16 May 2017, Computational Social Choice Seminar, Yuliya Veselova
We consider the problem of manipulation in an election by a single voter under incomplete information, i.e., in case the full preference profile is not known to the voters. Instead, voters know the result of an opinion poll (the outcome of a poll information function, e.g., a list of scores or a set of winners). In this case, a voter has an incentive to misrepresent his preferences if he knows that he will not become worse off and there is a chance of becoming better off. We consider six social choice rules and eight types of poll information functions differing in their informativeness. To compare manipulability, first we calculate the probability that there is a voter that has an incentive to manipulate and show that this measure is not illustrative in the case of incomplete information. Then we suggest considering two other measures: the probability of a successful manipulation and an aggregate stimulus of voters to manipulate, both of which demonstrate more intuitive behavior. We provide results of simulations as well as analytical proofs of some effects observed.