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). 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.

Keywords:

• Qualitative Comparative Analysis
• exclusive disjunction
• calibration

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. An inclusive ‘or’.

2. An exclusive ‘or’.

3. As Hackett (2015) notes, statements such as ‘Male XOR pregnant’ seems obviously exclusive amongst human beings but can be inclusive amongst members of the Sygnathidae family, such as seahorses and pipe fish. Domain matters.

4. Note that these figures are intended for illustration only.

5. Conversational implicature is something that can be worked out from how something was said, rather than simply what was said. See Grice (1989). Usually there are contextual clues that indicate whether the ‘or’ used is exclusive or inclusive. See Grice’s (1989) work Studies in the Way of Words for discussion of both conversational and conventional implicature.