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Title of Journal: Theory Decis

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Abbravation: Theory and Decision

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Springer US

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DOI

10.1016/0031-9163(66)90335-0

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1573-7187

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Social choice, the strong Pareto principle, and conditional decisiveness

Authors: Susumu Cato,

Publish Date: 2013/02/22
Volume: 75, Issue:4, Pages: 563-579
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Abstract

This paper examines social choice theory with the strong Pareto principle. The notion of conditional decisiveness is introduced to clarify the underlying power structure behind strongly Paretian aggregation rules satisfying binary independence. We discuss the various degrees of social rationality: transitivity, semi-transitivity, the interval-order property, quasi-transitivity, and acyclicity.I thank Tomoki Inoue and an anonymous referee of this journal for constructive suggestions. This paper was financially supported by Grant-in-Aid for Young Scientists (B) from the Japan Society for the Promotion of Science and the Ministry of Education, Culture, Sports, Science and Technology.Let \(W\) be a QSDF satisfying strong Pareto and binary independence, and let \(A \subsetneq \mathcal{N }\). If \(B \subseteq \mathcal{N } \setminus A\) is \(A\)-conditionally decisive over some pair \((x,y)\) for \(W\), then it is \(A\)-conditionally decisive for \(W\).Let \(W\) be a QSDF satisfying strong Pareto and binary independence, and let \(A \subsetneq \mathcal{N }\). Suppose that \(B \subseteq \mathcal{N } \setminus A\) is \(A\)-conditionally decisive over \((x,y)\) for \(W\). We first prove the following claim.By applying the claim again, it follows that if \(B\) is \(A\)-conditionally decisive over \((y,z)\) for \(W\), then \(B\) is \(A\)-conditionally decisive over \((z,w)\) for \(W\). Hence, we have established that \(B\) is \(A\)-conditionally decisive over \((z,w)\) for any choice of distinct alternatives \(z\) and \(w\). \(\square \)


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