A mathematical framework for probabilistic choice based on information theory and psychophysics.

Area of Science:

• Neuroeconomics
• Econophysics
• Decision Science
• Psychophysics

Background:

• Risky decision-making is linked to substance abuse, psychopathy, and gambling, while anxiety disorders show heightened sensitivity to risk and uncertainty.
• Economic theory distinguishes probability from uncertainty (Knightian uncertainty/ambiguity).
• Information theory quantifies uncertainty using Shannon entropy, measuring unpredictability even when probabilities are known.

Purpose of the Study:

• To present a mathematical framework that parametrizes an individual's level of aversion to probabilistic uncertainty and reward dependency.
• To explore the framework's applicability in understanding decision-making in neuropsychiatric disorders.
• To establish an analogue between the framework and thermodynamics for broader scientific application.

Main Methods:

• Combining Shannon entropy from information theory with Weber's law from psychophysics.
• Developing a mathematical model to parametrize decision-making traits.
• Drawing parallels with thermodynamic principles.

Main Results:

• The framework successfully parametrizes both aversion to probabilistic uncertainty and reward dependency.
• The model demonstrates an analogue in thermodynamics.
• The approach offers a quantifiable method to study decision-making variations.

Conclusions:

• The integrated framework provides a novel method for studying decision-making and its alterations in neuropsychiatric conditions.
• The thermodynamic analogue suggests potential for interdisciplinary applications in neuroeconomics and econophysics.
• This approach can elucidate maladaptive personality characteristics and inform future research.