A Computational Theory of Subjective Probability
This work addresses a foundational issue in probability theory and cognitive science, offering a computational theory that explains phenomena like the conjunction fallacy, but it appears incremental as it builds on existing subjective probability frameworks.
The paper tackles the problem of applying probability theory to situations with model uncertainty, arguing that classical probability is insufficient and subjective probability must be used instead. It demonstrates through experiments that people use subjective probability in lottery judgments and provides a formal proof that, under model uncertainty, conjunctions can be more subjectively probable than their individual components.
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.