# Choosing Poorly: Reward-Induced Strategy Shifts in Estimating the Probabilities of Conjunctions and Disjunctions

- James Tripp,
*University of Warwick*
- Adam Sanborn,
*University of Warwick*
- Neil Stewart,
*University of Warwick*
- Takao Noguchi,
*University College London*

## Abstract

Human estimates of the probabilities of combinations of events
show well-established violations of probability theory, most notably the
conjunction and disjunction fallacies. These violations have led researchers to
conclude that the rules of probability are too complex for most people to use,
and that cognitively-easier approximations such as averaging are used instead.
Unlike previous work that has assumed that individuals use only a single
combination rule, we collected repeated estimates of conjunctions and
disjunctions and investigated whether individuals consistently used a single rule
or used a repertoire of rules in a trial-by-trial Bayesian analysis. When not
incentivized, most participants were best described as randomly selecting a
combination rule on each trial, and the correct rule was the most often used.
Despite this, when incentivized to use their single-best strategy participants
were more likely to use the incorrect averaging rule. People do not seem to
understand their own strategies well.

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