbidden to teach by Vichy law.

Philosophers such as Condorcet, who drafted the French revolutionary chart for a people's education under the rule of reason, dismissed rhetoric as an instrument of oppression in the hands of clerics in particular.

Advocates of Condorcet methods argue that a candidate can claim to have majority support only if they are the " Condorcet winner " – that is, the candidate who would beat every other candidate in a series of one-on-one elections.

He left Besançon at the age of 14 years, relocating with his father to Paris, where he studied at the Lycée Condorcet, which was noted for its numerous literary alumni.

* Marquis de Condorcet ( 1743 – 1794 ) French.

Philosopher, mathematician, and early political scientist who devised the concept of a Condorcet method.

William Godwin and the Marquis de Condorcet, for example, believed in the possibility of almost limitless improvement of society.

The voting paradox ( also known as Condorcet's paradox or the paradox of voting ) is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic ( i. e. not transitive ), even if the preferences of individual voters are not.

* September 17 – Marquis de Condorcet, French mathematician, philosopher, and political scientist ( d. 1794 )

* March 28 – Marquis de Condorcet, French mathematician, philosopher, and political scientist ( died in prison ) ( b. 1743 )