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2. Suppose 3 students are running for student-body president: Ahmad, Beatriz, and Cathy. Students have the following true preferences among the choices: Player First-best Second-best Third-best Ahmad 150 25 125 Beatriz 100 125 75 Cathy 125 0 175 For example, 150 people believe Ahmad is the best option, 25 people believe Ahmad is the second-best option, and 125 people believe that Ahmad is the third-best option. The winner is determined via Borda count. (a) (5 points) Suppose people vote sincerely. First-place votes are worth X points, second-place votes are worth 2 points, and third-place votes are worth 1 point. For what values of X does Ahmad win? (b) (5 points) Now suppose first-place votes are worth 4 points, second-place votes are worth 2 points, and third-place votes are worth 1 point. Assume that Cathy-supporters (people with Cathy as first-choice) all have Beatriz as their second- choice - perhaps Cathy and Beatriz share many friends. Assume the table above is common knowl- edge. If Cathy voters vote strategically and everyone else votes sincerely, who wins