economics

economics Questions on Voting 1. Does the following family of preferences over the three alternatives X, Y, Z have the single-peak property? Explain. There are four preference orderings, each represented by a column, and a higher alternative is preferred to a lower one. X Z Z Y Z X Y Z Y Y X X 2. Suppose that an odd number of individuals have single-peak preferences. Explain why the mostpreferred alternative of the median voter will defeat every other proposal by a majority votes. 3. Consider majority rule with six people. Because there is an even number of individuals there is a possibility of ties. We will say that a is a unique majority winner if there is no feasible alternative that defeats a by a majority, and for every other feasible alternative ß there is at least one other feasible alternative that defeats ß by some majority. Use Tables 1 and 2 to show that the rule that selects the unique majority winner can be manipulated by a single individual. Table 1 Person 1 Person 2 Person 3 Person 4 Person 5 Person 6 X X W Y Z Z Y W Y Z X W Z Y X W W Y W Z Z X Y X Table 2 Person 1 Person 2 Person 3 Person 4 Person 5 Person 6 X X Y Y Z Z Y W Z Z X W Z Y W W W Y W Z X X Y X