Does Incomplete Information Reduce Manipulability?

Abstract

We consider the problem of individual manipulation under incomplete information, i.e. the whole preference profile is not known to 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 (manipulate) 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 which 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 which demonstrate more intuitive behaviour. We provide results of computational experiments and analytical proofs of some of the observed effects.