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 finite set of individuals (denote the number of elements in N by n ). i : individual i ’s linear ordering on X (a linear ordering is a preference relation with no indifferences, i.e., for no x = y , x i y ). Profile : An n -tuple of orderings ( 1 , . . . , n ) interpreted as a certain “state of society.” SWF ( Social Welfare Function ): A function that assigns a single (social) preference ( not necessarily a linear ordering) to every profile. Note that 1. The assumption that the domain of an SWF includes only strict preferences is made only for simplicity of presentation. 2. An SWF attaches a preference relation to every possible profile and not just to a single profile. 3. The SWF aggregation of preference relations is required to pro-
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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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  • Fall '10
  • aswa
  • Binary relation, Social Choice and Individual Values, social choice, preference relation, complete preference relation

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