The Goldilocks principle: applying the exclusive disjunction to fuzzy sets

Abstract

Qualitative Comparative Analysis (QCA), a technique by which the tools of Boolean algebra are applied to equifinal causal conditions, is gaining popularity amongst scholars. This paper draws upon a distinction largely overlooked by the QCA literature: the difference between inclusive-and exclusive-or (OR and XOR). Extending the work of Hackett (2015), I argue that XOR should be included amongst the tools of QCA, explain why XOR is more easily applied to crisp-than fuzzy-set QCA, and provide two original techniques for applying XOR to fuzzy sets: mechanical and calibrated. With the calibrated technique, the application of the exclusive-or is related to substantive knowledge of the cases with two threshold values: (1) how large two fuzzy set values need to be in order to violate a prior commitment or overshoot a target outcome, and (2) how similar two values need to be in order to violate the rule: 'A or B, but not both'. This paper improves the capacity of QCA expressions to mirror natural language closely, formalize conversational implicature, and deal with mutually exclusive clusters of sufficiency conditions. It includes a helpful step-by-step guide for QCA practitioners.