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HW 24 (+24) Federalism, Parliamentary Elections 1. (+16) Consider a parliamentary election in a country with six political parties, who compete for 100 seats by adopting platform policies in a one-dimensional policy space. Citizens’ preferences are single-peaked, and each citizen votes sincerely for the party whose platform is closest to her ideal policy. The outcome of this is that parties ??, ??, ??, ??, ??, and ?? receive 26, 7, 14, 19, 12, and 22 seats, respectively. From this position, parties must form a coalition government. a. Is there a majority party? b. Identify all minimum winning coalitions. c. Identify the minimum winning coalition(s) with the fewest parties. d. Identify the minimum winning coalition(s) with the fewest seats. e. Identify all minimum connected winning coalitions. f. Identify the minimum connected winning coalition(s) with the fewest parties. g. Identify the party of the median voter. h. What coalition do you predict will form, and why? 2. (+8) Consider the following variation on the Downsian model: there are a continuum [0,1] of policy alternatives and a continuum of voters with single-peaked preferences distributed uniformly across [0,1] , plus two parties, ?? and ?? , with preferences for left- and right-wing policies, respectively. Specifically, the two parties have utility ???? = 1 − ?? and ???? = ?? , respectively, where ?? ∈ [0,1] is the policy outcome. The two parties simultaneously adopt policy positions ???? and ????, and each citizen then votes for whichever party is closest to his own ideal point. That is, a fraction ???? = � ????+???? 2 − 0� vote ?? and a fraction ???? = �1 − ????+???? 2 � vote ?? . The resulting policy outcome is a weighted average ?? = ???????? + ???????? of the two parties’ platforms. a. (+2) Before working things out formally, conjecture what platforms the parties will adopt in equilibrium. What is the basis for your conjecture? b. (+4) Now work things out: in equilibrium, what platforms do the parties adopt? c. (+2) How does this compare with the predictions of a standard Downsian model? What is an intuition for why they are the same, or why they are different? HW 24 (+24) Federalism, Parliamentary Elections