Borgers, Tilman and Smith, Doug (2011): Robust mechanism design and dominant strategy voting rules.
Download (354kB) | Preview
We develop an analysis of voting rules that is robust in the sense that we do not make any assumption regarding voters’ knowledge about each other. In dominant strategy voting rules, voters’ behavior can be predicted uniquely without making any such assumption. However, on full domains, the only dominant strategy voting rules are random dictatorships. We show that the designer of a voting rule can achieve Pareto improvements over random dictatorship by choosing rules in which voters’ behavior can depend on their beliefs. The Pareto improvement is achieved for all possible beliefs. The mechanism that we use to demonstrate this result is simple and intuitive, and the Pareto improvement result extends to all equilibria of the mechanism that satisfy a mild refinement. We also show that the result only holds for voters’ interim expected utilities, not for their ex post expected utilities.
|Item Type:||MPRA Paper|
|Original Title:||Robust mechanism design and dominant strategy voting rules|
|Keywords:||robust mechanism design; dominant strategies; voting; Gibbard-Satterthwaite theorem|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory
|Depositing User:||Tilman Börgers|
|Date Deposited:||01. Mar 2012 15:51|
|Last Modified:||20. Feb 2013 05:52|
Yaron Azrieli and Semin Kim (2011), Pareto Efficiency and Weighted Majority Rules, unpublished, Ohio State University.
Salvador Barbera (2010), Strategy-proof Social Choice, Chapter 25 in: K. J. Arrow, A. K. Sen and K. Suzumura (eds.), Handbook of Social Choice and Welfare, Amsterdam: North-Holland.
Dirk Bergemann and Stephen Morris (2003), Robust Mechanism Design, Cowles Foundation Discussion Paper No. 1421.
Dirk Bergemann and Stephen Morris (2005), Robust Mechanism Design, Econometrica 73, 1771-1813.
Dirk Bergemann and Stephen Morris (2011), Robust Mechanism Design: An Introduction, mimeo., Yale and Princeton, New Haven and Princeton.
Dirk Bergemann and Stephen Morris (2011), Robust Implementation in General Mechanisms, Games and Economic Behavior 71, 261-281.
Jean-Marie Blin and Mark Satterthwaite (1977), On Preferences, Beliefs, and Manipulation within Voting Situations, Econometrica 45, 881-888.
Tilman Borgers (1991), Undominated Strategies and Coordination in Normalform Games, Social Choice and Welfare 8, 65-78.
Tilman Borgers and Peter Postl (2009), Efficient Compromising, Journal of Economic Theory 155, 2057-2076.
Steven Brams and Peter Fishburn (2007), Approval Voting, second edition, Heidelberg etc.: Springer.
Kim-Sau Chung and Jeff Ely (2007), Foundations of Dominant Strategy Mechanisms, Review of Economic Studies 74, 447-476.
Bhaskar Dutta, Hans Peters, and Arunava Sen (2007), Strategy- Proof Cardinal Decision Schemes, Social Choice and Welfare 28, 163-179.
Bhaskar Dutta, Hans Peters, and Arunava Sen (2008), Strategy- Proof Cardinal Decision Schemes (Erratum), Social Choice and Welfare 30, 701-702.
Jeffrey Ely and Marcin Peski (2006), Hierarchies of Belief and Interim Rationalizability, Theoretical Economics 1, 19-65.
Alan Gibbard (1973), Manipulation of Voting Schemes: A General Result, Econometrica 41, 587-602.
Jobst Heitzig and Forrest Simmons (2010), Some Chance for Consensus: Voting Methods For Which Consensus is an Equilibrium, Social Choice and Welfare, forthcoming.
Aanund Hylland (1980), Strategy Proofness of Voting Procedures with Lotteries as Outcomes and Infinite Sets of Strategies, mimeo., University of Oslo, Institute of Economics.
Bengt Holmstrom and Roger Myerson (1983), Efficient and Durable Decision Rules with Incomplete Information, Econometrica 51, 1799-1819.
Matthew Jackson (2001), A Crash Course in Implementation Theory, Social Choice and Welfare 18, 655-708.
Shasikanta Nandeibam (2004), The Structure of Decision Schemes with von Neumann Morgenstern Preferences, discussion paper, University of Bath.
Mark Satterthwaite (1975), Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions, Journal of Economic Theory 1975, 187-217.
Patrick W. Schmitz and Thomas Troger (2011), The (Sub-) Optimality of the Majority Rule, Games and Economic Behavior, forthcoming.
Doug Smith (2010), A Prior Free Efficiency Comparison of Mechanisms for the Public Goods Problem, mimeo., University of Michigan, Ann Arbor.
Takuro Yamashita (2011), Robust Welfare Guarantees in Bilateral Trading Mechanisms, mimeo., Stanford University, Palo Alto.