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Example Condorcet method voting ballot. Blank votes are equivalent to ranking that candidate last. A Condorcet method (English: / k ɒ n d ɔːr ˈ s eɪ /; French: [kɔ̃dɔʁsɛ]) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate.
The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates. [1] [2] The Condorcet winner is also called a majority winner, a majority-preferred candidate, [3] [4] [5] a beats-all winner, or tournament winner (by analogy with round-robin tournaments).
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently 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 scenario where a majority of voters will prefer ...
They looked at Condorcet cycles in voter preferences (an example of which is A being preferred to B by a majority of voters, B to C and C to A) and found that the number of them was consistent with small-sample effects, concluding that "voting cycles will occur very rarely, if at all, in elections with many voters."
The issue was noted by Nicolas de Condorcet in 1793 when he stated, "In single-stage elections, where there are a great many voters, each voter's influence is very small. . It is therefore possible that the citizens will not be sufficiently interested [to vote]" and "... we know that this interest [which voters have in an election] must decrease with each individual's [i.e. voter's] influence ...
Thus, the Condorcet loser L is elected Approval winner. Note, that if any voter would set the threshold between approvals and disapprovals at any other place, the Condorcet loser L would not be the (single) Approval winner. However, since Approval voting elects the Condorcet loser in the example, Approval voting fails the Condorcet loser criterion.
A Condorcet winner C only has to defeat every other candidate "one-on-one"—in other words, when comparing C to any specific alternative. To be the majority choice of the electorate, a candidate C must be able to defeat every other candidate simultaneously— i.e. voters who are asked to choose between C and "anyone else" must pick " C ...
Multiwinner variants of some other Condorcet rules. [20] A third adaptation was by Elkind, Lang and Saffidine: [21] a Condorcet winning set is a set that, for each member d not in the set, some member c in the set is preferred to d by a majority. Based on this definition, they present a different multiwinner variant of the Minimax Condorcet method.