Does Incomplete Information Reduce Manipulability?
We consider the problem of individual manipulation under incomplete information, when voters do not know a full preference profile. Instead, voters know the result of an opinion poll (the outcome of a poll information function π, e.g. a list of scores or a set of winners). In this case, a voter has an incentive to misrepresent her preferences (π-manipulate) if she knows that she will not become worse off and there is a chance of becoming better off. We consider six voting 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 which has an incentive to π-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, which demonstrate more intuitive behavior. We provide results of computational experiments as well as analytical proofs of some effects observed.