Examples of Condorcet's paradox are called Condorcet cycles or cyclic ties. In such a cycle, every possible choice is rejected by the electorate in favor of another alternative, who is preferred by more than half of all voters.

2006年10月4日 · The described situation yields a preference cycle, which contradicts transitivity of strict preference. (Notice the structural similarity to Condorcet's Paradox, discussed in section 7.2.) These and similar examples can be used to show …

2014年7月16日 · This paper investigated the conditions for social-preference cycles. We reformulated the Ferejohn–Fishburn condition (FF), and explored the logical relationship between it and the condition ImPart introduced by Schwartz . Under suitable background assumptions, both FF and ImPart are necessary and sufficient for a social-preference cycle ...

Abstract: In this paper, a theory of revealed preference that can be compatible with preference cycles is considered. The problem of preference cycles is treated in Schwartz(1972) and he advocated the notion of optimality.

Suppose players know each others’ preferences and voting is sincere. How should Andrew set the agenda? WP vs. RS → WP, WP vs. MFA → MFA. How should Bonnie set the agenda? MFA vs. RS → RS, RS vs. WP → WP. Because of the preference cycle, there is a way to set the agenda to get any winner. The agenda setter is very powerful! 8

Preference-Based Approach • Reflexivity: every alternative 𝑥𝑥is weakly preferred to, at least, one alternative: itself. • A preference relation satisfies reflexivity if for any alternative 𝑥𝑥∈𝑋𝑋, we have that: 1)𝑥𝑥∼𝑥𝑥: any bundle is indifferent to itself.

Condorcet methods may use preferential ranked, rated vote ballots, or explicit votes between all pairs of candidates. Most Condorcet methods employ a single round of preferential voting, in which each voter ranks the candidates from most (marked as number 1) to least preferred (marked with a higher number).

2023年1月1日 · We bespoke-design pairs of lotteries inspired by the paradox, over which individual preferences might cycle. We run an experiment to look for evidence of cycles, and violations of expansion/contraction consistency between choice sets.

It is then easy to see that majority voting over pairs of alternatives fails to yield a rational collective preference ordering: there are majorities for x over y, for y over z, and yet for z over x — a ‘preference cycle’.

2013年12月18日 · So, we are faced with a social preference cycle: \(x\) is socially preferred to \(y, y\) is socially preferred to \(z\), and \(z\) socially preferred to \(x\). Sen generalized this problem—now known as the ‘liberal paradox’—as follows.