By Gaertner W.
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Extra resources for A primer in social choice theory
Then, our argumentation used the ordering property of the social preference relation. What about the independence condition? We arrived at xPz without any information about the preferences of individuals other than person J on alternatives x and z. We have, of course, assumed yPi x and yPi z, but according to condition I , these preferences have no role to play in the social decision between x and z. Therefore, xPz must be the consequence of xPJ z alone, regardless of the other orderings (remember that individual preferences are assumed to be transitive).
N}. Conditions U , I and PI have very strong implications for F . 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.
Let us discuss more interesting cases. Consider a student who wants to live as closely to the university as possible or a frequent traveller who wants to have an apartment as close to the central railway station as possible. Both individuals will have decreasing preferences for locations further away from their optimal site. Or consider three individuals with low, medium, and high income, respectively, who plan to purchase cars. Let us assume that there are three categories of cars, a low-priced small car, a medium-priced and mediumsized car, and an expensive large car.