# Each councillor knows her own type, and she knows the probabilities of observing each type of voter,

Each councillor knows her own type, and she knows the
probabilities of observing each type of voter, pL, pC,
and pR (with pL 1 pC 1 pR 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.

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Each councillor knows her own type, and she knows the probabilities of observing each type of voter,
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(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?