Economic Theory

A Primer in Social Choice Theory (LSE Perspectives in by Wulf Gaertner

By Wulf Gaertner

This introductory textual content explores the idea of social selection. Written as a primer compatible for complicated undergraduates and graduates, this article will act as an incredible place to begin for college kids grappling with the complexities of social selection conception. Rigorous but obtainable, this primer avoids using technical language and gives an up to date dialogue of this speedily constructing box. this can be the 1st in a chain of texts released in organization with the LSE.

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Additional resources for A Primer in Social Choice Theory (LSE Perspectives in Economic Analysis)

Example text

On the other hand, from step 1 and the assumption that N (1) = N (−1), we must have g (d1 , . . , dn ) = g (−d1 , . . , −dn ). Since g is a function, the hypothesis that D = +1 therefore leads to a contradiction. The same argumentation can be used to show that D = −1 is not possible either. Thus, the only possibility in the case of N (1) = N (−1) is D = 0. Thirdly, assume that N (1) > N (−1). We want to show that D = g (d1 , . . , dn ) = +1. Let us suppose that N (1) = N (−1) + m, where m is a positive integer with m ≤ |N | − N (−1).

Un ) being a profile, F (U ) = RU is the ordering generated by F , when the utility profile is U . After unrestricted domain, the second condition on F that we introduce is Arrow’s independence of irrelevant alternatives, now defined for n-tuples of individual utility functions. The meaning of condition I is precisely the same as before. If for any two social alternatives x, y ∈ X and two utility profiles U and U , both x and y obtain the same n-tuple of utilities in U and U , then RU and RU must coincide on {x, y}.

For the moment, we do not consider the boundaries between the regions but only the interior of the four regions. From the weak Pareto principle, it is clear that all utility vectors in region I are socially preferred to the reference point u, ¯ and the latter is preferred to all vectors in region III. What can be said about the points in region II in comparison with u¯ and the points in region IV against u? ¯ In the following, it will be shown in several steps that either all points in II are preferred to u¯ and the latter is preferred to all points in IV or all points in IV are preferred to u¯ and u¯ again is preferred to all points in II.

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