this is problem of chance strategy and choice 21-6

21.6 (Condorcet Method) Condorcet described the following method for producing a social choice using pairwise comparisons called the Condorcet Method: given a preference table, construct the social preference graph, and label each arrow with 332 Special Topics the margin of victory. For example, if A beats B head to head by 30 votes, we write A -> B. If there is a Condorcet Winner, that candidate is the Condorcet social choice. Otherwise, remove arrows from the social preference graph one by one in increasing order until some candidate is the head of every arrow in the social preference graph. The unbeaten candidate is the Condorcet social choice. (a) Determine the Condorcet social choice for the following preference table: Number 10 20 16 15 |24 18 Ist choice B D 2nd choice B 3rd choice C E 4th choice D D 5th choice E (b) Prove that the Condorcet Method satisfies the Condorcet Winner Criterion. (c) Prove that the Condorcet Method satisfies the Condorcet Loser Criterion. (d) Give an example to show that the Condorcet Method is manipulable