Strongly nonmanipulable multi-valued collective choice rules

Strategy-proof Social Choice Correspondences

“…By replicating the appropriate arguments in Case A, it follows that One of the early papers on strategy-proofness to which our work is related is Feldman (1980). He considers decision schemes that map profiles of preferences over basic alternatives (i.e.…”

“…5 While several authors have shown that only dictatorial rules are strategy-proof, Feldman [11] shows that only bi-dictatorial rules are strategy-proof when individuals rank sets on the basis of an even-chance lottery. 6 However, see Section 4, where we point out that Duggan and Schwartz's dictatorship result cannot be derived as a corollary of ours in view of their definition of strategy-proofness.…”

Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized

“…M a 's test follows the colon and begins with three quanti®ers: ilil H u. The nonmanipulability condition of Zeckhauser (1973), Gibbard (1977), and Feldman (1980) weakens that test, strengthening M a , by weakening the universal quanti®cation to an instance of it: for us manipulability requires that a certain relation hold for every pair of lotteries with supports CP and CP H , but for them the relation need hold only for one pair, socially chosen along with CP and CP H . An even stronger nonmanipulability condition weakens the``all'' of our test to``some,'' ilil H u to ll H u.…”

“…In fact, under the assumption of countable choice sets used to prove M aLemma, the two nonmanipulability conditions are equivalent. 8 Another relaxation of M a worth investigating allows manipulations that contract CP while still forbidding all others. The idea is that if CP comprises welfare optima when P 1 Y F F F Y P n are true preferences then any contraction of CP still ensures an optimal choice.…”

Expected Utility Consistent Extensions of Preferences

“…This is a restriction of BEUC (hence of GEUC) that Feldman (1980) and Barberà, et al (2001) use in their analysis of strategy-proof social choice correspondences. 12 Letting ω ≈ be defined for each X ∈ A as ω ≈ X (x) = 1 #X for all x ∈ X, we have EEUC = {ω ≈ }.…”