Question

1. Throughout this question, assume that you are one of only three voters. Suppose voters are only concerned with the quality of candidates. In particular, let q R L be the difference in quality between candidate R and candidate L. There is no cost of voting and the utility is equal to one if the higher quality candidate wins and zero otherwise The winner is determined by majority rule. When q is observable, each voter votes for the higher quality candidate and gains utility of one. (a) From now on assume that q is unobserved by voters and that either c andidate is equally likely to be the higher quality candidate. Given these beliefs, would you turnout to vote? If so, who would you vote for? If not, explain why not. Compute your expected utility given the action you take.

Answer 1

a) Yes, I would turnout for vote because expected utility from voting is equal = 1/2 which o/w will be zero If I don't vote.

Note that there is no cost of voting.

Now,

There are two candidates and one of them is a good candidate hence,

the probability that a candidate is good candidate = 1/2.

this Pr(x=good) = 1/2

similarly, Pr(x=bad) = 1/2

we have utility function as,

$\fn_cm \small U(x)=\left\{\begin{matrix} 1 & If &x= good \\ & & \\ 0 & If &x= bad \end{matrix}\right.$

thus, Expected Utility (EU),

$\small EU = Pr(x=good)\times U(x=good)+Pr(x=bad)\times U(x=bad)$

$\small EU = (\frac{1}{2}\times 1)+(\frac{1}{2}\times 0)$

$\small EU = \frac{1}{2}$