Abstract
The application of Boolean logic using qualitative comparative analysis (QCA) is becoming more frequent in political science but is still in its relative infancy. Boolean ‘AND’ and ‘OR’ are used to express and simplify combinations of necessary and sufficient conditions. This paper draws out a distinction overlooked by the QCA literature: the difference between inclusive- and exclusive-or (OR and XOR). It demonstrates that many scholars who have used the Boolean OR in fact mean XOR, discusses the implications of this confusion, and explains the applications of XOR to QCA. Although XOR can be expressed in terms of OR and AND, explicit use of XOR has several advantages: it mirrors natural language closely, extends our understanding of equifinality and deals with mutually exclusive clusters of sufficiency conditions. XOR deserves explicit treatment within QCA because it emphasizes precisely the values that make QCA attractive to political scientists: contextualization, confounding variables, and multiple and conjunctural causation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
In H.P. Grice’s terms, the word ‘or’ has a conversational implicature, something that can be worked out from how something was said, rather than simply what was said. Usually there are contextual clues that indicate whether the ‘or’ used is exclusive or inclusive. For example, the ‘or’ in ‘you may have tea or coffee’ sounds inclusive when stated in a neutral tone, but exclusive if the ‘or’ is given heavy emphasis. See Grice’s (1989) work Studies in the Way of Words for discussion of both conversational and conventional implicature.
In Boolean logic, upper-case letters represent the presence of a condition and lower-case letters represent its absence.
The pathway to intermediate policies would, like the paths to restrictive policies, also require the XOR as follows: \(\hbox {gIar} \oplus \hbox {gImAR} \rightarrow \hbox {Intermediate policies}\).
Context also matters. A disjunct that seems obviously exclusive and therefore in no need of XOR formalization may not be so in other contexts. The ‘or’ in ‘male OR pregnant’, for example, is clearly exclusive amongst humans but inclusive amongst members of the Syngnathidae family, such as seahorses.
Latter two examples taken from (Goertz 2003).
References
Akers, S.B.: On a theory of boolean functions. J. Soc. Ind. Appl. Math. 7(4), 487–498 (1959)
Aus, J.P.: Conjunctural causation in comparative case-oriented research. Qual. Quant. 43(2), 173–183 (2009)
Carter, J.R., Schap, D.: Line-item veto: where is thy sting? J. Econ. Perspect. 4(2), 103–118 (1990)
Druckman, J.N.: Political preference formation: competition, deliberation, and the (ir)relevance of framing effects. Am. Political Sci. Rev. 98(4), 671–686 (2004)
Edwards, A.: Causes of bewilderment: necessity, sufficiency and facilitating conditions for democratization. Democratization 1(2), 444–460 (1994)
Felix, R.: Relationships between goals in multiple attribute decision making. Fuzzy Sets Syst. 67(1), 47–52 (1994)
Ferris, J.M.: A contractual approach to higher education performance: with an application to Australia. High. Educ. 24, 503–516 (1992)
Fish, S.M., Wittenberg, J.: Failed democratization. In: Haerpfer, C., Inglehart, R., Welzel, C. (eds.) Democratization, pp. 249–265. Oxford University Press, London (2009)
Fleisher, H., Tavel, M., Yeager, J.: Exclusive-OR representations of boolean functions. IBM J. Res. Dev. 27(4), 412–416 (1983)
Goertz, G.: The substantive importance of necessary condition hypotheses. In: Goertz, G., Starr, H. (eds.) Necessary conditions: theory, methodology, and applications. Rowman & Littlefield, Lanham (2003)
Goertz, G., Levy, J.S.: Explaining war and peace: case studies and necessary condition counterfactuals. Routledge (Taylor and Francis Group), London (2007)
Goertz, G., Mahoney, J.: Methodological Rorschach tests: contrasting interpretations in qualitative and quantitative research. Comp. Political Stud. 46(2), 236–251 (2012)
Greenawalt, K.: All or nothing at all: the defeat of selective conscientious objection. Supreme Court Rev. 31, 31–94 (1971)
Grice, H.P.: Studies in the way of words. Harvard University Press, Cambridge (1989)
Haan, J.D., Sturm, J.E.: Political and institutional determinants of fiscal policy in the European Community. Public Choice 80, 157–172 (1994)
Hodder-Williams, R.: British politicians: to rehabilitate or not? Parliam. Aff. 49(2), 285–297 (1996)
Hurford, J.R.: Exclusive or inclusive disjunction. Found. Lang. 11(3), 409–411 (1974)
Jennings, G.: The geneology of disjunction. Oxford University Press, New York (1994)
Keren, G.: Framing, intentions, and trust-choice incompatibility. Organ. Behav. Hum. Decis. Proces. 103(2), 238–255 (2007)
Kitchener, M., Beynon, M., Harrington, C.: Qualitative comparative analysis and public services research: lessons from an early application. Public Manag. Rev. 4(4), 485–504 (2002)
Mackie, J.L.: Causes and conditions. Am. Philos. Q. 2(4), 245–264 (1965)
Milesi-Ferretti, G.M.: Good, bad or ugly? on the effects of fiscal rules with creative accounting. J. Public Econ. 88(1–2), 377–394 (2004)
Moore, B.: Social origins of dictatorship and democracy: lord and peasant in the making of the modern world. Beacon Press, Boston (1967)
Pennings, P.: The diversity and causality of welfare state reforms explored with fuzzy-sets. Qual. Quant. 39, 317–339 (2005)
Ragin, C.C.: The comparative method: moving beyond qualitative and quantitative strategies. University of California Press, Berkely (1987)
Ragin, C.C.: Set relations in social research: evaluating their consistency and coverage. Political Anal. 14(3), 291–310 (2006)
Ragin, C.C.: Redesigning social inquiry: fuzzy sets and beyond. University of Chicago Press, Chicago (2008)
Rihoux, B.: Qualitative comparative analysis (QCA) and related systematic comparative methods: recent advances and remaining challenges for social science research. Int. Sociol. 21(5), 679–706 (2006)
Rihoux, B., Ragin, C.C. (eds.): Applied social research methods series. Configurational comparative methods: qualitative comparative analysis (QCA) and related techniques, vol. 51. Sage Publishing, Los Angeles (2009)
Romme, A.G.L.: Boolean comparative analysis of qualitative data. Qual. Quant. 29, 317–329 (1995)
Schaechter, A., Kinda, T., Budina, N., Weber, A.: Fiscal rules in response to the crisis—toward the ‘next-generation’ rules. A New Dataset. International Monetary Fund Working Paper 1–49 (2012)
Schneider, C.Q., Wagemann, C.: Reducing complexity in qualitative comparative analysis (QCA): remote and proximate factors and the consolidation of democracy. Eur. J. Political Res. 45(5), 751–786 (2006)
Simpson, J. (ed.): Or, Conj. 2. In correlative constructions. Oxford english dictionary. Oxford University Press, Oxford (2004)
Sweet, C.: Democratization without democracy: political openings and closures in modern Morocco. Middle East Rep. 218, 22–25 (2001)
Taagepera, R.: Making social sciences more scientific: the need for predictive models. Oxford University Press, New York (2008)
Tilly, C.: Inequality, democratization, and de-democratization. Sociol. Theory 21(1), 37–43 (2003)
Varone, F., Rothmayr, C., Montpetit, E.: Regulating biomedicine in Europe and North America: a qualitative comparative analysis. Eur. J. Political Res. 45(2), 317–343 (2006)
Vis, B.: Under what conditions does spending on active labor market policies increase? an fsQCA analysis of 53 governments between 1985 and 2003. Eur. Political Sci. Rev. 3(2), 229–252 (2011)
Wagemann, C., Schneider, C.Q.: Qualitative comparative analysis (QCA) and fuzzy-sets: agenda for a research approach and data analysis technique. Comp. Sociol. 9(3), 376–396 (2010)
Whitehead, F: Student recruitment strategy: four universities, five key questions. The guardian higher education network. (2012) http://www.guardian.co.uk/higher-education-network/blog/2012/nov/13/student-recruitment-strategy-international-universities. Accessed 3 June 2013
Author information
Authors and Affiliations
Corresponding author
Glossary of Terms
Glossary of Terms
Term | Definition |
|---|---|
Exclusive disjunction | A or B, but not both |
Inclusive disjunction | A or B, or both |
Logical incompatibility | Where two conditions cannot logically occur simultaneously |
Practical incompatibility | Where two conditions cannot occur simultaneously because they would together violate a prior commitment or overshoot the outcome of interest |
Target category | The outcome of interest |
Intermediate outcome/Mid-range values | A distinctive outcome condition (dependent variable) that lies between two other conditions along a particular dimension, so that its values on that dimension are between the two extremes. |
Overshoot/ Overkill | Where the presence of just one of two causal conditions (independent variables) results in the target intermediate outcome, but the presence of both causal conditions results in a value along a particular dimension that is higher than the target outcome. The target outcome is not reached. |
Undershoot | Where the presence of precisely one of two causal conditions (independent variables) results in the target intermediate outcome, but the presence of neither causal condition results in a value along a particular dimension that is lower than the target outcome. The target outcome is not reached. |
Fuzzy Set XOR application | Split the exclusive disjunction into its component parts to find the fuzzy set value of each case according to the formula: min(max(A,B),max(a,b)) |
Rights and permissions
About this article
Cite this article
Hackett, U. But not both: the exclusive disjunction in qualitative comparative analysis (QCA). Qual Quant 49, 75–92 (2015). https://doi.org/10.1007/s11135-013-9975-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11135-013-9975-5