By Wulf Gaertner
This introductory textual content explores the idea of social selection. Written as a primer compatible for complex undergraduates and graduates, this article is going to act as an immense place to begin for college students grappling with the complexities of social selection idea. Rigorous but available, this primer avoids using technical language and offers an up to date dialogue of this speedily constructing box. this is often the 1st in a sequence 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)
Dn ) = −1. 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).
Let us therefore assume that there is no almost decisive individual. As the reader will see shortly, this leads to a contradiction. Remember that our frame of argumentation is given by conditions U , P and I together with the ordering property of f . By condition P, there is at least one decisive set for any ordered pair (x, y), viz. the set of all individuals. Therefore, there also exists at least one almost decisive set. Among all the sets of individuals that are almost decisive for some pair of alternatives, let us choose the smallest one (not necessarily unique).
In other words, the better-than-orindifferent set and the worse-than-or-indifferent set with reference to any point in Euclidian space are assumed to be closed sets. The second point to remember is that given any preference ordering and its corresponding utility function, any other utility function which is generated by applying a strictly monotone transformation to the original utility function has the same informational content as the original. This property of ordinal utility will prove to be important in the sequel (remember that the Arrovian framework is purely ordinal).