this is problem of chance strategy and choice 21-5

21.5 (Nanson Method) The Nanson Method is the social choice method defined as follows: given a preference table, run the Borda count. All candidates receiving less than Bava Borda points are eliminated. The Borda count is run again without these candidates, and again, all candidates with less than the average Borda points in the new election are eliminated. Repeat until one candidate remains. This candidate is the Nanson social choice. (a) Determine the Nanson social choice for the following preference table: Number 11 13 8 14 10 16 Ist choice A B D E C 2nd choice B D E A B 3rd choice C D B 4th choice D E 5th choice E A E (b) Prove that the Nanson Method satisfies the Condorcet Winner Criterion. (c) Prove that the Nanson Method satisfies the Condorcet Loser Criterion. (d) Give an example to show that the Nanson Method is manipulable