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By Gaertner W.

ISBN-10: 0199565309

ISBN-13: 9780199565306

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Extra resources for A primer in social choice theory

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The reader will easily see that also the constellations (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1) yield a cycle. Therefore, with respect to the left-hand block, there are six different constellations that lead to a Condorcet cycle. Exactly the same holds for the right-hand block. So, all in all, there are 12 preference constellations that generate a voting cycle. In total, there are 6 × 6 × 6 = 216 logically possible profiles for 3 alternatives and 3 voters. 0555. Guilbaud (1952) probably was the first to look at this problem systematically.

B a · · · Rm b a · · · Rm+1 a · · · b . . Rn ... 1. 2. 2. We move alternative a to the lowest position of individual i’s ordering for i < m and move a to the second lowest position in the orderings of i > m. 2, the reader will realize that moving a downwards does not alter anything in the relationship between b and any of the other alternatives. Therefore, due to condition I , b must remain top-ranked in the social ordering. The only difference between the new constellations, let’s call them 1 and 2 , lies in m’s ranking of alternatives a and b.

State in this context (it is due to 30 ARROW’S IMPOSSIBILITY RESULT D’Aspremont and Gevers (1977)) says that if the social evaluation functional F satisfies the three axioms of welfarism (viz. conditions U , I , and PI ), there exists an ordering R ∗ of IR n such that for all x, y ∈ X and all logically possible ¯¯ where u¯ = U (x) and u¯¯ = U (y). utility profiles U , xRU y ↔ uR ¯ ∗ u, D’Aspremont and Gevers show that when the functional F fulfils the three axioms of welfarism, the ordering R ∗ in utility space inherits these properties.

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A primer in social choice theory by Gaertner W.


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