Ignorance and Indifference: Decision-Making in the Lab and in the Market

Abstract

Economic agents face an evolving, non-ergodic environment. The corresponding permanently undersampled “population” distribution naturally permits unseen, rare events. The principle of indifference, implemented through the methods of parameterization invariance and maximum entropy, provides a disciplined, rational approach to learning, inference and decision in this underinformed setting. Canonical economic problems of choice under uncertainty from both the micro (binary lotteries) and macro (consumption-investment) domains can be formulated in terms of dynamic online learning, with new gambles and new regimes regularly arising. Accordingly, Bayesian updating under invariant ignorance priors allows us to reverse-engineer and rationalize, in a mutually consistent way, the Allais paradox/prospect theory’s probability distortions identified in laboratory experiments, as well as the equity premium/risk-free rate, non-monotone pricing kernel and portfolio underdiversification puzzles observed in financial markets.