Rationalizable voting

When is a finite number of binary voting choices consistent with the hypothesis that the voter has preferences that admit a (quasi)concave utility representation? I derive necessary and sufficient conditions and a tractable algorithm to verify their validity. I show that the hypothesis that the voter has preferences represented by a concave utility function is observationally equivalent to the hypothesis that she has preferences represented by a quasiconcave utility function, I obtain testable restrictions on the location of voter ideal points, and I apply the conditions to the problem of predicting future voting decisions. Without knowledge of the location of the voting alternatives, voting decisions by multiple voters impose no joint testable restrictions on the location of their ideal points, even in one dimension. Furthermore, the voting records of any group of voters can always be embedded in a two-dimensional space with strictly concave utility representations and arbitrary ideal points for the voters. The analysis readily generalizes to choice situations over general finite budget sets.Voting, revealed preferences, ideal points

Dynamics of Westminster Parliamentarism

Policy dynamics; 2-party system; median voter.

Proposal Rights and Political Power

In a canonical model of sequential collective bargaining over a divisible good we show that equilibrium expected payoffs are not restricted by players’ voting rights or their impatience. For all monotonic voting rules and discount factors, and for all divisions of the good among players, there exists a stationary proposal-making rule such that this division represents players’ expected payoffs in a Stationary Subgame Perfect Nash equilibrium in pure strategies. The result attests to the significance of proposal rights in determining political power in collective deliberations.Power, Proposal Rights, Voting Rights.

Genericity of Minority Governments : The Role of Policy and Office

We develop a general theory for the emergence of minority governments in multiparty parliamentary systems using a bargaining model in the tradition of Baron and Ferejohn, 1989. We show that generically (i.e. except for a set of Lebesgue measure zero in the space of the model’s parameters) minority governments form with strictly positive probability when office utility from cabinet positions is small relative to political disagreement. The result holds for policy spaces of arbitrary finite dimension and a general class of preferences over the government agreements space.Coalition theory, Minority Governments, Parliamentary systems.

A Reputational Theory of Two Party Competition

We study a dynamic game of incomplete information in which two political parties contest elections with endogenously formed reputations regarding the preferences that prevail within each party. Party preferences exhibit serial correlation and change with higher probability following defeat in elections. We show that when partisans care sufficiently about office, extreme policies are pursued with positive probability by the government if the ruling party is perceived relatively more extreme than the opposition. In equilibrium such policies occur when (a) both parties are perceived to be more extreme than a fixed benchmark level, and (b) elections are close in that both parties have similar reputations. Two qualitatively different equilibrium dynamics are possible depending on the relative speed with which preferences of parties in government or in the opposition change: One produces regular government turnover and extreme policies along the path of play, another involves a strong incumbency advantage and policy moderation.

A Theory of Minority and Majority Governments

We develop a theory of the emergence of minority and majority governments in multiparty parliamentary systems using a canonical non-cooperative bargaining model and assuming a policy space of arbitrary finite dimension, any number of political parties, and a general class of preferences over the government agreement space. Only majority governments form in the absence of significant political disagreement. Generically, minority governments form with positive probability when parties represented in parliament are ideologically polarized (or when utility from holding cabinet office is small relative to partisan political disagreement). Rather than being paradoxical, minority governments are a regular equilibrium phenomenon.

Majority Rule Dynamics with Endogenous Status Quo

We analyze a stochastic bargaining game in which a new dollar is divided among committee members in each of an infinity of periods. In each period, a committee member is recognized and offers a proposal for the division of the dollar. The proposal is implemented if it is approved by a majority. If the proposal is rejected, then last period’s allocation is implemented. We show existence of equilibrium in Markovian strategies. It is such that irrespective of the initial status quo, the discount factor, or the probabilities of recognition, the proposer extracts the entire dollar in all periods but the initial two. We also derive a fully strategic version of McKelvey’s (1976), (1979) dictatorial agenda setting, so that a player with exclusive access to the formulation of proposals can extract the entire dollar in all periods except the first. The equilibrium collapses when within period payoffs are sufficiently concave. Winning coalitions may comprise players with high instead of low recognition probabilities, ceteris paribus.

Robust Rational Turnout

We establish that, except for a finite set of common costs of participation, all equilibria of a class of complete information voting games (as in Palfrey and Rosenthal (1983)) are regular. Thus, all the equilibria of these games (including those exhibiting high turnout rates) are robust to small but arbitrary payoff perturbations, and survive in nearby games with incomplete information about voting costs and/or about the fraction of supporters of the two candidates. We also show that all the equilibria of these complete information games exhibit minimal heterogeneity of behavior, so that the strategies of indifferent players are characterized by at most two probabilities.Turnout, Regular Equilibrium.

Robust Rational Turnout

We establish that, except for a finite set of common costs of participation, all equilibria of a class of complete information voting games (as in Palfrey and Rosenthal (1983)) are regular. Thus, all the equilibria of these games (including those exhibiting high turnout rates) are robust to small but arbitrary payoff perturbations, and survive in nearby games with incomplete information about voting costs and/or about the fraction of supporters of the two candidates. We also show that all the equilibria of these complete information games exhibit minimal heterogeneity of behavior, so that the strategies of indifferent players are characterized by at most two probabilities.Turnout, Regular Equilibrium.

Regularity of Pure Strategy Equilibrium Points in a Class of Bargaining Games

For a class of n-player (n ? 2) sequential bargaining games with probabilistic recognition and general agreement rules, we characterize pure strategy Stationary Subgame Perfect (PSSP) equilibria via a finite number of equalities and inequalities. We use this characterization and the degree theory of Shannon, 1994, to show that when utility over agreements has negative definite second (contingent) derivative, there is a finite number of PSSP equilibrium points for almost all discount factors. If in addition the space of agreements is one-dimensional, the theorem applies for all SSP equilibria. And for oligarchic voting rules (which include unanimity) with agreement spaces of arbitrary finite dimension, the number of SSP equilibria is odd and the equilibrium correspondence is lower-hemicontinuous for almost all discount factors. Finally, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.Local Uniqueness of Equilibrium, Regularity, Sequential Bargaining.