‘But Not Both: The Exclusive Disjunction in Qualitative Comparative Analysis (QCA)’ Ursula Hackett Department of Politics and International Relations, University of Oxford
[email protected] This paper has been accepted for publication and will appear in a revised form, subsequent to editorial input by Springer, in Quality and Quantity, International Journal of Methodology. Copyright: Springer (2013) 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. The primary function of the phrase ‘either…or’ is ‘to emphasize the indifference of the two (or more) things…but a secondary function is to emphasize the mutual exclusiveness’, that is, either of the two, but not both (Simpson 2004). The word ‘or’ has two meanings: Inclusive ‘or’ describes the relation ‘A or B or both’, and can also be written ‘A and/or B’.