TY - JOUR

T1 - Free entropy minimizing persuasion in a predictor–corrector dynamic

AU - Goehle, Geoff

AU - Griffin, Christopher

N1 - Publisher Copyright:
© 2024 Elsevier B.V.

PY - 2024/6/1

Y1 - 2024/6/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.physa.2024.129819

DO - 10.1016/j.physa.2024.129819

M3 - Article

AN - SCOPUS:85193580496

SN - 0378-4371

VL - 643

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 129819

ER -