Qual Quant (2015) 49:657–674
Parameters of ﬁt and intermediate solutions
in multi-value Qualitative Comparative Analysis
Published online: 8 March 2014
© Springer Science+Business Media Dordrecht 2014
Abstract Multi-value Qualitative Comparative Analysis (mvQCA) is a variant of QCA that
continues to exist under the shadow of crisp and fuzzy-set QCA. The lack of support for
parameters of ﬁt and intermediate solutions has contributed to this undeserved status. This
article introduces two innovations that put mvQCA on a par with its two sister variants.
First, consistency and coverage as the two most important parameters of ﬁt are generalized.
Second, the concepts of easy and difﬁcult counterfactuals for deriving intermediate solutions
are imported. I demonstrate how to leverage these features in the QCA software package for
the R environment. For researchers who do not use QCA, I explain how to exploit Veitch–
Karnaugh maps instead for solving set-theoretic minimization problems of low to moderate
Keywords Conﬁgurational comparative methods · Consistency · Coverage · csQCA ·
fsQCA · mvQCA · QCA · Qualitative Comparative Analysis
Multi-value Qualitative Comparative Analysis (mvQCA) has long led a niche existence under
the shadow of its two sister variants crisp-set QCA (csQCA) and fuzzy-set QCA (fsQCA).
Although Rihoux et al (2013, p. 177) speak of an upward trend, the comprehensive COM-
PASSS bibliographic database reveals that, out of currently 347 applications of QCA in
peer-reviewed academic journals since 1984, the share of mvQCA amounts to a meagre
2.9 per cent and is, if anything, on the decline again. For a method that was introduced
as a promising generalization of csQCA at about the same time as fsQCA, this ﬁgure is
A. Thiem (
Department of Philosophy, University of Geneva, Rue de Candolle 2 / Bât.
Landolt, 1211 Geneva, Switzerland