Suppose we have a group of 55 individuals, choosing among five alternatives: (A,B,C,D,E). Each individual has complete and transitive preference ordering. We allow only strict orderings, so that ties are not allowed at the individual level. 

(a) If we impose no restriction on individual preferences, how many complete and transitive strict preference orderings would be possible for each individual? 

Of the possible complete and transitive strict individual preference orderings that you computed in part (a), we consider the following six distinct orderings. The number of individuals holding each ordering is shown in the parenthesis. Thus we are considering six groups, each of which has the same preference ordering. 

(b) Which alterative would be a Condorcet winner? (If there are more than one, list all of them.) 

(c) If plurality voting is used, which alternative (or alternatives) would be the winner(s)? Is the plurality winner a Condorcet winner? 

(d) If Borda count is used, which alternative (or alternatives) would be the winner(s)? Is the Borda count winner a Condorcet winner? 

(e) If single transferrable voting (Hare voting) is used, which alternative (or alternatives) would be the winner(s)? Is the Hare voting winner a Condorcet winner? 

(f) Suppose approval voting is used. Each group is assumed to approve of all the alternatives above the line in the table. For example, members of group III approve of four (CBE D) out of the five alternatives. Which alterative(s) would be the approval voting winner(s)? Does the approval voting select a Condorcet winner?

Transcribed Image Text:

Group 1 (18) Group II(12) Group III(10) A D E C B B E D с A C B E D A Group IV(9) Group V(4) D C E B A E B D с A Group VI(2) E с D B A Group 1 (18) Group II(12) Group III(10) A D E C B B E D с A C B E D A Group IV(9) Group V(4) D C E B A E B D с A Group VI(2) E с D B A

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