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Unformatted text preview: which implies . In this case, 2 is decisive over and , and therefore (Exercise 1.60) decisive. 1.62 Assume is a social order which is Pareto and satisfies Independence of Irrelevant Alternatives. By the Pareto principle, the whole group is decisive over any pair of alternatives. By the previous exercise, some proper subgroup is decisive. Continuing in this way, we eventually arrive at a decisive subgroup of one individual. By the Field Expansion Lemma (Exercise 1.60), that individual is decisive over every pair of alternatives. That is, the individual is a dictator. 1.63 Assume is decisive over and and is decisive over and . That is, assume = = Also assume for every for every This implies that and (Pareto principle). Combining these preferences, transitivity implies that...
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.
- Fall '10