2. Society consists of three types of individuals, and has to choose between three alternatives, x, y and 2. Type A has preferences 3: > y > 2. Type B has preferences 2 > y > m. Type C has preferences y > z > m. Suppose that there are 45 percent type A's, 35 per cent type B and 20 percent type C in the population. a) Is there a Condorcet winner in the population? b) Suppose that the voters are asked to list their preference ranking over alternatives, and the Maine voting procedure is adopted. That is, if no alternative commands a majority of rst preference votes, then the one with the lowest rst preference votes is eliminated, and then the choice between the two remaining alternatives is based on which is preferred by more voters. What will be the outcome of the election if voters truthfully report their preferences? Does any type of voter have an incentive to misrepresent her preferences? c) Are the preferences singlepeaked