A Solution Concept for Majority Rule in Dynamic Settings

We define and explore the notion of a Dynamic Condorcet Winner (DCW), which extends the notion of a Condorcet winner to dynamic settings. We show that, for every DCW, every member of a large class of dynamic majoritarian games has an equivalent equilibrium, and that other equilibria are not similarly portable across this class of games. Existence of DCWs is guaranteed when members of the community are sufficiently patient. We characterize sustainable and unsustainable outcomes, study the effects of changes in the discount factor, investigate efficiency properties, and explore the potential for achieving renegotiation-proof outcomes. We apply this solution concept to a standard one-dimensional choice problem wherein agents have single-peaked preferences, as well as to one involving the division of a fixed aggregate payoff.

[1]  Antonio Rangel.  Forward and Backward Intergenerational Goods: Why Is Social Security Good for the Environment? , 2003 .

[2]  Per Krusell,et al.  Politico-economic equilibrium and economic growth , 1997 .

[3]  Dilip Abreu.  Extremal equilibria of oligopolistic supergames , 1986 .

[4]  Thomas F. Cooley,et al.  A Positive Theory of Social Security Based on Reputation , 1999, Journal of Political Economy.

[5]  Nicholas R. Miller,et al.  Graph- Theoretical Approaches to the Theory of Voting* , 1977 .

[6]  E. Stacchetti,et al.  Towards a Theory of Discounted Repeated Games with Imperfect Monitoring , 1990 .

[7]  D. Epple,et al.  Cooperation and punishment under repeated majority voting , 1987 .

[8]  M. Breton,et al.  On the core of voting games , 1987 .

[9]  Barry R. Weingast,et al.  Uncovered Sets and Sophisticated Voting Outcomes with Implications for Agenda Institutions , 1984 .

[10]  Eric Maskin,et al.  Renegotiation in Repeated Games , 1987 .

[11]  Gerald H. Kramer,et al.  On a Class of Equilibrium Conditions for Majority Rule , 1973 .

[12]  Debraj Ray,et al.  Collective Dynamic Consistency in Repeated Games , 1989 .

[13]  J. Ferejohn,et al.  Bargaining and Agenda Formation in Legislatures , 1987 .

[14]  John Duggan,et al.  Repeated Downsian electoral competition , 2006, Int. J. Game Theory.

[15]  Roberto Perotti.  Political Equilibrium, Income Distribution, and Growth , 1993 .

[16]  R. McKelvey.  Intransitivities in multidimensional voting models and some implications for agenda control , 1976 .

[17]  A. Downs.  An Economic Theory of Democracy , 1957 .

[18]  G. Cox.  Non-collegial simple games and the nowhere denseness of the set of preference profiles having a core , 1984 .

[19]  David P. Baron,et al.  A Dynamic Theory of Collective Goods Programs , 1996, American Political Science Review.

[20]  Antonio Rangel,et al.  The Power of the Last Word in Legislative Policy Making , 2006 .

[21]  John E. Roemer,et al.  The Democratic Political Economy Of Progressive Income Taxation , 1999 .

[22]  N. Schofield.  Generic Instability of Majority Rule , 1983 .

[23]  Charles R. Plott,et al.  A Notion of Equilibrium and Its Possibility Under Majority Rule , 1967 .

[24]  Gene M. Grossman,et al.  Intergenerational Redistribution with Short-Lived Governments , 1996 .

[25]  G. Thompson,et al.  The Theory of Committees and Elections. , 1959 .

[26]  Stephen Coate,et al.  An Economic Model of Representative Democracy , 1997 .

[27]  Per Krusell,et al.  Vested Interest In a Positive Theory of Stagnation and Growth , 1996 .

[28]  N. Schofield,et al.  Instability of Simple Dynamic Games , 1978 .

[29]  Kevin Roberts.  Condorcet cycles? A model of intertemporal voting , 2007, Soc. Choice Welf..

[30]  B. Ravikumar,et al.  Public versus Private Investment in Human Capital: Endogenous Growth and Income Inequality , 1992, Journal of Political Economy.

[31]  Jerzy A. Filar,et al.  Dynamic Cooperative Games , 2000, IGTR.

[32]  Jos E-V,et al.  On the Size of U.S. Government: Political Economy in the Neoclassical Growth Model , 1999 .

[33]  S. Banks Jerey.  A Bargaining Model of Collective Choice , 1999 .

[34]  R. McKelvey.  General Conditions for Global Intransitivities in Formal Voting Models , 1979 .

[35]  G. Tabellini,et al.  Is Inequality Harmful for Growth , 1994 .

[36]  Nicholas R. Miller.  A New Solution Set for Tournaments and Majority Voting: Further Graph- Theoretical Approaches to the Theory of Voting , 1980 .

[37]  Ariel Rubinstein,et al.  A NOTE ABOUT THE "NOWHERE DENSENESS" OF SOCIETIES HAVING AN EQUILIBRIUM UNDER MAJORITY RULE' , 1979 .

[38]  John Duggan,et al.  A Social Choice Lemma on Voting Over Lotteries with Applications to a Class of Dynamic Games , 2006, Soc. Choice Welf..

[39]  Richard D. McKelvey,et al.  Sophisticated Voting and Agenda Independence in the Distributive Politics Setting , 1987 .

[40]  Jeffrey S. Banks,et al.  Singularity theory and core existence in the spatial model , 1995 .

[41]  S. Slavov.  Age Bias in Fiscal Policy: Why Does the Political Process Favor the Elderly? , 2006 .

[42]  J. Ferejohn,et al.  Bargaining in Legislatures , 1989, American Political Science Review.

[43]  Richard D. McKelvey,et al.  Covering, Dominance, and Institution Free Properties of Social Choice , 1986 .