The Complexity of Probabilistic Lobbying

TL;DR

This paper models probabilistic lobbying, analyzing the complexity of influencing voters' preferences under various criteria, and provides algorithms and hardness results for different problem variants.

Contribution

It introduces formal models for probabilistic lobbying, analyzes their computational complexity, and offers approximation results for various problem variants.

Findings

Some lobbying problems are solvable in polynomial time.

Certain variants are NP-complete but fixed-parameter tractable.

Other variants are W[2]-complete, indicating high computational complexity.

Abstract

We propose models for lobbying in a probabilistic environment, in which an actor (called "The Lobby") seeks to influence voters' preferences of voting for or against multiple issues when the voters' preferences are represented in terms of probabilities. In particular, we provide two evaluation criteria and two bribery methods to formally describe these models, and we consider the resulting forms of lobbying with and without issue weighting. We provide a formal analysis for these problems of lobbying in a stochastic environment, and determine their classical and parameterized complexity depending on the given bribery/evaluation criteria and on various natural parameterizations. Specifically, we show that some of these problems can be solved in polynomial time, some are NP-complete but fixed-parameter tractable, and some are W[2]-complete. Finally, we provide approximability and inapproximability results for these problems and several variants.