Costello, FintanFintanCostelloWatts, PaulPaulWatts2021-04-222021-04-222017 Elsev2018-02Cognitive Psychology0010-0285http://hdl.handle.net/10197/12115Recent research has identified three invariants or identities that appear to hold in people's probabilistic reasoning: the QQ identity, the addition law identity, and the Bayes rule identity (Costello and Watts, 2014, 2016a, Fisher and Wolfe, 2014, 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 judgements despite the presence of strong and systematic biases against the requirements of normative probability theory in those very same judgements. These results suggest that the systematic biases seen in people's probabilistic reasoning follow mathematical rules: for these particular identities, these rules cause an overall cancellation of biases and so produce agreement with normative requirements. We assess two competing mathematical models of probabilistic reasoning (the ‘probability theory plus noise’ model and the ‘quantum probability’ model) in terms of their ability to account for this pattern of systematic biases and invariant identities.Print-ElectronicenThis is the author’s version of a work that was accepted for publication in Cognitive Psychology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Cognitive Psychology (100, (2018)) https://doi.org/10.1016/j.cogpsych.2017.11.003HumansBayes TheoremProbability TheoryRationalityBiasesProbabilityJournal Article10011610.1016/j.cogpsych.2017.11.0032020-06-05https://creativecommons.org/licenses/by-nc-nd/3.0/ie/