# Mathematical invariants in people's probabilistic reasoning

- Fintan Costello,
*University College Dublin*
- Paul Watts,
*National University of Ireland Maynooth*

## Abstract

Recent research has identified three invariants or identities that
appear to hold in people’s probabilistic decision making: the addition law
identity, the Bayes rule identity, and the QQ identity (Costello and Watts, 2014,
Fisher and Wolfe, 2014, Costello and Watts, 2016, Wang and Busemeyer, 2013, Wang
et al., 2014). Each of these identities represent specific agreement with the
requirements of normative probability theory; strikingly, these identities seem
to hold in people’s probability judgments despite the presence of strong
and systematic biases against the requirements of normative probability theory in
those very same judgments. We assess the degree to which two formal models of
probabilistic reasoning (the ‘probability theory plus noise’ model
and the ‘quantum probability’ model) can explain these identities and
biases in probabilistic reasoning.

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