Influence modeling: Mathematical programming representations of persuasion under either risk or uncertainty

Persuasion is a fundamental element of human interaction applied to both individuals and populations. Although persuasion is a well-studied, interdisciplinary field of research, this work advances its prescriptive, quantitative characterization, and future use. That is, this research complements the qualitative psychological literature with respect to the processing of persuasive messages by developing mathematical programming formulations to identify an optimal influence campaign. We adapt the classic Decision Analysis problem to a bilevel mathematical program, wherein a persuader has the opportunity to affect the environment prior to the decisionmaker’s choice. Thereby, we define a new class of problems for modeling persuasion. Utilizing Cumulative Prospect Theory as a descriptive framework of choice, we transform the persuasion problem to a single level mathematical programming formulation, adaptable to conditions of either risk or uncertainty. These generalized models allow for the malleability of prospects as well as Cumulative Prospect Theory parameters through persuasion update functions. We detail the literature that supports the quantification of such effects which, in turn, establishes that such update functions can be realized. Finally, the efficacy of the model is illustrated through three use cases under varying conditions of risk or uncertainty: the establishment of insurance policies, the construction of a legal defense, and the development of a public pension program.