Delft University of Technology 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 Piazzai, Michele DOI 10.4233/uuid:25e95813-c9e9-4eae-a1e7-f24920fbe592 Publication date 2018 Document Version Final published version Citation (APA) Piazzai, M. (2018). 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. https://doi.org/10.4233/uuid:25e95813-c9e9-4eae-a1e7-f24920fbe592 Important note To cite this publication, please use the final published version (if applicable). Please check the document version above. 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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 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 Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnicus prof.dr.ir. T.H.J.J. van der Hagen, voorzitter van het College voor Promoties, in het openbaar te verdedigen op donderdag 22 februari 2018 om 10:00 uur door Michele Piazzai Master of Arts in Arts & Culture, Erasmus Universiteit Rotterdam, Nederland, geboren te Avezzano, Italië. This dissertation has been approved by the promotors: Dr. A. Palmigiano, Prof. I. R. van de Poel, Prof. N. M. Wijnberg Composition of the doctoral committee: Rector Magnicus, Chairman Prof. N. M. Wijnberg, University of Amsterdam Prof. I. R. van de Poel, Delft University of Technology Dr. A. Palmigiano, Delft University of Technology Independent members: Prof. M. T. Hannan, Stanford University Prof. M. Ma, Sun Yat-sen University Prof. N. Doorn, Delft University of Technology Dr. W. Conradie, University of Johannesburg Reserve member: Prof. M. J. van den Hoven, Delft University of Technology Keywords: Categorization, organization theory, applied logic Design: Michele Piazzai, Delft University of Technology Cover: Standard Industrial Classication (background), concept lattice (back) Printed by: ProefschriftMaken || www.proefschriftmaken.nl Funded by the Netherlands Organisation for Scientic Research, Vidi 016-138-314. Copyright © 2018 by Michele Piazzai. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the author. ISBN 978-90-90306-12-4 An electronic version of this dissertation is available at https://repository.tudelft.nl/. What one wishes to gain from one’s categories is a great deal of information about the environment while conserving nite resources as much as possible. Eleanor Rosch on the principle of cognitive economy Contents Summary xi Samenvatting xv Preface xix 1 Introduction1 1.1 Categories: Why Bother?.......................2 1.2 Main Themes..............................7 1.2.1 Cognitive Economy......................7 1.2.2 Structure of Classication Systems............ 10 1.2.3 Category Dynamics...................... 12 1.2.4 Logics for Categorization.................. 14 1.3 References............................... 16 I Empirical Studies 27 2 Categorization and Strategic Deterrence 29 2.1 Motivation............................... 30 2.2 Theory and Hypotheses....................... 33 2.2.1 The Geometric Structure of Markets............ 33 2.2.2 Complexity as a Category Property............. 37 2.3 Methodology.............................. 42 2.3.1 Empirical Setting....................... 42 2.3.2 Sample and Variables.................... 45 2.3.3 Estimation Procedure.................... 52 2.4 Results................................. 54 2.5 Discussion............................... 60 2.6 References............................... 63 3 Prototypes, Goals, and Cross-Classication 73 3.1 Motivation............................... 74 3.2 Theory and Hypotheses....................... 76 3.2.1 The Feature Space...................... 76 3.2.2 Atypicality and its Consequences............. 80 vii viii Contents 3.2.3 Suitability for Multiple Goals................ 84 3.2.4 The Eect of Spanning in Dierent Systems....... 87 3.3 Methodology.............................. 89 3.3.1 Empirical Setting....................... 89 3.3.2 Sample and Variables.................... 91 3.3.3 Estimation Procedure.................... 98 3.4 Results................................. 99 3.5 Discussion............................... 106 3.6 References............................... 110 II Logical Formalizations 119 4 Classication Systems as Concept Lattices 121 4.1 Motivation............................... 122 4.2 Preliminaries.............................. 126 4.2.1 Perfect Lattices and Birkho’s Theorem......... 126 4.2.2 Duality with RS-Polarities.................. 127 4.2.3 RS-Frames and Models.................... 131 4.2.4 Standard Translation..................... 133 4.3 Application to Organization Theory................. 136 4.3.1 Categorization via RS-Semantics.............. 136 4.3.2 Category Emergence..................... 143 4.4 Discussion............................... 145 4.5 References............................... 147 5 Toward an Epistemic Logic of Categories 153 5.1 Motivation............................... 154 5.2 Theoretical Foundations....................... 155 5.2.1 Cognitive Perspectives on Categorization......... 155 5.2.2 Extant Formal Approaches.................. 157 5.3 Building an Epistemic-Logical Language.............. 159 5.3.1 Basic Logic and Intended Meaning............. 159 5.3.2 Interpretation in Enriched Formal Contexts....... 160 5.3.3 Introducing Common Knowledge.............. 162 5.3.4 Hybrid Expansions of the Basic Language........ 163 5.4 Soundness and Completeness................... 163 5.4.1 Denition of I -Compatible Relations........... 163 5.4.2 Interpretation of C ...................... 165 5.4.3 Soundness........................... 168 5.4.4 Completeness......................... 170 Contents ix 5.5 Proposed Formalizations....................... 176 5.6 Discussion............................... 180 5.7 References............................... 182 6 Conclusions 187 6.1 Summary of Findings......................... 188 6.2 Implications for the Themes..................... 191 6.3 Limitations and Further Research.................. 194 6.4 References............................... 196 List of Figures 203 List of Tables 205 Index of Names 207 Acknowledgements 211 Curriculum Vitæ 215 List of Publications 217 Summary his dissertation addresses the question of how the information en- coded by category labels is interpreted by agents in a market for T the purpose of decision-making. To this end, we rst examine the inuence 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 classication systems. Consistently with Formal Concept Analysis (FCA), this theory builds on the fundamental mathemati- cal 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 aect economic activity. Chapter1 oers a concise overview of the extant research on categorization in cognitive psy- chology, economic sociology, and organization theory. We build extensively on this diverse literature during the course of our exposition. The rst part of this thesis includes our empirical studies. In Chapter2, we synthesize insights from industrial economics, strategic management, and organizational ecology to examine the eects of product proliferation strategies. Conceptualizing the market as a multidimensional (Lancastrian) space of product features, we argue that product categories guide rms’ strategic decisions by partitioning the space into subsets or regions. Prod- uct proliferation occurs when a rm 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 dierentiated markets, we predict proliferation to have a negative eect on the likelihood of rival product introductions in the targeted category; however, we also predict that this eect 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 rms’ patterns of new product introduc- tions in the US recording industry supports these hypotheses; in addition, it suggests