Qualitative Comparative Analysis

Crisp-Set QCA

Originally, QCA performed calculations on Boolean, that is dichotomized, data only. In terms of set theory, this means that QCA deals with “crisp sets” as opposed to “fuzzy sets.” All data included in a csQCA analysis must therefore be coded dichotomously, which means that it has to be considered for each case whether the case fulfills the condition or not. The outcome has to be coded dichotomously as well. By convention, in csQCA, an uppercase notation indicates the presence of a condition, whereas a lowercase notation signifies the absence of this condition. By using Boolean algebra, the configuration for a case can then be written by concatenating the values for all the conditions included in the analysis. For example, in a study concerning the conditions of development of new ecological parties in Western democracies in the 1980s, it is theoretically feasible that the success of these parties depended on conditions such as the electoral system (proportional representation or not), a high level of socioeconomic development (measured by gross national product [GNP]), the construction of nuclear power plants, and the density of the population. In the case of [Page 2174]Norway, for example, a high level of socioeconomic development can be observed, as well as a system of proportional representation; these two conditions are met, but there are no nuclear power plants, and the density of the population is low. Thus, for Norway, the configuration can be written as VOTING ∗ GNP ∗ nuclear ∗ density (∗ indicating the Boolean AND).

In the first step, all cases with the same configuration are grouped together. For each configuration, the outcomes of the cases included are compared. If all cases show the same outcome, the common value (positive or negative) is assigned; if not, the configuration is marked as contradictory. In the second step, for all configurations with the same outcome, the minimization rule is used to identify conditions that are not relevant for the outcome to occur: “If two Boolean expressions differ in only one condition yet produce the same outcome, then the causal condition that distinguishes the two expressions can be considered irrelevant and can be removed to create a simpler, combined expression” (Ragin, 1987, p. 93). So if, for example, all cases with the configuration VOTING ∗ GNP ∗ nuclear ∗ density and voting ∗ GNP ∗ nuclear ∗ density show the same outcome, the condition VOTING can be considered to be superfluous. The minimization rule is applied iteratively to the identified simpler expression, minimizing the included logical expression as far as possible. This produces a number of “prime implicants,” each explaining only cases with the outcome examined.

...