Dominating Manipulations in Voting with Partial Information

TL;DR

This paper investigates the computational complexity of manipulation in voting systems under partial information, showing that limited information can prevent strategic manipulation or make it computationally hard.

Contribution

It introduces a formal framework for analyzing dominating manipulations with partial information and establishes complexity results for various voting rules.

Findings

No dominating manipulation with no information for many rules.

NP-hardness of computing manipulations with partial order preferences.

Full information allows easy computation of manipulations.

Abstract

We consider manipulation problems when the manipulator only has partial information about the votes of the nonmanipulators. Such partial information is described by an information set, which is the set of profiles of the nonmanipulators that are indistinguishable to the manipulator. Given such an information set, a dominating manipulation is a non-truthful vote that the manipulator can cast which makes the winner at least as preferable (and sometimes more preferable) as the winner when the manipulator votes truthfully. When the manipulator has full information, computing whether or not there exists a dominating manipulation is in P for many common voting rules (by known results). We show that when the manipulator has no information, there is no dominating manipulation for many common voting rules. When the manipulator's information is represented by partial orders and only a small portion of the preferences are unknown, computing a dominating manipulation is NP-hard for many common voting rules. Our results thus throw light on whether we can prevent strategic behavior by limiting information about the votes of other voters.