A Computational Theory of Subjective Probability

TL;DR

This paper applies algorithmic probability theory to model how humans update beliefs under uncertainty, demonstrating that subjective probability better explains certain cognitive biases than classical probability.

Contribution

It introduces a formal framework linking subjective probability with algorithmic probability and shows its relevance through experiments on lottery judgments and the conjunction fallacy.

Findings

People use subjective rather than classical probability in lottery judgments.

The materials for the conjunction fallacy involve model uncertainty.

A formal proof shows that uncertain models can make conjunctions more probable than individual outcomes.

Abstract

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We argue that classical probability cannot be applied in such cases, and that subjective probability must instead be used. In Experiment 1 we show that, when judging the probability of lottery number sequences, people apply subjective rather than classical probability. In Experiment 2 we examine the conjunction fallacy and demonstrate that the materials used by Tversky and Kahneman (1983) involve model uncertainty. We then provide a formal mathematical proof that, for every uncertain model, there exists a conjunction of outcomes which is more subjectively probable than either of its constituents in isolation.