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 (d) Suppose that two of you are busy studying for an exam and would prefer not to vote, but the third will definitely vote. How high does your benefit from studying need to be to prevent you and your study partner from voting?

Answer 1

As per the utility theory, which assumes rationality, a decision is made based on utility of one decision as compared to another.

Given there are only 3 voters and assuming q is observable. In this case even if one voter votes, the candidate of better quality wins and everyone derives utility one.

The other two people who didn't vote derive utility one even when only the third friend votes. Moreover, they derive utility of time by studying through the time that they would have used in voting. Thus, this leads to additional utility over and above the utility of the better quality candidate winning. Thus, their utility is more than 1 even when only the third friend goes to vote.

Thus, my benefit needs to be more than 1 to prevent me from voting which I am deriving by not going to vote and only the third friend going to vote.