Free Entropy Minimizing Persuasion in a Predictor-Corrector Dynamic

TL;DR

This paper models persuasion as an optimal control problem on belief distributions, using a modified Fisher-Rao metric to minimize free entropy and analyze belief change paths in various models.

Contribution

It introduces a novel control framework for persuasion based on a modified Fisher-Rao metric, enabling analysis of belief dynamics beyond geodesic paths.

Findings

Optimal control paths are non-geodesic under the modified metric.

Comparison with standard Fisher metric shows differences in belief trajectory efficiency.

Application to Kalman and Boltzmann models demonstrates the framework's versatility.

Abstract

Persuasion is the process of changing an agent's belief distribution from a given (or estimated) prior to a desired posterior. A common assumption in the acceptance of information or misinformation as fact is that the (mis)information must be consistent with or familiar to the individual who accepts it. We model the process as a control problem in which the state is given by a (time-varying) belief distribution following a predictor-corrector dynamic. Persuasion is modeled as the corrector control signal with the performance index defined using the Fisher-Rao information metric, reflecting a fundamental cost associated to altering the agent's belief distribution. To compensate for the fact that information production arises naturally from the predictor dynamic (i.e., expected beliefs change) we modify the Fisher-Rao metric to account just for information generated by the control signal. The resulting optimal control problem produces non-geodesic paths through distribution space that are compared to the geodesic paths found using the standard free entropy minimizing Fisher metric in several example belief models: a Kalman Filter, a Boltzmann distribution and a joint Kalman/Boltzmann belief system.