# A Computational Theory of Subjective Probability [Featuring a Proof that the Conjunction Effect is not a Fallacy]

- Phil Maguire,
*NUI Maynooth*
- Philippe Moser,
*NUI Maynooth*
- Rebecca Maguire,
*National College of Ireland*
- Mark Keane,
*University College Dublin*

## 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.

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