Analysis

As noted above, the main goal of MVQCA is to find a parsimonious solution which explains the success and failure of UN mediation efforts. This is done by performing a minimization procedure on the dataset.

7.2.1. Extracting Equations from the Truth Table

The truth table is used to extract equations to explain the respective outcomes. MVQCA uses the same principles of Boolean notation: Addition is equivalent to the logical operator OR, meaning that either expression has to be present for the outcome to be true, whereas multiplication indicates the logical operator AND, meaning that all expressions have to be present for the outcome to be true. With these basic rules, one can easily construct the following “sums of products” expressions (Ragin, 1987: 91). In these equations, each case in the table is represented by a combination of causal factors; the numbers in parentheses indicate the level of the factor:

Success = Impartiality (2) * Leverage (2) * Status (2) + Impartiality (2) * Leverage (1) * Status (1) + Impartiality (1) * Leverage (2) * Status (2) + Impartiality (0) * Leverage (2) * Status (2) Failure = Impartiality (0) * Leverage (0) * Status (0)

+ Impartiality (1) * Leverage (0) * Status (2)

7.2.2. Minimization Procedure

Theses equations are rather complex and do not allow to draw clear conclusions. In order to arrive at concise explanations of the outcomes, Ragin (1987) has suggested a minimization procedure. His fundamental rule states that

“If two expressions differ in only one causal 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: 93).

As it focuses on pairs of configurations which differ in only one cause, this logic parallels the logic of experimental design and therefore fulfills the ideal of social scientific comparison (Ragin, 1987: 27 ff., 94). But Ragin introduced this method for dichotomous data only, so that the rule needs to be rewritten for multi-value reduction:

“If all n multi-value expressions differ in only one causal condition C while all n possible values of c produce the same outcome, then the causal condition C that distinguishes these n expressions can be considered irrelevant and can be removed to create a simpler, combined expression” (Cronqvist, 2005: 5).

This rule for multi-value reduction is a generalization of Ragin’s rule for Boolean reduction because QCA datasets can also be processed with the MVQCA rules (Cronqvist, 2003a: 9;

Cronqvist, 2005: 2, 5). The procedure is conducted in a bottom-up fashion until no further reduction of expressions is possible (Ragin, 1987: 94).

In line with this rule, the following reductions are possible for all successful UN mediation cases:

Impartiality (2) * Leverage (2) * Status (2) for East Timor, Impartiality (1) * Leverage (2) * Status (2) for Cambodia and

Impartiality (0) * Leverage (2) * Status (2) for El Salvador can be reduced to

Leverage (2) * Status (2) because these three terms differ only in their level of impartiality yet otherwise produce the same outcome. Impartiality distinguishes the three expressions and can therefore be considered irrelevant and can be eliminated. Leverage (2) * Status (2) is a so-called prime implicant which covers several primitive expressions. The fourth expression for

Guatemala cannot be reduced. Thus, the minimization procedure for all positive cases generates the final, reduced equation:

Success = Leverage (2)*Status (2) + Impartiality (2)*Leverage (1)*Status (1)

The same logic applies to the negative outcomes: But

Impartiality (0) * Leverage (0) * Status (1) for Myanmar and Impartiality (1) * Leverage (0) * Status (2) for Cyprus

cannot be reduced because the two cases differ in their levels of impartiality and status and not in only one single variable which could be omitted. Therefore, UN mediation failure is expressed with the long-winded equation:

Failure = Impartiality (0)*Leverage (0)*Status (0) + Impartiality (1)*Leverage (0)*Status (2)

The respective outcomes of the six UN mediation cases are fully explained by the prime implicants in these two equations (see Appendix 8.1 and 8.2.). All successful cases are explained by a high level of leverage and status or by a high level of impartiality and a medium level of leverage and status. All failed UN mediation cases are explained by a low level of leverage in combination either with a low level of impartiality and a low level of status or with a medium level of impartiality and a high level of status. The Manual Selection window in TOSMANA confirms that no other solution is possible (Cronqvist, 2006: 14).

7.2.3. Remainders

The number of cases that exist logically but are not in the dataset is higher in MVQCA than in QCA. In QCA, there are eight logically possible configurations for three binary causal variables (2³=8; see Ragin, 1987: 87). In MVQCA, where each causal variable can take on three different values, the number of logically possible configurations is increased to 27 (3³=27). As there are only six real cases in my UN mediation dataset which encompass the

maximum number of six different configurations, both methods necessarily include ‘logical remainders’.

Even in studies where there are far more cases than logically possible configurations, the problem of logical remainders arises. Ragin (1987: 104 ff.; Ragin and Sonnet, 2004) calls it the problem of ‘limited diversity’: naturally occurring social phenomena hardly ever display all logically possible combinations of features. Although an annoyance to comparative social scientists who seek to construct perfect models, limited diversity in the real world is meaningful and is in fact “evidence of a socially constructed order” (Ragin, 1987: 105).

In 6.2.2., concrete statements about causation were only made about those combinations of factors which exist in the real world. The universe of cases in this study is relatively small because the analysis is restricted to UN mediation cases since 1990. However, one can assume that other combinations of factors might actually exist in the future as none of the elements are evidently incompatible, i.e. logically impossible.

MVQCA allows for the inclusion of these logical remainders into the analysis. As indicated above, the reasoning behind this modus operandi is that the 21 logical remainders in this analysis can theoretically have either outcome because such cases have not been observed (yet). The ‘new’ goal is then to identify a concise expression of factors which represents all cases having a specific outcome or being undecided (Ragin calls these ‘don’t care’ cases) but does not explain any of the other cases. In other words: one can remove all causal conditions which are not needed to explain successful UN mediation cases as long as the reduced expression does not imply any failed UN mediation case and vice versa.

Formally, the rule is stated as follows:

“If two ore more multi-value expressions differ in only one causal condition C with n possible values yet produce the same outcome, then the causal condition C that distinguishes these n expressions can be considered irrelevant and can be removed to create a simpler, combined expression if there is no expression implied by the new expression producing a different outcome.” (Cronqvist, 2005: 6;

Cronqvist, 2003a: 10)

The algorithm for reducing the primitive expressions is the same as above. When the logical remainders are included in the calculation of the prime implicants, the following reductions are possible (see 8.3. and 8.4. in the Appendix):

Success = Leverage (1,2)

and

Failure = Leverage (0)

This means that of all 18 logically possible combinations with a medium and with a high level of leverage, four are the successful UN mediation cases and 14 are logical remainders which can theoretically be successful. No failed UN mediation cases have a medium or high level of leverage. Accordingly, a low level of leverage implies the failed UN mediation cases Myanmar and Cyprus and the other seven logical configurations with a low level of leverage – but no successful case has a low level of leverage. Again, the Manual Selection window in TOSMANA confirms that there were no other possible prime implicants to be included in the minimal solutions (Cronqvist, 2006: 14). Thus, all 27 logically possible combinations with low, medium and high levels of the three factors impartiality, leverage and status are represented in these two minimal solutions.

The above two expressions are obviously more parsimonious than the ones where logical remainders are excluded and make a much more comprehensible result. The interpretation of the results and a discussion of their quality will be part of the next section.