Quality & Quantity

, Volume 49, Issue 1, pp 75–92 | Cite as

But not both: the exclusive disjunction in qualitative comparative analysis (QCA)

  • Ursula HackettEmail author


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.


Qualitative comparative analysis QCA Exclusivity Boolean OR  Disjunction 


  1. Akers, S.B.: On a theory of boolean functions. J. Soc. Ind. Appl. Math. 7(4), 487–498 (1959)CrossRefGoogle Scholar
  2. Aus, J.P.: Conjunctural causation in comparative case-oriented research. Qual. Quant. 43(2), 173–183 (2009)CrossRefGoogle Scholar
  3. Carter, J.R., Schap, D.: Line-item veto: where is thy sting? J. Econ. Perspect. 4(2), 103–118 (1990)CrossRefGoogle Scholar
  4. Druckman, J.N.: Political preference formation: competition, deliberation, and the (ir)relevance of framing effects. Am. Political Sci. Rev. 98(4), 671–686 (2004)CrossRefGoogle Scholar
  5. Edwards, A.: Causes of bewilderment: necessity, sufficiency and facilitating conditions for democratization. Democratization 1(2), 444–460 (1994)CrossRefGoogle Scholar
  6. Felix, R.: Relationships between goals in multiple attribute decision making. Fuzzy Sets Syst. 67(1), 47–52 (1994)CrossRefGoogle Scholar
  7. Ferris, J.M.: A contractual approach to higher education performance: with an application to Australia. High. Educ. 24, 503–516 (1992)CrossRefGoogle Scholar
  8. Fish, S.M., Wittenberg, J.: Failed democratization. In: Haerpfer, C., Inglehart, R., Welzel, C. (eds.) Democratization, pp. 249–265. Oxford University Press, London (2009)Google Scholar
  9. Fleisher, H., Tavel, M., Yeager, J.: Exclusive-OR representations of boolean functions. IBM J. Res. Dev. 27(4), 412–416 (1983)CrossRefGoogle Scholar
  10. 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)Google Scholar
  11. Goertz, G., Levy, J.S.: Explaining war and peace: case studies and necessary condition counterfactuals. Routledge (Taylor and Francis Group), London (2007)CrossRefGoogle Scholar
  12. Goertz, G., Mahoney, J.: Methodological Rorschach tests: contrasting interpretations in qualitative and quantitative research. Comp. Political Stud. 46(2), 236–251 (2012)CrossRefGoogle Scholar
  13. Greenawalt, K.: All or nothing at all: the defeat of selective conscientious objection. Supreme Court Rev. 31, 31–94 (1971)Google Scholar
  14. Grice, H.P.: Studies in the way of words. Harvard University Press, Cambridge (1989)Google Scholar
  15. Haan, J.D., Sturm, J.E.: Political and institutional determinants of fiscal policy in the European Community. Public Choice 80, 157–172 (1994)CrossRefGoogle Scholar
  16. Hodder-Williams, R.: British politicians: to rehabilitate or not? Parliam. Aff. 49(2), 285–297 (1996)CrossRefGoogle Scholar
  17. Hurford, J.R.: Exclusive or inclusive disjunction. Found. Lang. 11(3), 409–411 (1974)Google Scholar
  18. Jennings, G.: The geneology of disjunction. Oxford University Press, New York (1994)Google Scholar
  19. Keren, G.: Framing, intentions, and trust-choice incompatibility. Organ. Behav. Hum. Decis. Proces. 103(2), 238–255 (2007)CrossRefGoogle Scholar
  20. 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)CrossRefGoogle Scholar
  21. Mackie, J.L.: Causes and conditions. Am. Philos. Q. 2(4), 245–264 (1965)Google Scholar
  22. 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)CrossRefGoogle Scholar
  23. Moore, B.: Social origins of dictatorship and democracy: lord and peasant in the making of the modern world. Beacon Press, Boston (1967)Google Scholar
  24. Pennings, P.: The diversity and causality of welfare state reforms explored with fuzzy-sets. Qual. Quant. 39, 317–339 (2005)CrossRefGoogle Scholar
  25. Ragin, C.C.: The comparative method: moving beyond qualitative and quantitative strategies. University of California Press, Berkely (1987)Google Scholar
  26. Ragin, C.C.: Set relations in social research: evaluating their consistency and coverage. Political Anal. 14(3), 291–310 (2006)CrossRefGoogle Scholar
  27. Ragin, C.C.: Redesigning social inquiry: fuzzy sets and beyond. University of Chicago Press, Chicago (2008)CrossRefGoogle Scholar
  28. 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)CrossRefGoogle Scholar
  29. 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)Google Scholar
  30. Romme, A.G.L.: Boolean comparative analysis of qualitative data. Qual. Quant. 29, 317–329 (1995)CrossRefGoogle Scholar
  31. 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)Google Scholar
  32. 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)CrossRefGoogle Scholar
  33. Simpson, J. (ed.): Or, Conj. 2. In correlative constructions. Oxford english dictionary. Oxford University Press, Oxford (2004)Google Scholar
  34. Sweet, C.: Democratization without democracy: political openings and closures in modern Morocco. Middle East Rep. 218, 22–25 (2001)CrossRefGoogle Scholar
  35. Taagepera, R.: Making social sciences more scientific: the need for predictive models. Oxford University Press, New York (2008)CrossRefGoogle Scholar
  36. Tilly, C.: Inequality, democratization, and de-democratization. Sociol. Theory 21(1), 37–43 (2003)CrossRefGoogle Scholar
  37. 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)CrossRefGoogle Scholar
  38. 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)CrossRefGoogle Scholar
  39. 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)CrossRefGoogle Scholar
  40. Whitehead, F: Student recruitment strategy: four universities, five key questions. The guardian higher education network. (2012) Accessed 3 June 2013

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Politics and International RelationsUniversity of OxfordOxfordUK

Personalised recommendations