A primer in social choice theory by Gaertner W.

By Gaertner W.

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The proof starts by postulating a finite set of alternatives X and n individuals who have strict orderings over these alternatives. The social ordering is assumed to be a weak order. We pick any two distinct alternatives a and b from X . In step 1, alternative a is ranked highest and alternative b lowest by every person i ∈ {1, . . , n}. Condition P then requires that a is strictly at the top of the social ordering. Imagine now that alternative b is raised, step by step or rank by rank, to the top of individual 1’s ordering, while the ranking of all other alternatives is left unchanged.

Remember that in situation 1 , a was ranked lowest for i < m and second lowest for i > m. Individual m had a at the top of the ordering. 3 which is such that the ranking of a in relation to any other alternative in any individual’s ordering remains the same as in situation 1 . A SECOND PROOF 27 A preference profile is picked where every individual has c ordered above b. The main insight within this step is that due to condition I , alternative a must again be top-ranked socially. R1 · · c b a . .

6(a). e. u¯ 2 is mapped into u¯ 2 and a2 is mapped into b2 . 5 are ranked the same in relation to u, ¯ then all points on their common boundary have the same preference relationship to u. 7(a) and (b)? , and Weymark J. A. (1984). ‘Social Choice with Interpersonal Utility Comparisons: A Diagrammatic Introduction’. International Economic Review, 25: 327–356. Reny, Ph. J. (2001). ‘Arrow’s Theorem and the Gibbard–Satterthwaite Theorem: A Unified Approach’. Economics Letters, 70: 99–105. Sen, A. K. (1970).

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