Costello Fintan, Watts Paul
School of Computer Science and Informatics, University College Dublin, Belfield, Dublin 4, Ireland.
Department of Theoretical Physics, National University of Ireland Maynooth, Maynooth, Co Kildare, Ireland.
Cogn Psychol. 2018 Feb;100:1-16. doi: 10.1016/j.cogpsych.2017.11.003. Epub 2017 Dec 6.
Recent 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.
QQ恒等式、加法法则恒等式以及贝叶斯规则恒等式（科斯特洛和瓦茨，2014年、2016年a；费舍尔和沃尔夫，2014年；王和布西迈尔，2013年；王等人，2014年）。这些恒等式中的每一个都代表了与规范概率论要求的特定一致性；引人注目的是，尽管在这些相同的判断中存在对规范概率论要求的强烈且系统的偏差，但这些恒等式似乎在人们的判断中仍然成立。这些结果表明，在人们概率推理中看到的系统偏差遵循数学规则：对于这些特定的恒等式，这些规则会导致偏差的整体抵消，从而产生与规范要求的一致性。我们根据它们解释这种系统偏差和不变恒等式模式的能力，评估了两种相互竞争的概率推理数学模型（“概率论加噪声”模型和“量子概率”模型）。
