TITLE:
On the Validity of Probabilities in Uncertainty Assessment: The Role of Learning
AUTHORS:
Jean-Paul Chavas
KEYWORDS:
Uncertainty, Probability, Kolmogorov Axioms, Countable Additivity, Learning, Shadow Prices, Nonconvexity
JOURNAL NAME:
Theoretical Economics Letters,
Vol.14 No.3,
June
28,
2024
ABSTRACT: Probabilities have been accepted as providing a general representation of uncertainty. We investigate the validity of probability assessments using a state-contingent model under uncertainty, with a focus on the role of learning. We use the model to define shadow prices of state-contingent goods under general conditions. Interpreting probabilities as normalized shadow prices of state-contingent goods, we obtain new insights into why and when probability theory fails to provide an adequate representation of uncertainty. Our analysis focuses on the validity of Kolmogorov’s additivity axiom in probability theory. We identify three sets of factors contributing to non-additive probabilities: 1) uncertainty-loving behavior, 2) active learning under costly information, and 3) the presence of an infinite number of states.