Homework Answers
1.Yes There is a Condorcet winner.
Condorcet winner is one who wins majority of vote in every pairing of head to head election against other candidates.
In this case let's take A,
A vs B,
A wins 3 votes(person 1,2,4) and B wins 2.Therefore A is the winner.
A vs C,
A wins 3 votes against C (person 1,4,5) and C wins 2.Again A is the winner.
Therefore A is the Condorcet winner.
Since A wins in pairwise election against B and C,we can see that B and C will lose in their corresponding elections against A.
No there is no preference cycle because there is a Condorcet winner.
If there was a preference cycle,there wouldn't be a winner and all methods elect same candidate.But this is not the case.We can see that A is the winner against B and C in Condorcet method.
2.In the given case if all people votes sincerely then A would win 3 votes (person 1,4,5) against C with 2 votes in the first process.
In the second step also A would win with 3 votes against B with person 1,2,4 favouring A.
One individual who would gain from not voting sincerely is person 5.Person 5 prefers B against A and C and would prefer B as the winner.
Therefore in the first step,if he favors C against A then the winner of the first step of voting would be C instead of A.In the subsequent step B would be declared winner having person 1,3,5 favouring B thereby making person 5's first choice as winner.
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Question 2
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A three-person committee has to choose a winner for a national art prize. After some debate, there are three candidates still under consideration: a woman who draws antelope in urban settings, a man who makes rectangular lead boxes, and a woman who sculpts charcoal. Lets call these candidates a, b and c and call the committee members 1, 2 and 3. The...
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1. What's the payoff of each situation?
2. How many strategies does each player A and B have?
A three-person committee has to choose a winner for a national art prize. After some debate, there are three candidates still under consideration: a woman who draws antelope in urban settings, a man who makes rectangular lead boxes, and a woman who sculpts charcoal. Lets call these candidates a, b and c and call the committee members 1, 2 and 3. The...
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