Assignment:

Problem 1:

Assume a voter has a strict preference over any two candidates in the set of Clinton, Obama and Edwards; in other words, it is not the case that he is indifferent between some two candidates in this set. In addition, assume that the voter is not rational.

(1) Prove that a voter who prefers Obama over Clinton has to prefer Edwards over Obama and Clinton over Edwards. Present your reasoning.

(2) Prove that if all voters are not rational then either (i) all of them have identical preferences or (ii) the set of all voters is split into two subsets such that in each subset all voters have identical preferences.

Problem 2:

Let's go back to explaining the survey data in which 60% chose Edwards over Obama, 60%chose Edwards over Clinton, 60% chose Clinton over Obama and then when asked to cast a single vote for one of the three candidates, 45% chose Clinton, 30% Obama, and 25%Edwards.

(1) Prove that it is not possible that all voters are rational (have transitive preferences.)

(2) Suppose now that the distribution of votes was not 45% chose Clinton, 30% Obama, and25% Edwards but 38% Clinton, 32% Obama and 30% Edwards; pair-wise data remains unchanged. Prove that it is possible now that all voters are rational (have transitive preferences) and calculate the percentage of votes for each of the six different orderings of the three candidates.