Game Theory

Say that three people are deciding among four candidates, a, b, c, d. Each person has preferences over the candidates: for example, a person might prefer b best, c second-best, a third-best, and d least. 

a. Say that I tell you that b has 9 Borda count points. Can you conclude that b is the Condorcet winner? If so, please explain why. If not, please write down preferences for each person which make it so that b has 9 Borda count points but c is the Condorcet winner. 

b. Say that I tell you that b has 8 Borda count points. Can you conclude that b is the Condorcet winner? If so, please explain why. If not, please write down preferences for each person which make it so that b has 8 Borda count points but c is the Condorcet winner. 

c. Say that I tell you that b has 7 Borda count points. Can you conclude that b is the Condorcet winner? If so, please explain why. If not, please write down preferences for each person which make it so that b has 7 Borda count points but c is the Condorcet winner. 

d. Is it possible for the Borda count winner to be different from the Condorcet winner? If so, please write down preferences for each person which make it so that the Borda count winner is different from the Condorcet winner. If not, please explain why not.