Threats, counter-threats and strategic manipulation for non-binary group decision rules

Abstract We prove that a class of unanimity rules (the k -Pareto rule, 1≤ k ≤ N ) is the only class of group decision functions which is non-manipulable even after the possibility of counter-threats is taken into consideration. We also prove that the 1-Pareto rule is the only group decision function which is strictly nonmanipulable after the possibility of counter-threats is taken into consideration.

[1]  Allan M. Feldman.  Manipulation and the Pareto rule , 1979 .

[2]  Jerry S. Kelly,et al.  STRATEGY-PROOFNESS AND SOCIAL CHOICE FUNCTIONS WITHOUT SINGLEVALUEDNESS , 1977 .

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

[4]  Y. Murakami.  Logic and Social Choice , 1968 .

[5]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[6]  Kenneth O. May,et al.  A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision , 1952 .

[7]  P. Gärdenfors.  Manipulation of social choice functions , 1976 .

[8]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[9]  Prasanta K. Pattanaik,et al.  Strategic voting under minimally binary group decision functions , 1981 .

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

[11]  Salvador Barberà,et al.  THE MANIPULATION OF SOCIAL CHOICE MECHANISMS THAT DO NOT LEAVE "TOO MUCH" TO CHANCE' , 1977 .

[12]  Salvador Barberà.  Manipulation of social decision functions , 1977 .

[13]  Taradas Bandyopadhyay.  Coalitional manipulation and the Pareto rule , 1983 .

[14]  Bhaskar Dutta,et al.  Strategy and group choice , 1978 .

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

[16]  Prasanta K. Pattanaik,et al.  Threats, Counter-Threats, and Strategic Voting , 1976 .

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