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(8+3+3+5+3-22 points) Answer the following questions based on the preference sch

ID: 3210081 • Letter: #

Question

(8+3+3+5+3-22 points) Answer the following questions based on the preference schedule to the right for an election decided with the Borda Count method 9 4 5 4 6 1st A C D B D 2nd C ABA A 3rd D B A C C a. Determine the winner of the election (Show point totals for each player.) b. Explain whether or not there was a Majority candidate in this election. c. Does this election demonstrate a violation of the Majority criterion? Explain why or why not d. Determine whether or not there was an Anti-Condorcet candidate in this election. Provide justification for your answer. e. Does this election demonstrate a violation of the anti-Condorcet criterion? Explain why or why not

Explanation / Answer

a) Let us assign 4 points for first place, 3 for second , 2 for third and 1 for fourth place respectively.

Now we do the count:

A = 4 (9) + 3(4+4+6) + 2(5) + 1(0) = 88

B = 4(4) + 3(5) + 2(4) + 1(9+6) = 54

C = 4(4) + 3(9) + 2(4+6) + 1(5) = 68

D = 4(5+6) + 3(0) + 2(9) + 1(4+4) = 70

As candidate A scored the maximum points , A is clearly the winner of the election

b) Candidate D got majority of the first preference votes (received 11 votes) hence D is the majority candidate.

c)As per the majority criteria, if a candidate has majority of the first-preference votes, then that candidate should be the winner of the election. However, in this case A is the winner even though D was the majority candidate.

Hence, this election violates the majority criterion.

d) A is beaten by B, C and D for the fourth preference and D is beaten by A, C and D for the second preference

as such A and D can be considered anti-condorcet. candidates

e) As per the anti-condorcet criteria, an anti-condorcet candidate must loose the election. However, in this case, A is the winner even thoughit is an anti-condorcet candidate