Each councillor knows her own type, and she knows the probabilities of observing each type of voter, p L , p C , and p R (with p L 1 p C 1 p R 5 1). The behavior of the Center-type voters in the...

Each councillor knows her own type, and she knows the probabilities of observing each type of voter, p_L, p_C, and p_R
(with p_L
1 p_C
1 p_R
5 1). The behavior of the Center-type voters in the first-round election is the only unknown in this situation and will depend on the probabilities that the various preference types occur. Suppose here that a Center-type voter believes (in contrast with the case considered in the chapter) that other Center types will vote strategically; suppose further that the Center-type’s payoffs are as in Section 4.C: 1 if A wins, 0 if G wins, and 0 , u , 1 if D wins.

(a) Under what configuration of the other two votes does the Centertype voter’s first-round vote matter to the outcome of the election? Given her assumption about the behavior of other Center-type voters, how would she identify the source of the first-round votes?

(b) Following the analysis in Section 4.C, determine the expected payoff to the Center type when she votes truthfully. Compare this with her expected payoff when she votes strategically. What is the condition under which the Center type votes strategically?