To request a copy of this paper, please e-mail: [email protected].
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| Keith L. Dougherty | |||||||
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Abstract. Sen's Liberal Paradox describes a conflict between weak Pareto, minimal liberalism, and either transitivity or a best element over a domain of individual preferences. This paper determines the probability that variants of that paradox arise in various populations. We show that if individual preferences for a personal attribute are independent of the personal choices of others (a domain restriction), then in the absence of Pareto there can be no cycles. Furthermore, if each individual's preferences are also unconditioned on the non-decisive attributes in a social state, then there can be no cycles with or without Pareto. For complete social relations this implies a best element. We then determine the probability of a cycle assuming a much weaker independence condition that does not restrict the domain. This probability converges to one as the number of non-decisive attributes in the social states increases. Finally, we use simulations to determine the magnitudes of the probabilities for best elements, maximal elements, and transitivity separately.
To request a copy of this paper, please e-mail: [email protected].
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| Last Modified: 6/1/20 | |||||||
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| Keith L. Dougherty | Department of Political Science | SPIA | University of Georgia |