The Complexity of Campaigning
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.
The authors thank three anonymous reviewers for their helpful feedback and thank Alec Gilbert for catching errors in a late draft. All remaining errors are the responsibility of the authors. This material is based upon work partially supported by the National Science Foundation under Grants No. IIS-1646887 and No. IIS-1649152. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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