Two-Level Theories and Fuzzy Sets

Two-level theories explain outcomes with causal variables at two levels of analysis that are systematically related to one another. Although many prominent scholars in the field of comparative analysis have developed two-level theories, the empirical and methodological issues that these theories raise have yet to be investigated. In this article, we explore different structures of two-level theories and consider the issues involved in testing these theories with fuzzy-set methods. We show that grasping the overall structure of two-level theories requires both specifying the particular type of relationship (i.e., causal, ontological, or substitutable) that exists between and within levels of analysis and specifying the logical linkages between levels in terms of necessary and sufficient conditions. We argue that for the purposes of testing these theories fuzzy-set analysis provides a powerful set of tools. However, to realize this potential, investigators using fuzzy-set methods must be clear about the two-level structure of their theories from the onset. We illustrate these points through an empirical, fuzzy-set test of Skocpol’s States and Social Revolutions. With rare exceptions, theories utilize nonhierarchical, single-level causal structures. Whether statistical or qualitative, the results of the empirical analysis are represented in one equation. In this article, we show that two-level theories have distinctive theoretical properties and advantages, and in fact that many prominent theories really are two level in nature. Two-level theories offer explanations of outcomes by conceptualizing causal variables at two levels of analysis that are systematically related to one another. One level represents the core of the theory, focusing on the central causal variables and main outcome under investigation. The variables at this level refer to easily grasped and remembered concepts around which our social science vocabulary is primarily organized. We use the expression “basic level” to describe this part of the theory (c.f., Brown 1965; Rosch et al. 1976). A second level focuses on causal variables at a less central level of aggregation, often at a lower level. The variables at this “secondary level” are also causes of the main outcome under investigation, but their effects cannot be understood independently of their relationship with the causal factors at the basic level. Thus, one must grasp the structure of the relationship between the basic level and the secondary level before the theory as a whole can be understood and evaluated. We explore different structures of two-level theories and examine the methodological issues involved in employing fuzzy-set analysis test to these theories. We are centrally concerned with theories that propose relationships among variables using ideas about necessary and sufficient conditions. At either level, we examine two specific logical structures: (1) a set of causal factors that are individually necessary and jointly sufficient; and (2) a set of causal factors that are individually sufficient but not necessary. These kinds of causal relationships are commonly formulated in comparative studies, and they can be usefully analyzed with Ragin’s (1987; 2000) methods. However, methodologists have yet to explore either of these causal structures in the context of two-level theories. We also focus attention on how variables at a secondary level relate to the causal variables of the basic level. We examine three possible theoretical relationships: causal, ontological, and substitutable. With a causal relationship, the variables at the secondary level are treated as the causes of the causal variables at the basic level. In this sense, one can think about this kind of relationship as modeling “causes of causes.” With an ontological relationship, the variables at the secondary level represent features that define or constitute causal variables at the basic level. These secondary-level variables are not indicators of the basic-level variables, but rather are the elements that literally constitute basic-level phenomena. Finally, with a substitutable relationship, the variables at the secondary level are different ways by which it is possible arrive at basiclevel states. Here secondary-level variables often refer to alternative means of achieving ends represented by variables at the basic level. Ideas of necessary and sufficient conditions are essential to understanding each of these three relationships. For example, an ontological relationship traditionally has referred to a set of secondary-level variables that are necessary and sufficient for the existence of a given basic-level variable; in the classical approach to concepts, categories are defined via necessary and sufficient conditions (Sartori 1970; Collier and Mahon 1993; Lakoff 1987). A substitutable relationship refers to a set of secondary-level variables that are individually sufficient but not necessary for the presence of a given basic-level variable; they are various means to attain a given end (Most and Starr 1984). Finally, a causal relationship might be characterized by either necessity or sufficiency, including complex combinations of the two. Grasping the link between the secondary level and the basic level therefore requires both specifying the theoretical nature of the relationship (i.e., casual, ontological, or substitutable) and specifying the logical structure of the relationship in terms of necessary and sufficient conditions.