Evaluating gambles using dynamics.

Area of Science:

• Decision Theory
• Behavioral Economics
• Mathematical Finance

Background:

• Classic decision theory relies on utility functions and expectation values to assess gambles.
• Utility functions have limited predictive power due to their generality.
• Expectation values require ensembles or ergodic properties, which are inaccessible to individual decision-makers.

Purpose of the Study:

• To address the limitations of utility functions and expectation values in decision theory.
• To propose a new method for evaluating gambles based on time-averaged wealth growth.
• To reconcile inconsistencies in decision theory and validate a new perspective.

Main Methods:

• Proposed evaluating gambles by averaging wealth growth over time.
• Specified dynamics to compute time averages, eliminating the need for utility functions.
• Analyzed linear and logarithmic transformations as ergodic observables for additive and multiplicative dynamics.

Main Results:

• Demonstrated that averaging wealth growth over time provides a legitimate way to evaluate gambles.
• Showed that linear and logarithmic transformations generate ergodic observables for specific dynamics.
• Identified and corrected inconsistencies in decision theory development.

Conclusions:

• The proposed method of time-averaged wealth growth offers a valid alternative to traditional decision theory.
• This approach bypasses the need for utility functions and overcomes limitations of expectation values.
• The findings invalidate common arguments for bounded utility functions and clarify decision theory.