What leads to representations?

3.2.2.1.1. Sufficient conditions

As we did previously, we will start with the truth table to see if there are any differences to the complex solution term. The truth table is given in Table 14:

Table 14: Truth table for outcome condition ‘representations’ with disjunction of economic conditions

eco-nomyor

seces-sion

pat-ron

free-dom

num-ber

cases

represen-tations consistency

1 0 1 0 1 Taiwan 1980 1 1.000000

1 0 1 1 1 Taiwan 2010 1 1.000000

1 1 1 1 1 TRNC 1 0.826087

1 1 1 0 3 PMR; Abkhazia;

Kosovo 0 0.577689 0 1 1 0 1 South Ossetia 0 0.522013

1 1 0 0 2 NKR;

Somaliland 0 0.512397

As we can see from the table, there are three sufficient paths to the outcome, as was the case with ‘economy’. The main difference is that the ‘economyor’

condition is represented in all paths; previously, economic conditions did not have such influence. To see the exact influence that different economic variables can have, we have to look at the results. These are presented in Table 15:

Table 15: Solution terms of sufficient combinations for representations with disjunction of economic conditions

Complex solution 0.667 0.912

economyor*~secession

*patron 0.444 0.120 1

economyor*patron*freedom 0.546 0.223 0.895

Parsimonious solution 0.735 0.904

~secession 0.452 0.120 1 freedom 0.614 0.283 0.887

Intermediate solution 0.667 0.912

patron*~secession

*economyor 0.444 0.120 1 freedom*patron*economyor 0.546 0.223 0.895 Notes: consistency threshold 0.8; ‘~’ indicates the absence of a condition

There are several things of note in the table. First of all, the complex solution term is not identical to the truth table rows with outcome. This, as one may recall, was the case when economic conditions were tied together with the logical AND operator. Here the complex solution term is available for logical minimisation using the Quine-McCluskey algorithm. Therefore, we get two results but both include three conditions rather than four, as in the truth table.

Secondly, the intermediate and complex solution terms are identical, consisting of the same conjunctures. The same was the case with the analysis of the absence of outcome. Thirdly, the economic condition is on a par with the patron condition in the sense that it is present in both combinations. That was not the case with the conjunction. Fourth, the most parsimonious solution is exactly the same as it was with the conjunction of economic conditions. This shows that, when taking into account difficult counterfactuals, the results are not influenced by economic conditions. There is no difference whether we treat them as one or give each component a weight.

The whole intermediate solution covers around two thirds of the outcome, therefore around one third must be explained by some other reasons. This is similar to the result obtained with the conjunction of economy. The solution consistency is over 0.9, which means that we can quite confidently speak about sufficiency here. And it is also slightly higher than the analysis with economy conjunction.

Coming to independent paths, ‘patron*~secession*economyor’ has a con-sistency score of ‘1,’ therefore there is no need to check for possible contra-dictory cases. The statement of sufficiency holds; all cases would be above the main diagonal on an XY-plot. However, the coverage of this path is under 0.5 and its unique coverage a very low 0.12. The reason for this is, first, that the solution coverage itself is not very high and, second, there are two conditions that overlap in both paths. Their unique coverage has to be rather low because of this overlap.

The path ‘freedom*patron*economyor’ has a better coverage score of 0.546, but overall it is also not very impressive. Its unique coverage score is almost twice that of ‘patron*~secession*economyor’ at 0.223, but the overlap effect is still there. The difference between the two paths must come from the different condition and we can say that ‘freedom’ seems to have more coverage on the outcome than ‘~secession’.

The consistency score of ‘freedom*patron*economyor’ is just under 0.9.

This does not prevent us from considering the path to be sufficient for the outcome because the consistency score is still relatively high. However, with no perfect subset-superset relations, we have to check which cases contribute to the lowering of the consistency score and whether there are logically contradictory cases. The results are shown in Figure 12 below.

As we can see, there are two data-points below the main diagonal. They represent two cases – Abkhazia on the lower left side and TRNC on the upper right side. Even though they contribute to the low consistency score, they are not logically contradictory cases. To be that, a case must have a score higher than 0.5 in the condition and lower than 0.5 in the outcome. Here, Abkhazia has scores (0.35, 0.27) which are both below 0.5 and TRNC has scores (0.88, 0.64) which are both above 0.5. Hence, even though the consistency does not reflect perfect subset-superset relations, we can say that the statement of sufficiency holds because there are no logically contradicting cases.

Figure 12: Cases of the path ‘freedom*patron*economyor’ against representations from Table 15

3.2.2.1.2. Necessary conditions

The analysis of necessity has to confirm or disconfirm the hunch that both conditions which featured in both paths in the intermediate solution term are necessary conditions. Furthermore, as there was logical minimisation involved in the calculation of the most complex solution term, there might be conditions that are redundant as sufficient conditions yet still necessary. However, the truth table shows that the possibility of this is small. The analysis of necessity is presented in Table 16 below.

over the threshold of 0.9 or very close to it. And these conditions are exactly those that figure in both causal paths in complex and intermediate solution terms: ‘patron’ and ‘economyor’. As one can observe, the results for ‘patron’ are exactly the same as they were in the previous analysis. This is certainly logical, because nothing has changed in the relation between ‘patron’ and the outcome. Therefore, everything that was said earlier about the statement of necessity still applies. This means the slightly lower consistency score than recommended in the literature and the logically contradictory case of Somaliland reduce the possibility of ‘patron’ being a necessary condition.

F r e e d o m A N D p a t r o n A N D e c o n o m y o r

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1

Representations

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1

As we can see, two conditions are either

Table 16: Necessary conditions for the outcome ‘representations’ with disjunction of economic conditions

Condition Consistency Coverage

secession 0.616466 0.454815

~secession 0.451807 1

patron 0.897590 0.644092

~patron 0.138554 0.334951 freedom 0.614458 0.886956

~freedom 0.558233 0.500901 economyor 0.937751 0.674855

~economyor 0.176707 0.423077

The other condition ‘economyor’ has a consistency score of 0.94, which is comfortably above the recommended threshold but still some way short of perfect subset-superset relations. As we may recall, with necessity the con-ditions were the superset and the outcome was the subset. With sufficiency it is the other way round. To identify the cases that deviate from perfect set-relations, we use the XY-plot which is presented in Figure 13:

Figure 13: Cases of disjunction of economic conditions (‘economyor) against representations from Table 16

E c o n o m y o r

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1

Representations

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1

The XY-plot shows us one case that is not consistent with the statement of necessity. It is located on the lower left corner of the plot and is South Ossetia.

There are three cases in the upper right corner that also seem to be above the main diagonal, but their scores in both the condition and the outcome are very high, so they do not influence the overall score too much. The main case which does so is South Ossetia with its scores of (0.05, 0.27).

Still, with this score, it is not a logically contradictory case. For necessity, the contradiction would be a higher than 0.5 score in the outcome but a lower than 0.5 score in the condition. On the XY-plot, the upper left corner should be empty, and in the case of ‘economyor’ it is. Therefore, we can state that ‘eco-nomyor’ is a necessary condition for the outcome. Compared to the conjunction

‘economy’ this gives the economic conditions a more prominent role in the acceptance of de facto states. To view economic conditions separately adds to our knowledge about de facto states in the international system.

Overall, for the outcome ‘representations’ or the presence of representations, the use of economic conditions separately gave a different insight. Next we will see if the same applies to ‘~representations’.