By Gaertner W.
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Additional resources for A primer in social choice theory
Chapter 5. New York: John Wiley. MORE ADVANCED Sen, A. K. (1995). ‘Rationality and Social Choice’. American Economic Review, 85: 1–24. 1. The simple majority rule We have seen in Chapter 2 that any social welfare function satisfying unrestricted domain and the weak Pareto condition as well as Arrow’s independence condition and the requirement that the generated social relation be an ordering is doomed to be dictatorial. As already mentioned in Chapter 2, Arrow considered these conditions as necessary requirements in the sense that they express both rationality and the doctrines of citizens’ sovereignty in a very general way.
Since a, by assumption, is preferred to u, ¯ this relationship continues to hold after the transformations, viz. u¯ is preferred to c. And from our earlier steps in this proof we infer that u¯ is preferred to all points in region IV. Remember that assuming region II to be preferred to u¯ was arbitrary. If region II had been assumed to be worse than u, ¯ all points in region IV would turn out to be better than u. ¯ The proof is almost complete. We still have to deal with points on the boundaries.
The reader certainly remembers our remark at the end of the ﬁrst (original) proof that two individuals would sufﬁce to show the Arrovian impossibility. The diagrammatic proof unfolds in utility space. Strictly speaking, this would require us to redeﬁne the whole Arrovian set-up in terms of utility functions that are deﬁned in Euclidian space. This would be extremely cumbersome and very tiring for the reader. Therefore, in the process of redeﬁning concepts, we shall try to be as parsimonious as possible.
A primer in social choice theory by Gaertner W.