Manipulability, Decomposability, and Rationalizability

Social choice theory, as the name suggests, deals with techniques for finding an alternative for a society respecting their preferences over the set of alternatives. Of course, such a technique must satisfy some desirable properties such as strategy-proofness and unanimity. Strategy-proofness ensures that the individuals can not be better off by misrepresenting their true preferences, whereas unanimity implies that if all agents report the same preference, then the rule selects the top of that common preference. However, the classic results of Gibbard (1973) and Satterthwaite (1975) have shown that if we allow for all possible preferences of the individuals then the only rule that satisfies these properties is the dictatorial one. As all the non-dictatorial rules are manipulable, the natural question arises, which one is least manipulable, i.e., manipulable at minimum number of profiles. Furthermore, this impossibility result leaves another question open as to whether in a more restricted context rules other than dictatorships can be strategy-proof. We address these two fundamental questions in this research