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April 5, 2017 | Economic Theory | By admin | 0 Comments

By Wulf Gaertner

This introductory textual content explores the idea of social selection. Written as a primer appropriate for complicated undergraduates and graduates, this article will act as a big place to begin for college kids grappling with the complexities of social selection thought. Rigorous but available, this primer avoids using technical language and gives an updated dialogue of this swiftly constructing box. this is often the 1st in a chain of texts released in organization with the LSE.

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The functional F then is a mapping from the set of all logically possible n-tuples or profiles of utility functions into the set of all orderings of X , which we denoted by E earlier on. For U = (u1 , u2 , . . , 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.

The simple majority rule is clearly non-dictatorial, from May’s theorem we know that this rule satisfies unrestricted domain and the independence condition (remember that the 38 MAJORITY DECISION UNDER RESTRICTED DOMAINS latter is weaker than neutrality), and one can easily see that the method of majority rule fulfils the weak Pareto principle (actually, neutrality and positive responsiveness together imply the Pareto rule). Where lies the problem? The problem comes from the fact that simple majority voting can yield a social relation that is not transitive.

The requirement of single-peakedness is a sufficient condition on the set of individual preferences. This means that whenever a set of individual preferences satisfies this condition, the social relation generated by the method of majority decision is an ordering, given the oddness requirement. It also means that single-peakedness is not a necessary condition in order to obtain an ordering (see Sen and Pattanaik (1969) for the precise meaning of necessary and sufficient conditions in the present context).

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