Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences

Abstract Collective decision problems are considered with a finite number of agents who have single-peaked preferences on the real line. A probabilistic decision scheme assigns a probability distribution over the real line to every profile of reported preferences. The main result of the paper is a characterization of the class of unanimous and strategy-proof probabilistic schemes with the aid of fixed probability distributions that play a role similar to that of the phantom voters in H. Moulin ( Public Choice 35 (1980), 437–455). Thereby, the work of Moulin (1980) is extended to the probabilistic framework. Journal of Economic Literature Classification Numbers: D71, D81.

[1]  M. Jackson,et al.  A characterization of strategy-proof social choice functions for economies with pure public goods , 1994 .

[2]  Stephen Ching,et al.  Strategy-proofness and “median voters” , 1998, Int. J. Game Theory.

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

[4]  Xavier Freixas,et al.  A cardinal approach to straightforward probabilistic mechanisms , 1984 .

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

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

[7]  Atila Abdulkadiroglu,et al.  RANDOM SERIAL DICTATORSHIP AND THE CORE FROM RANDOM ENDOWMENTS IN HOUSE ALLOCATION PROBLEMS , 1998 .

[8]  Bhaskar Dutta.  Strategic Voting in a Probabilistic Framework , 1980 .

[9]  Hans Peters,et al.  Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods , 2002, J. Econ. Theory.

[10]  Kim C. Border,et al.  Straightforward Elections, Unanimity, and Phantom Voters , 1983 .

[11]  M. Satterthwaite,et al.  Strategy-proofness and single-peakedness , 1976 .

[12]  Stephen Ching,et al.  Strategy-proofness and “median voters” , 1998 .

[13]  Salvador Barberà,et al.  Preference aggregation with randomized social orderings , 1978 .

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

[15]  Allan Gibbard,et al.  Straightforwardness of Game Forms with Lotteries as Outcomes , 1978 .

[16]  P. Pattanaik,et al.  The structure of coalitional power under probabilistic group decision rules , 1982 .

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

[18]  Bezalel Peleg,et al.  Distribution of Power under Stochastic Social Choice Rules , 1986 .