The Complexity of Campaigning

TL;DR

This paper investigates the computational complexity of modeling voter preferences in campaigning, showing that evaluating voter utility and candidate strategies are computationally hard under certain models, raising questions about preference modeling.

Contribution

It introduces formal models of voter preferences based on Boolean formulas and proves their associated computational problems are hard, including #P-hardness in some cases.

Findings

Voter utility evaluation is computationally hard under these models.

Candidate strategic reasoning problems are also computationally hard.

Raises questions about the design of voter preference models.

Abstract

In "The Logic of Campaigning", Dean and Parikh consider a candidate making campaign statements to appeal to the voters. They model these statements as Boolean formulas over variables that represent stances on the issues, and study optimal candidate strategies under three proposed models of voter preferences based on the assignments that satisfy these formulas. We prove that voter utility evaluation is computationally hard under these preference models (in one case, #P-hard), along with certain problems related to candidate strategic reasoning. Our results raise questions about the desirable characteristics of a voter preference model and to what extent a polynomial-time-evaluable function can capture them.