Electing Ideological Representatives(pdf, 365K, updated July 25, 2006)

Synopsis: In this paper, I address the question of how stationary equilibrium play in the infinite horizon bargaining game described in the first paper ("Polarized Coalitions ..."), shapes the incentives for voters electing representatives who go on to play that game. Results are preliminary, but numerical analysis suggests that while voters rarely want ``vote for themselves'' it is true that optimal choice of representative ideal point in weakly increasing in the ideal point of the voter. The origin of forces which tug at voters to vote either more moderately than their own ideal point or more extreme than their own ideal point are discussed.

Expected Utility Calculator (Java Jar File) This calculator shows how a voter utility expected utility is calculated based on the elected of a representative with a given ideal point. Parameters are the ideal point of the voter, the ideal point of candidate to represent the voter in the subsequent bargaining game and the ideal points of the other legislators with whom the voter's representative will interact in that game. "Voter alpha" is the relative weight in the voter's utility function on the public policy term. Voter's alpha = 1 means the voter only cares about the public policy outcome, alpha = 0 means that the voter only cares about the share of the pot of money his representative ends up with in the bargaining session.

Voter Best Response / Voter Utility (Java Jar File) 2-Period Bargaining Model Version This allow the user to see two graphs. The first shows the voter's utility as a function of the ideal point of their representative in the bargaining game. User can change the value of the voter's ideal point, the value of voter's alpha (the relative weight in the voter's utility function on the public policy outcome) as well as the ideal points of the other legislators in the game. The second shows the best-response of the voters as a function of voter ideal points. That is it shows for each voter ideal point, the ideal point of the representative, who if elected to the legislature, would maximize the voter's expected utility. All calculations are based on the assumption that the subsequent legislative bargaining game has a two-period horizon length.

Voter Best Response / Voter Utility (Java Jar File) Infinite-Horizon Bargaining Model Version User sets the ideal points of 4 out of 5 legislative representatives and a range of ideal points for a fifth. A bargaining equilibrium is calculated for each ideal point of the 5th legislator. Data tables returned include all aspects of every equilibrium requested including how voters in that 5th district ("district A") with as many ideal points as the user specifies and 100 different values of alpha are affected. All calculations are based on the assumption that the subsequent legislative bargaining game has an infinite horizon and that players arrive at the stationary equilibrium. Since no analytic solution for the equilibrium exists, each equilibrium requested must be calculated numerically.