Continuity and incentive compatibility in cardinal mechanisms

Abstract In models without transfers, we show that every cardinal incentive compatible voting mechanism satisfying a continuity condition, can only take ordinal, but not cardinal information into account. Our results apply to many standard models in mechanism design without transfers, including the standard voting models with any domain restrictions.

[1]  Muriel Niederle,et al.  Boston versus deferred acceptance in an interim setting: An experimental investigation , 2016, Games Econ. Behav..

[2]  Marek Pycia The Cost of Ordinality , 2014 .

[3]  I. Hafalir,et al.  Welfare-Maximizing Assignment of Agents to Hierarchical Positions , 2014 .

[4]  M. Utku Ünver,et al.  Incentive Compatible Allocation and Exchange of Discrete Resources , 2015 .

[5]  Gabriel D. Carroll On mechanisms eliciting ordinal preferences , 2018 .

[6]  Arunava Sen,et al.  Ordinally Bayesian incentive compatible voting rules , 2004 .

[7]  Itai Ashlagi,et al.  Optimal allocation without money: an engineering approach , 2014, Manag. Sci..

[8]  V. Krishna,et al.  Convex Potentials with an Application to Mechanism Design , 2001 .

[9]  H. Moulin The strategy of social choice , 1983 .

[10]  Tilman Börgers,et al.  Efficient compromising , 2009, J. Econ. Theory.

[11]  Yaron Azrieli,et al.  Pareto Efficiency and Weighted Majority Rules , 2014 .

[12]  C. d'Aspremont,et al.  Ordinal Bayesian incentive compatible representations of committees , 1988 .

[13]  Alex Gershkov,et al.  Optimal Voting Rules , 2013 .

[14]  A. Camacho,et al.  On cardinal utility , 1979 .

[15]  Eddie Dekel,et al.  Optimal Allocation with Costly Verification Online Appendix , 2014 .

[16]  Hans Peters,et al.  Probabilistic strategy-proof rules over single-peaked domains , 2013 .

[17]  Gerald Beer The Hausdorff metric and convergence in measure. , 1974 .

[18]  William J. Baumol,et al.  The Cardinal Utility Which is Ordinal , 1958 .

[19]  A. Gibbard Manipulation of Schemes That Mix Voting with Chance , 1977 .

[20]  Aytek Erdil,et al.  Strategy-proof stochastic assignment , 2014, J. Econ. Theory.

[21]  L. Dubins Resolving Conflicting Preferences in School Choice : The “ Boston , 2009 .

[22]  Paul R. Milgrom,et al.  Envelope Theorems for Arbitrary Choice Sets , 2002 .

[23]  Antonio Miralles,et al.  Cardinal Bayesian allocation mechanisms without transfers , 2012, J. Econ. Theory.

[24]  Arunava Sen,et al.  The Structure of Strategy-Proof Random Social Choice Functions over Product Domains and Lexicographically Separable Preferences ⁄ , 2012 .

[25]  Semin Kim,et al.  Ordinal versus cardinal voting rules: A mechanism design approach , 2017, Games Econ. Behav..

[26]  S. Pápai,et al.  Strategyproof Assignment by Hierarchical Exchange , 2000 .

[27]  Salvador Barberà,et al.  Strategy-Proof Probabilistic Rules for Expected Utility Maximizers , 1998 .

[28]  M. Satterthwaite Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[29]  R. Vohra Mechanism Design: A Linear Programming Approach , 2011 .

[30]  Hans Peters,et al.  Strategy-proof cardinal decision schemes , 2008, Soc. Choice Welf..

[31]  Peter Postl,et al.  Strategy-Proof Compromises , 2011 .

[32]  Mridu Prabal Goswami,et al.  Strategy proofness and Pareto efficiency in quasilinear exchange economies , 2014 .

[33]  A. Gibbard Manipulation of Voting Schemes: A General Result , 1973 .

[34]  W. Rudin Principles of mathematical analysis , 1964 .

[35]  Hervé Moulin,et al.  A New Solution to the Random Assignment Problem , 2001, J. Econ. Theory.

[36]  M. Pycia,et al.  Prices and Efficient Assignments Without Transfers , 2014 .

[37]  M. Utku Ünver,et al.  Decomposing Random Mechanisms , 2014 .

[38]  Patrick W. Schmitz,et al.  The (sub-)optimality of the majority rule , 2012, Games Econ. Behav..

[39]  Lars Ehlers,et al.  Coalitional Strategy-Proof House Allocation , 2002, J. Econ. Theory.

[40]  Lars-Gunnar Svensson Strategy-proof allocation of indivisible goods , 1999 .

[41]  James C. D. Fisher,et al.  Efficient Random Assignment With Cardinal and Ordinal Preferences , 2018, Journal of Mechanism and Institution Design.

[42]  Arunava Sen,et al.  Random dictatorship domains , 2012, Games Econ. Behav..

[43]  M. Satterthwaite,et al.  Strategy-Proof Allocation Mechanisms at Differentiable Points , 1981 .

[44]  Yeon-Koo Che,et al.  Resolving Conflicting Preferences in School Choice: The 'Boston' Mechanism Reconsidered , 2009 .

[45]  Lin Zhou On a conjecture by gale about one-sided matching problems , 1990 .

[46]  R. Zeckhauser,et al.  The Efficient Allocation of Individuals to Positions , 1979, Journal of Political Economy.

[47]  Peter Troyan,et al.  Comparing school choice mechanisms by interim and ex-ante welfare , 2012, Games Econ. Behav..

[48]  P. Bag Optimal auction design and R&D , 1997 .