Eliminating the Influence of Irrelevant Cases on the Consistency and Coverage of Necessary and Sufficient Conditions in Fuzzy-Set QCA

Consistency and coverage have been firmly established as central measures within Qualitative Comparative Analysis (QCA). Consistency indicates how well the empirical cases are in line with the hypothesis that a condition (or set of conditions) is necessary or sufficient for the outcome, while coverage delineates the empirical relevance of a consistent solution. When the consistency and coverage measures are applied in fuzzy-set analysis, however, one problem arises that has not been sufficiently addressed so far: the inclusion of irrelevant cases. For evaluating the consistency of sufficient or the coverage of necessary conditions, cases that are not part of the condition are irrelevant. The same is true for cases not showing the outcome with regard to the consistency of necessary or coverage of sufficient conditions. In crisp-set analysis, such cases are always zero and hence excluded. Fuzzy-sets, on the other hand, allow cases with low membership in condition or outcome to count positively for consistency and coverage, thus creating the possibility that QCA solutions are driven by irrelevant cases. To solve this problem, a refinement of the formulae for consistency and coverage is proposed that excludes irrelevant cases by using dichotomized values as a multiplier within the fuzzy-set calculations. The paper provides empirical evidence for both the problem and the effects of the proposed solution based on data taken from a recently finished research project on the adoption, implementation and sustainability of minority protection rules in ten new EU member states from Central and Eastern Europe. It is also shown that the recently suggested solution for a similar issue – the inspection of Ragin’s PRI measure to evade the possibility that a condition can be sufficient for both the presence and absence of the outcome, which is also most likely when membership is low – does not solve the discussed problem.