The Cognitive Infrastructures of Markets: Empirical Studies on the Role of Categories in Valuation and Competition, and a Formal Theory of Classification Systems Based on Lattices and Order

This dissertation addresses the question of how the information encoded by category labels is interpreted by agents in a market for the purpose of decision-making. To this end, we first examine the influence of categorization on economic and strategic outcomes with two empirical studies, and then use the insights provided by these studies to develop a formal theory of classification systems. Consistently with Formal Concept Analysis (FCA), this theory builds on the fundamental mathematical notions of lattices and order, and it is thus uniquely suited to yield an ontological perspective on category representations. As a result, we are much better equipped to understand how categories serve as the "cognitive infrastructures'" of markets and affect economic activity. Chapter 1 offers a concise overview of the extant research on categorization in cognitive psychology, economic sociology, and organization theory. We build extensively on this diverse literature during the course of our exposition.

The first part of this thesis includes our empirical studies. In Chapter 2, we synthesize insights from industrial economics, strategic management, and organizational ecology to examine the effects of product proliferation strategies. Conceptualizing the market as a multidimensional (Lancastrian) space of product features, we argue that product categories guide firms' strategic decisions by partitioning the space into subsets or regions. Product proliferation occurs when a firm bids to occupy a product category at the expense of competitors by saturating the corresponding region of space. Consistently with game-theoretic models of product competition in differentiated markets, we predict proliferation to have a negative effect on the likelihood of rival product introductions in the targeted category; however, we also predict that this effect is weaker if the region of space to which the category maps is more complex (i.e., heterogeneous in terms of product features). Our analysis of firms' patterns of new product introductions in the US recording industry supports these hypotheses; in addition, it suggests that product proliferation effectively deters competitors who can alter their positioning in feature space, but those who are constrained to particular positions remain virtually unaffected.

In Chapter 3, we turn to consumers' perspective and examine how the categorization of products according to different classification systems affects the attribution of value. Focusing on the distinction between categories based on prototypes and categories based on goals, we argue that these category labels of these two kinds map to structurally different regions of the feature space. Valuation requires consumers to infer the location of products from their labels, but because type- and goal-based categories have different internal structures, they enable different sorts of inferences. Building on this argument, we theorize that under particular conditions spanning type-based categories has a U-shaped effect on consumers' evaluations, whereas spanning goal-based categories has a negative effect. At the same time, we predict that spanning goal-based categories can moderate the U-shaped effect of spanning type-based categories by enabling consumers to make more precise inferences from fewer type-based labels. Our analysis of product ratings on a popular music website offers empirical support for these hypotheses.

In the second part of this thesis, we develop a formal theory of categorization that accounts for the key aspects highlighted by our empirical studies. In Chapter 4, we introduce an order-theoretic account of classification systems as RS-frames. These are algebraic structures based on RS-polarities, which we enrich with additional relations to interpret modalities. Consistently with FCA, we propose to interpret an RS-polarity as a database consisting of a set of objects (such as products or organizations in a market), a set of features, and an incidence relation linking objects with their features. All the possible categories whereby the objects and the features may be grouped arise as the Galois-stable sets of this polarity, just like formal concepts in FCA. An agent's perception of the objects and their features, which can be unique, incomplete, or even mistaken, is modeled by a relation giving rise to a normal modal operator that expresses an agent's beliefs about a category's intensional and extensional meaning. The fixed points of the iterations of belief modalities are used to model categories whose meaning is shared as they arise from social interaction.

In Chapter 5, we clarify how the order-theoretic perspective on concepts enabled by FCA complements the geometric perspective allowed by the theory of conceptual spaces. In addition to introducing a sound and complete epistemic-logical language, we refine the framework presented in the previous chapter both technically and conceptually: Technically, because we free its semantics from the restrictions imposed by the RS-conditions and generalize to more natural Kripke-style frames. This makes our formalism better suited to represent formal contexts (i.e., databases) as they occur in real-world domains. Conceptually, because we enhance our theory of classification systems as concept lattices and propose formalizations for some of the most important theoretical constructs in the categorization literature, including typicality, similarity, contrast, and leniency. In particular, we elaborate our interpretation of the fixed-point construction introduced before by tying it directly to the notion of typicality. Possible extensions are discussed, especially with regard to dynamic updates.

Chapter 6 summarizes the main findings of this dissertation, elucidates their implications for organizational research, identifies key areas for improvement, and presents promising directions for future study. Special consideration is given to the possibility of unifying FCA and conceptual spaces using the framework of correspondence theory. We conclude with a general reflection on the role of logic in the social sciences.