When and Why is Persuasion Hard? A Computational Complexity Result

TL;DR

This paper models informational persuasion as a computational problem, revealing that discovering persuasive messages is NP-Hard while adopting them is NP, explaining human susceptibility and the impact of AI on persuasion activities.

Contribution

It formalizes persuasion as a decision problem and proves its computational complexity, bridging human and AI agents in understanding persuasion's costs and challenges.

Findings

Discovering persuasive messages is NP-Hard.

Adopting persuasive messages is NP.

Explains human susceptibility to persuasion despite public information.

Abstract

As generative foundation models improve, they also tend to become more persuasive, raising concerns that AI automation will enable governments, firms, and other actors to manipulate beliefs with unprecedented scale and effectiveness at virtually no cost. The full economic and social ramifications of this trend have been difficult to foresee, however, given that we currently lack a complete theoretical understanding of why persuasion is costly for human labor to produce in the first place. This paper places human and AI agents on a common conceptual footing by formalizing informational persuasion as a mathematical decision problem and characterizing its computational complexity. A novel proof establishes that persuasive messages are challenging to discover (NP-Hard) but easy to adopt if supplied by others (NP). This asymmetry helps explain why people are susceptible to persuasion, even in contexts where all relevant information is publicly available. The result also illuminates why litigation, strategic communication, and other persuasion-oriented activities have historically been so human capital intensive, and it provides a new theoretical basis for studying how AI will impact various industries.