Condorcet’s paradox is a classic problem in democracy, first formalised by the Marquis de Condorcet at the time of the French revolution, stating that majority preferences can become intransitive with three or more options.
Condorcet proposed a method whereby alternative x should be declared the winner if for all y ≠ x, x is preferred to y by more voters than the number who prefer y to x. Similarly, y would be ranked second if for all z ≠ x or y, y is preferred to z by more voters than the number who prefer z to y. Consider the following example.
A Condorcet Cycle occurs when there is a violation of transitivity in the social preference ordering.
A Condorcet Winner is an alternative such that it gains a majority of votes when paired against each of the other alternatives. A Condorcet Cycle occurs when there is a violation of transitivity in the social preference ordering. Arrow’s Impossibility Theorem: “There is no social ranking function > such...
Condorcet’s paradox is a classic problem in democracy, first formalised by the Marquis de Condorcet at the time of the French revolution, stating that majority preferences can become intransitive with three or more options. It is possible for a certain electorate to express a preference for A over B, a preference for B over C, and a preference for C over A, all from the same set of ballots.
A Condorcet Cycle occurs when there is a violation of transitivity in the social preference ordering.
Condorcet started studying the calculus of probabilities as early as 1770.
Condorcet proposed a method whereby alternative x should be declared the winner if for all y ≠ x, x is preferred to y by more voters than the number who prefer y to x. Similarly, y would be ranked second if for all z ≠ x or y, y is preferred to z by more voters than the number who prefer z to y. Consider the following example.
The theory of preference aggregation in the long and established tradition of Condorcet and Arrow addresses the following question: How can a group of individuals arrive at a collective preference ordering on some set of alternatives on the basis of the group members' individual preference orderings on them? Condorcet's classic paradox illustrates some of the challenges raised by this problem.
Although Poisson only wrote the occasional paper on probability prior to the 1830 s, in the last decade of his life he became interested in the problems of legal decision-making addressed earlier by Condorcet and Laplace.
Sjoerd D. Zwart, in Philosophy of Technology and Engineering Sciences, 2009
In order to win a race, it is better to exercise the legs than to reason upon the mechanism of walking.
In voting theory, the result of a paired comparison method such as the one suggested by Condorcet can be represented by a tournament, i.e., a complete asymmetric directed graph.