Analysis of information sources in references of the Wikipedia article "Condorcet method" in English language version.
although Ware's method cannot return the worst, it may return the next worst.
CC [Condorcet] systems typically allow tied ranks. If a voter fails to rank a candidate, they are typically presumed to rank them below anyone whom they did rank explicitly.
The Condorcet criterion for single-winner elections (section 4.7) is important because, when there is a Condorcet winner b ∈ A, then it is still a Condorcet winner when alternatives a1,...,an ∈ A \ {b} are removed. So an alternative b ∈ A doesn't owe his property of being a Condorcet winner to the presence of some other alternatives. Therefore, when we declare a Condorcet winner b ∈ A elected whenever a Condorcet winner exists, we know that no other alternatives a1,...,an ∈ A \ {b} have changed the result of the election without being elected.
Briefly, one can say candidate A defeats candidate B if a majority of the voters prefer A to B. With only two candidates [...] barring ties [...] one of the two candidates will defeat the other.
A first objective of this paper is to propose a formalization of this idea, called the Extended Condorcet Criterion (XCC). In essence, it says that if the set of alternatives can be partitioned in such a way that all members of a subset of this partition defeat all alternatives belonging to subsets with a higher index, then the former should obtain a better rank than the latter.
The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections.
A common definition of a voting cycle is the absence of a strict pairwise majority rule winner (SPMRW) … if no candidate beats all other candidates in pairwise comparisons.
Condorcet's paradox [6] of simple majority voting occurs in a voting situation [...] if for every alternative there is a second alternative which more voters prefer to the first alternative than conversely.
Binary procedures of the Jefferson/Robert variety will select the Condorcet winner if one exists
A weak Condorcet winner (WCW) is an alternative, y, that no majority of voters rank below any other alternative, z, but is not a SCW [Condorcet winner].
A common definition of a voting cycle is the absence of a strict pairwise majority rule winner (SPMRW) … if no candidate beats all other candidates in pairwise comparisons.
Formally, the Smith set is defined as the smaller of two sets:
1. The set of all alternatives, X.
2. A subset A ⊂ X such that each member of A can defeat every member of X that is not in A, which we call B=X − A.
Condorcet's paradox [6] of simple majority voting occurs in a voting situation [...] if for every alternative there is a second alternative which more voters prefer to the first alternative than conversely.
then the vote shall be performed using either a Condorcet voting system or a score voting system, as the participants shall decide
The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections.
Condorcet's paradox [6] of simple majority voting occurs in a voting situation [...] if for every alternative there is a second alternative which more voters prefer to the first alternative than conversely.
Binary procedures of the Jefferson/Robert variety will select the Condorcet winner if one exists
A weak Condorcet winner (WCW) is an alternative, y, that no majority of voters rank below any other alternative, z, but is not a SCW [Condorcet winner].
For a vote between several mutually exclusive options, the votetaking organisation will establish, for each possible pair of options A and B, how many voters prefer A over B and vice versa. … The method of determining the result when there are several mutually exclusive options, as described in paragraph 4 of The Result, is essentially that devised by the French mathematician the Marquis de Condorcet (1743-94).
then the vote shall be performed using either a Condorcet voting system or a score voting system, as the participants shall decide
A common definition of a voting cycle is the absence of a strict pairwise majority rule winner (SPMRW) … if no candidate beats all other candidates in pairwise comparisons.
empirical studies ... indicate that some of the most common paradoxes are relatively unlikely to be observed in actual elections. ... it is easily concluded that Condorcet's Paradox should very rarely be observed in any real elections on a small number of candidates with large electorates, as long as voters' preferences reflect any reasonable degree of group mutual coherence
