Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud

TL;DR

This paper examines the computational complexity of designing optimal signaling schemes to influence voting outcomes, revealing efficient solutions for private signals and hardness results for public signals under various voting rules.

Contribution

It introduces efficient algorithms for private signaling schemes and proves hardness of approximation for public signaling in voting influence problems.

Findings

Optimal private signaling schemes can be computed efficiently.

Public signaling schemes cannot be approximated within any factor.

Extensions of existing results to more general settings and utility functions.

Abstract

We focus on the following natural question: is it possible to influence the outcome of a voting process through the strategic provision of information to voters who update their beliefs rationally? We investigate whether it is computationally tractable to design a signaling scheme maximizing the probability with which the sender's preferred candidate is elected. We focus on the model recently introduced by Arieli and Babichenko (2019) (i.e., without inter-agent externalities), and consider, as explanatory examples, $k$-voting rule and plurality voting. There is a sharp contrast between the case in which private signals are allowed and the more restrictive setting in which only public signals are allowed. In the former, we show that an optimal signaling scheme can be computed efficiently both under a $k$-voting rule and plurality voting. In establishing these results, we provide two general (i.e., applicable to settings beyond voting) contributions. Specifically, we extend a well known result by Dughmi and Xu (2017) to more general settings, and prove that, when the sender's utility function is anonymous, computing an optimal signaling scheme is fixed parameter tractable w.r.t. the number of receivers' actions. In the public signaling case, we show that the sender's optimal expected return cannot be approximated to within any factor under a $k$-voting rule. This negative result easily extends to plurality voting and problems where utility functions are anonymous.