There are three individuals and four alternatives, a, b, c and d. The individual preferences are:...

 

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There are three individuals and four alternatives, a, b, c and d. The individual preferences are: Individual 1 Individual 2 Individual 3 a> b>c>d a> b>c>d b>c>d> a | Suppose the voting proceeds with the use of Borda count. The alternative listed first on a ballot gets 4 points, the alternative listed second gets 3 points, the alternative listed third gets 2, the alternative listed fourth gets 1. (a) How many points are gained by each alternative? What is the social preference? Now suppose alternatives c and d move to the top for all agents. The new individual preferences are: Individual 1 Individual 2 c>d>abc>d>a>b|c>d>b>a Individual 3 (b) How many points are gained by each alternative? What is the new social preference? (c) Use your answers to (a) and (b) to illustrate the concept of the reversal paradox. There are three individuals and four alternatives, a, b, c and d. The individual preferences are: Individual 1 Individual 2 Individual 3 a> b>c>d a> b>c>d b>c>d> a | Suppose the voting proceeds with the use of Borda count. The alternative listed first on a ballot gets 4 points, the alternative listed second gets 3 points, the alternative listed third gets 2, the alternative listed fourth gets 1. (a) How many points are gained by each alternative? What is the social preference? Now suppose alternatives c and d move to the top for all agents. The new individual preferences are: Individual 1 Individual 2 c>d>abc>d>a>b|c>d>b>a Individual 3 (b) How many points are gained by each alternative? What is the new social preference? (c) Use your answers to (a) and (b) to illustrate the concept of the reversal paradox.