Consider the following preference orderings of 1000 agents for candidates O = {a, b, c}147 agents: a b c401 agents: b a c32 agents: c b a420 agents: a c b(a) Who wins under Plurailty? Explain.(b) Who wins in the Borda voting? Explain.(c) Who is the Condorcet winner? Explain.(d) If you are the agenda setter and strongly prefer b. What ordering would you chose forpairwise elimination such that b wins.
Question
Consider the following preference orderings of 1000 agents for candidates O = {a, b, c}147 agents: a b c401 agents: b a c32 agents: c b a420 agents: a c b(a) Who wins under Plurailty? Explain.(b) Who wins in the Borda voting? Explain.(c) Who is the Condorcet winner? Explain.(d) If you are the agenda setter and strongly prefer b. What ordering would you chose forpairwise elimination such that b wins.
Solution
(a) Under Plurality, the candidate with the most first preference votes wins. In this case, candidate 'a' has 147 + 420 = 567 first preference votes, candidate 'b' has 401 first preference votes, and candidate 'c' has 32 first preference votes. Therefore, candidate 'a' wins under Plurality.
(b) In Borda voting, each candidate gets points based on their ranking. A first preference vote gives 2 points, a second preference vote gives 1 point, and a third preference vote gives 0 points.
For candidate 'a': (147 * 2) + (401 * 1) + (32 * 0) + (420 * 2) = 1135 points For candidate 'b': (147 * 1) + (401 * 2) + (32 * 1) + (420 * 0) = 981 points For candidate 'c': (147 * 0) + (401 * 0) + (32 * 2) + (420 * 1) = 884 points
Therefore, candidate 'a' wins in the Borda voting.
(c) A Condorcet winner is a candidate who would win a head-to-head competition against each of the other candidates. To determine this, we need to compare each pair of candidates:
'a' vs 'b': 'a' wins (567 votes to 433 votes) 'a' vs 'c': 'a' wins (567 votes to 433 votes) 'b' vs 'c': 'b' wins (548 votes to 452 votes)
Therefore, candidate 'a' is the Condorcet winner.
(d) If you are the agenda setter and strongly prefer 'b', you would want to eliminate the candidate who is most likely to beat 'b' in a head-to-head competition first. In this case, that would be 'a'. So, you would choose the ordering 'a', 'c', 'b' for pairwise elimination. This way, 'a' would be eliminated first (losing to 'c'), and then 'b' would beat 'c' in the final round.
Similar Questions
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