确证度和双重合取谬误——推广CF公式的“$A\to B$范式”解释

Confirmation and Dual Conjunction Errors—Extending the CF Formula’s “$A\to B$ Paradigm” Interpretation

摘要: 合取谬误现象说明人们在判断不确定事件的可能性时，可能违背合取规则。有学者提出贝叶斯确证度理论，用CF (合取谬误发生概率)公式解释合取谬误。但是该理论解释了“$A\to B$ 范式”的合取谬误，却没有进一步解释该范式下的特殊合取谬误，即双重合取谬误。由此，自然产生一个问题：确证度理论能否解释双重合取谬误？本文通过将CF公式的“$A\to B$ 范式”解释推广到“$A\leftrightarrow B$ 范式”，建立推广模型。推广模型解释了双重合取谬误，并拓宽了普通合取谬误的边界。推广模型统一了普通合取谬误与双重合取谬误，为进一步研究双重合取谬误奠定基础，并指明了双重合取谬误进一步的研究方向。

Abstract: The conjunction fallacy phenomenon demonstrates that when judging the likelihood of uncertain events, individuals may violate the conjunction rule. Some scholars have proposed Bayesian confirmation theory and utilized the CF (the probability that a conjunction fallacy occurs) formula to explain the conjunction fallacy. However, while this theory accounts for the conjunction fallacy within the “$A\to B$ paradigm”, it does not further explain a specific subtype within this paradigm—namely, the dual conjunction errors. This naturally raises the question: Can confirmation theory account for the dual conjunction errors? This paper addresses this by extending the CF formula’s interpretation from the “$A\to B$ paradigm” to the “$A\leftrightarrow B$ paradigm”, thereby establishing an extended model. The extended model explains the dual conjunction errors and broadens the boundaries of the ordinary conjunction fallacy. By unifying the ordinary conjunction fallacy and the dual conjunction errors, this extended model lays a foundation for further research on the dual conjunction errors and delineates directions for future investigation.