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ECO316H1 (3)

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Ettore Damiano

Solutions to Chapter 16 ExercisesSOLVED EXERCISESS1Under truthful voting A should match Geology and Sociology in the first vote with the winner Geology to face Philosophy in the second round Under strategic voting A should match Philosophy and Sociology in the first round In order to prevent a Geology outcome B casts a strategic vote for Philosophy Philosophy goes on to beat GeologyS2Allocate points in the following way 5 for a firstplace vote 2 for a secondplace vote and 1 for a thirdplace vote A then receives 551112 points B gets 225211 and C gets 11259S3aUnder a plurality voting system with truthful voting Proposal 1 gets 20 votes and Proposals 2 and 3 get 15 votes eachbUnder a 321 Borda count with truthful voting Proposal 1 gets 601530105 points Proposal 2 gets 404515100 points and Proposal 3 gets 20304595 pointscFor both the second and third type of voter to gain Proposal 3 must win rather than Proposal 1 This can be achieved if types 2 andor 3 change their votes in such a way that Proposal 1 gets fewer points andor Proposal 3 gets more One example would be if types 2 and 3 vote as though their rankings were Proposal 3 Proposal 2 Proposal 1 With this voting pattern Proposal 1 gets 60151590 points Proposal 2 gets 403030100 and Proposal 3 gets 204545110Note two things First other voting schemes will also result in Proposal 3s winning For example if only the type 2s vote with a 321 ranking Proposal 3 still wins Second a single member of types 2 or 3 cant alter the outcome by changing only her vote coordinated action is requiredS4aThe preferences create a standard intransitive ordering so none of the three alternatives would win a majority vote with truthful votingSolutions to Chapter 16 Exercises1 of 4
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