Rubinstein2005-page133

Rubinstein2005-page133 - duce a complete preference...

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October 21, 2005 12:18 master Sheet number 131 Page number 115 Social Choice 115 The Basic Model A basic model of social choice consists of the following: X : a set of social alternatives. N : a Fnite set of individuals (denote the number of elements in N by n ). Â i : individual i ’s linear ordering on X (a linear ordering is a preference relation with no indifferences, i.e., for no x 6= y , x i y ). Profle :A n n -tuple of orderings ( Â 1 , ... , Â n ) interpreted as a certain “state of society.” SWF ( Social Wel±are Function ): A function that assigns a single (social) preference ( not necessarily a linear ordering) to every proFle. Note that 1. The assumption that the domain of an SW± includes only strict preferences is made only for simplicity of presentation. 2. An SW± attaches a preference relation to every possible proFle and not just to a single proFle.
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Unformatted text preview: duce a complete preference relation. An alternative concept, called Social Choice ±unction, attaches a social alternative, in-terpreted as the society’s choice, to every proFle of preference relations. 4. An SW± aggregates only ordinal preference relations. The framework does not allow us to make a statement such as “the society prefers a to b since agent 1 prefers b to a but agent 2 prefers a to b much more.” 5. In this model we cannot express a consideration of the type “I prefer what society prefers.” 6. The elements in X are social alternatives. Thus, an individual’s preferences may exhibit considerations of fairness and concern about other individuals’ well-being. Examples Let us consider some examples of aggregation procedures. We will often use % as a short form of F ( Â 1 , . . . , Â n ) ....
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

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