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A primer in social choice theory by Gaertner W. PDF

By Gaertner W.

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We know that since we are in the framework of ordinal and non-comparable utilities, these transformations do not change the rankings of the two persons. Therefore, if aP ∗ u¯ as assumed, then bP ∗ u. ¯ Notice that this result holds for any points a, b in the interior of region II. Therefore, all points in the interior of region II are ranked identically with respect to reference point u¯ (but not, of course, ranked identically with respect to each other). The reasoning above holds analogously for all points in region IV with respect to u.

Then again, one of Arrow’s basic properties would be violated as we shall see in a moment. We now wish to state and discuss Arrow’s general result in greater detail. 3. Let E denote the set of preference orderings on X and let E stand for a subset of orderings that satisfies a particular restriction. E n will denote the cartesian product E × · · · × E , n times. An element of E n is an n-tuple of preference orderings (R1 , . . , Rn ) or the profile of an n-member society consisting of preference orderings.

Sen (1977b) has shown that the three conditions together imposed on F are equivalent to a property called strong neutrality. Strong neutrality requires that the social evaluation functional F ignore all non-utility information with respect to the alternatives, such as names or rights or claims or procedural aspects. The only information that counts is the vector of individual utilities associated with any social alternative. This ‘fact’ has been termed ‘welfarism’ in the literature of social choice theory as well as bargaining theory (we briefly discussed this issue in our introduction) and has been sharply criticized from different angles.

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