The Goldilocks principle: applying the exclusive disjunction to fuzzy sets

Journal article

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.

Authors: Hackett, U

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Routledge
• Journal: International Journal of Social Research Methodology
• Volume: 19
• Issue: 5
• Pages: 551-574
• Publication date: 2015-06-15
• Acceptance date: 2015-05-19
• DOI: 10.1080/13645579.2015.1053708
• EISSN: 1464-5300
• ISSN: 1364-5579
• Language: English
• Keywords: calibration; exclusive disjunction; qualitative comparative analysis