Still an Era of Fragmented Authoritarian 1.0? A Probabilistic Crucial Case Analysis

Abstract

Now that the concepts of authoritarian institutions and dictator’s growth curse have been properly given corresponding interpretations in China’s political context, this chapter adopts a probabilistic crucial case analysis to determine the composition of China’s sectoral players in the trade policy game and justifies my choice of who should and should not be included in it. It is precisely because of the analysis in this chapter that it makes sense for the narratives to zero in on the Communist Party of China central committee members’ promotion expectations within the hierarchy.

Appendix: A Qualitative Research Design: Probabilistic “Crucial Case” Method and Bayesian Inference

Given the lack of systematic (linear) measures of agency slack and societal actors’ political activities in various policy areas, the testing of the FA 2.0 thesis, as a consequence, has to resort mainly to case study methods. However, it is beyond the scope of the book to conduct a comparative case study of different policy areas. Consequently, on the one hand, we sift out from the qualitative methodologists’ tool kit a single-case research design of Harry Eckstein’s crucial case method (1975) that provides such a possibility of making inference from a case that is “critical” either in the confirmatory or in the disconfirmatory sense. On the other hand, as suggested by Gerring (2007), realistically, the crucialness of a case is chiefly not a question of “either/or,” but one of degree. The following analysis therefore reformulates the crucial case method in Eckstein (1975) to switch the logic of inference from deterministic to probabilistic so we can assess how much more confidence will be gained from our analysis of the Labor Contract Law vis-à-vis the findings in the burgeoning literature based on the FA 2.0 thesis.

1.1 Crucial Case Analysis and Bayesian Inference

The analytical leverage of the crucial case method in making inferences is principally based on how “crucial” is defined. According to Eckstein (1975), a “crucial” case is one that “must closely fit a theory if one is to have confidence in the theory’s validity, or, conversely, must not fit equally well any rule contrary to that proposed” (p. 118). This statement reveals clearly why (causal) inferences can be made from a single case study. Cases differ in how much empirical support they can provide for a given theory of interest. In other words, it is more cost-efficient to focus on cases that are more informative in the sense of either confirming or disconfirming the proposed theory.

Moreover, it can be readily recognized that the logic of inference lying within this idea is Bayesian (McKeown 1999; Sekhon 2004).²¹ In Bayesian terms, as Colin Howson and Peter Urbach put it (Gerring 2007, p. 234), the degree to which a hypothesis (denoted by $h$) derived from the theory of interest is confirmed or disconfirmed by a set of evidence or cases (denoted by $e$) is a function of the expression²²

$$ \mathit{\Pr}(e|h)-\mathit{\Pr}(e) $$

(6.11)

which is essentially a difference between the likelihood of $e$ when $h$ is true and that when $h$ is false. If $h$ is true (false), then Eq. (6.11) is positive (non-positive).²³ Alternatively, applying Bayes’ theorem to Eq. (6.11) yields

$$ \mathit{\Pr}(e)\left[\frac{\mathit{\Pr}(h|e)}{\mathit{\Pr}(h)}-1\right] $$

(6.12)

which shows patently that the degree of confirmation or disconfirmation depends on three parameters: (1) $\mathit{\Pr}(e)$, (2) $\mathit{\Pr}(h)$ (prior), and (3) $\mathit{\Pr}\left(h|e\right)$ (posterior).²⁴

More specifically, as far as confirmatory crucial cases are concerned, the degree of confirmation is negatively associated with the Bayesian prior—$\mathit{\Pr}(h)$, that is, our (subjective) assessment of how likely it is that $h$ holds before the evidence is examined—and this implies that, ceteris paribus, our confidence in confirming the theory is raised to a higher level when the hypothesized relationship for a certain case is more counterintuitive and less likely to happen. The probability for the theory to hold in a case is minimal if, except the variable of interest, the case has almost all the characteristics that run counter to the presence of the predicted relationship. For instance, in Reilly and Phillpot (2002), Papua New Guinea is selected as a confirmatory crucial case to test Robert Putnam’s social capital theory (1993) for its high degree of ethnic fragmentation. In other words, the prior probability for the hypothesis derived from the social capital theory to hold in Papua New Guinea, $\mathit{\Pr}\left({h}_{\mathrm{social}\ \mathrm{capital}}^{\mathrm{Papua}}\right)$, is believed to be substantially low. As a consequence, if the democracy in Papua New Guinea does “work,” it implies that

$$ \frac{\mathit{\Pr}\left({h}_{\mathrm{social}\ \mathrm{capital}}^{\mathrm{Papua}}|{e}^{\mathrm{Papua}}\right)}{\mathit{\Pr}\left({h}_{\mathrm{social}\ \mathrm{capital}}^{\mathrm{Papua}}\right)}>1 $$

(6.13)

and therefore not only will Eq. (6.12) be positive, but our confidence in the social capital theory is also enhanced to a higher level than that based on other cases $\left\{\sim i\right\}$ with higher $\mathit{\Pr}\left({h}_{\mathrm{social}\ \mathrm{capital}}^{\left\{\sim i\right\}}\right)$.

Regarding disconfirmatory crucial cases, the degree of disconfirmation is, on the contrary, positively related to the prior $\mathit{\Pr}(h)$. That is, ceteris paribus, we can be more confident in rejecting the theory of interest under the condition that the predicted relationship is more intuitive and very likely to happen. In Westman (1985), for example, the Brazilian minicomputer industry is the most likely case for the dependency theory because the Brazilian capital, private or public, was non-existent in this industry before 1977, and the technology was also entirely controlled by multinational corporations by then. In Bayesian terms, this implies that arguably the prior, $\mathit{\Pr}\left({h}_{\mathrm{dependency}\ \mathrm{theory}}^{\mathrm{Brazil}}\right)$, is believed to be very high in this case. Nonetheless, despite these two typical signs of dependence, the Brazilian government and national firms were still able to gain control over the industry after the former launched a series of policies to develop its own minicomputer industry. In other words, updated with this Brazilian case, we actually become less confident about the validity of the dependency theory. Applying the same Bayesian framework to this example yields the following set of relationships,

$$ \frac{\mathit{\Pr}\left({h}_{\mathrm{dependency}\ \mathrm{theory}}^{\mathrm{Brazil}}|{e}^{\mathrm{Brazil}}\right)}{\mathit{\Pr}\left({h}_{\mathrm{dependency}\ \mathrm{theory}}^{\mathrm{Brazil}}\right)}<1 $$

(6.14)

which not only makes Eq. (6.12) negative, but also increases our confidence in disconfirming the dependency theory as opposed to other cases with lower priors. In Jack Levy’s words, the logic of inference in both confirmatory and disconfirmatory crucial case studies can be intuitively explained by what he calls “Sinatra inferences” (2002). That is, the confirmatory crucial case method follows a Sinatra inference: “If I can make it there, I can make it anywhere.” By contrast, as far as the disconfirmatory crucial case method is concerned, the inverse Sinatra inference is applied that “If I cannot make it there, I cannot make it anywhere.”

1.2 Probabilistic Crucial Case Analysis and Fragmented Authoritarianism

1.2.1 Operationalizing the FA 2.0 Thesis

To apply the crucial case design to our question of interest, the FA 2.0 thesis, I use Fig. 6.3 to present the test in schematic form. As mentioned in Sect. 6.1.2, the transition from FA 1.0 to FA 2.0 means more than just an increase in the number of players in the policy game; it also means a qualitative transformation. To operationalize this transition for the sake of our empirical testing, however, the following analysis still uses changes in the number of members taking part in the process as a way to capture the effect of this transformation.

Fig. 6.3

Crucial case test and China’s fragmented authoritarianism

To denote all the actors in Fig. 6.3, we use their initial letters, and therefore the set of China’s policymakers, $P$, is a subset of the full set, $F$, that contains all actors in Fig. 6.3 as its members

$$ P\subseteq F=\left\{B,C,L,M,O,T\right\} $$

(6.15)

When $P=F$, China’s policymaking is characterized by the highest degree of fragmentation (i.e., democracy). Under the same notation, the other extreme of $P$ where only top leaders matter in the policymaking process then becomes a singleton $P=\left\{T\right\}$ It would be absurd to set $P=F$, since the Chinese government so far has offered no effective institutional channels for its citizens to get organized and voice their concerns over policies. Regarding the other extreme, according to the long tradition in the literature on China’s post-reform policymaking (Liebertha l and Oksenberg 1988; Liebertha l 1992; Shirk 1993), setting

$$ P=\left\{T\right\} $$

(6.16)

does not reflect China’s political reality, either. Instead, as visualized by Fig. 6.3, the theory of transition assumed by the FA 2.0 thesis predicts an evolution in China’s policymaking process from FA 1.0

$$ {P}^{V1}=\left\{L,M,T\right\} $$

(6.17)

to FA 2.0

$$ {P}^{V2}=\left\{B,C,L,M,T\right\} $$

(6.18)

when agency slack is present in a given policy area.

1.2.2 Probabilistic Crucial Case Framework

After operationalizing the FA 2.0 thesis, we also make it clear here that our crucial case analysis in this chapter relaxes the assumption of deterministic theory made in the bulk of the literature.²⁵ In other words, the key parameter of the FA 2.0 theory of transition, agency slack, will be treated as a continuous and probabilistic measure,²⁶ $\mathit{\Pr}\left(\mathbf{Agency}\ \mathbf{Slack}\right)$ (i.e., how likely it is for agency slack to take place in a given policy area), instead of a dichotomous variable with two outcomes, presence or absence of agency slack. Similarly, the outcome of interest, ${P}^{V1}$ and ${P}^{V2}$, will also be transformed into a probabilistic continuous measure, $\mathit{\Pr}\left({P}^{V2}\right)$ (i.e., how likely it is for the FA 2.0 thesis to hold and societal actors to be able to exercise influence over policymaking process). According to this reading of the theory, as Gerring suggests (2007, p. 238), a case is crucial not in terms of its quality, but its degree of crucialness.

Form a Bayesian perspective, the probabilistic reading of the theory of interest makes it more straightforward to understand the logic of inference according to which gaining or losing confidence for a theory is determined by how crucial the case under scrutiny is. To put this in the context of the FA 2.0 thesis, a case is more crucial, confirmatorily, when $\mathit{\Pr}\left(\mathbf{Agency}\ \mathbf{Slac}{\mathbf{k}}_i\right)$ for policy area $i$ is lower, since, as per the thesis, the expectation for the FA 2.0 thesis to hold under this circumstance is supposedly lower than it is when $\mathit{\Pr}\left(\mathbf{Agency}\ \mathbf{Slac}{\mathbf{k}}_{\sim i}\right)$ is higher. More critically, the corollary of this is that our theoretical prior for policy area $i$, $\mathit{\Pr}\left({h}_{\mathbf{FA}\ \mathbf{2.0}}^i\right)$, will also be lower, and according to ([howurba2]), the resulting confidence in the theory of interest will increase when both the likelihood for the data (i.e., case), $\mathit{\Pr}\left({e}^i\right)$, and the posterior, $\mathit{\Pr}\left({h}_{\mathbf{FA}\ \mathbf{2.0}}^i|{e}^i\right)$, are held constant. Intuitively, when policy area $i$ is less subject to agency slack, the FA 2.0 thesis is expected accordingly to be less likely to hold. As a result, the examination of policy area $i$ can be much more rewarding in terms of our confidence in the validity of the thesis when the degree of policy tinkering is consistent with the theoretical prediction.