Social Choice_Majority Judgment

Social Choice_Majority Judgment - Majority Judgment Matt...

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Majority Judgment Matt Van Essen University of Alabama Van Essen (U of A) MJ 1 / 24
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New Environment In this set of notes we outline a new method of social choice called "Majority Judgment" due to Balinski and Laraki. The new social choice environment again begins by identifying the people involved in the decision making process, the alternatives these people must somehow decide between, and a method for summarizing an individuals°preferences of these alternatives. Van Essen (U of A) MJ 2 / 24
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Set of Individuals The collection of individuals or voters is still denoted by the set I . This set is just the list of names of all voters who are allowed to participate in the group decision. Speci±c individuals in this set are referenced using numbers 1 , 2, etc. If we want to talk about an arbitrary voter then we use i . We use N to refer to the total number of individuals. Thus, the set of individuals is I = f 1 , ..., N g . Van Essen (U of A) MJ 3 / 24
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Set of Alternatives This set of alternatives is still denoted A , where an individual element will be a i where i = 1 , ..., M . Thus, A = f a 1 , a 2 , ..., a M g . Van Essen (U of A) MJ 4 / 24
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Grades and Preferences Last, we need some way of representing an individual°s preferences over the set of alternatives. In particular, we need a set of messages that allow the voters to communicate their preferences. In this new model, we are going to let voters send grades from a common language . Van Essen (U of A) MJ 5 / 24
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Grades and Preferences A language Λ is a set of grades. We denote the grades by using lowercase g °s. So Λ = f g 1 , g 2 , g 3 , ..., g L g . The grades are ordered and we will make the convention that g 1 , the grade listed ±rst in Λ , is the highest grade, g 2 , the second highest grade, etc. Van Essen (U of A) MJ 6 / 24
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Grades and Preferences In the model, individuals will choose a grade for each of the M alternatives.
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  • Spring '12
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