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.
Cognition. 2018 Jan;170:280-297. doi: 10.1016/j.cognition.2017.08.012. Epub 2017 Nov 5.
We describe 4 experiments testing contrasting predictions of two recent models of probability judgment: the quantum probability model (Busemeyer, Pothos, Franco, & Trueblood, 2011) and the probability theory plus noise model (Costello & Watts, 2014, 2016a). Both models assume that people estimate probability using formal processes that follow or subsume standard probability theory. One set of predictions concerned agreement between people's probability estimates and standard probability theory identities. The quantum probability model predicts people's estimates should agree with one set of identities, while the probability theory plus noise model predicts a specific pattern of violation of those identities. Experimental results show the specific pattern of violation predicted by the probability theory plus noise model. Another set of predictions concerned the conjunction fallacy, which occurs when people judge the probability of a conjunction P(A∧B) to be greater than one or other constituent probabilities P(A) or P(B), contrary to the requirements of probability theory. In cases where A causes B, the quantum probability model predicts that the conjunction fallacy should only occur for constituent B and not for constituent A: the noise model predicts that the fallacy should occur for both A and B. Experimental results show that the fallacy occurs equally for both, contrary to the quantum probability prediction. These results suggest that people's probability estimates do not follow quantum probability theory. These results support the idea that people estimate probabilities using mechanisms that follow standard probability theory but are subject to random noise.
我们描述了 4 项实验，这些实验检验了最近两种概率判断模型的对比预测：量子概率模型（Busemeyer、Pothos、Franco 和 Trueblood，2011）和概率理论加噪声模型（Costello 和 Watts，2014、2016a）。这两个模型都假设人们使用遵循或包含标准概率论的正式过程来估计概率。一组预测涉及人们的概率估计与标准概率论恒等式之间的一致性。量子概率模型预测人们的估计应该与一组恒等式一致，而概率理论加噪声模型则预测这些恒等式的特定违反模式。实验结果显示了概率理论加噪声模型预测的违反模式。另一组预测涉及合取谬误，即当人们判断合取的概率 P(A∧B)大于一个或另一个组成概率 P(A)或 P(B)时，违反了概率论的要求。在 A 导致 B 的情况下，量子概率模型预测合取谬误应该只发生在组成部分 B 上，而不是在组成部分 A 上：噪声模型预测谬误应该同时发生在 A 和 B 上。实验结果表明，该谬误同时发生在两者上，与量子概率预测相反。这些结果表明，人们的概率估计并不遵循量子概率理论。这些结果支持这样一种观点，即人们使用遵循标准概率论但受到随机噪声影响的机制来估计概率。
