SetTheoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis
Qualitative Comparative Analysis (QCA) and other settheoretic methods distinguish themselves from other approaches to the study of social phenomena by using sets and the search for set relations. In virtually all social science fields, statements about social phenomena can be framed in terms of set relations, and using settheoretic methods to investigate these statements is therefore highly valuable. This book guides readers through the basic principles of settheory and then on to the applied practices of QCA. It provides a thorough understanding of basic and advanced issues in settheoretic methods together with tricks of the trade, software handling, and exercises. Most arguments are introduced using examples from existing research. The use of QCA is increasing rapidly and the application of set theory is both fruitful and still widely misunderstood in current empirical comparative social research. This book provides the comprehensive guide to these methods for researchers across the social sciences.
Carsten Q. Schneider is Associate Professor in the Department of Political Science and Founding Director of the Center for the Study of Imperfections in Democracies at Central European University, Hungary.
Claudius Wagemann is Professor of Qualitative Social Science Methods at Goethe University, Frankfurt.
SetTheoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis
Strategies for Social InquiryEditors
Editorial Board
This new book series presents texts on a wide range of issues bearing upon the practice of social inquiry. Strategies are construed broadly to embrace the full spectrum of approaches to analysis, as well as relevant issues in philosophy of social science.
Published Titles
John Gerring, Social Science Methodology: A Unified Framework, 2nd edition
Michael Coppedge, Democratization and Research Methods
Thad Dunning, Natural Experiments in the Social Sciences: A DesignBased Approach
Forthcoming Titles
Diana Kapiszewski, Lauren M. MacLean and Benjamin L. Read, Field Research in Political Science
Jason Seawright, MultiMethod Social Science: Combining Qualitative and Quantitative Tools
SetTheoretic Methods for the Social Sciences
A Guide to Qualitative Comparative Analysis
Carsten Q. Schneider and Claudius Wagemann
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9781107601130
Translated and adapted from Qualitative Comparative Analysis (QCA) und Fuzzy Sets: Ein Lehrbuch für Anwender und alle, die
es werden wollen published in German by Verlag Barbara Budrich 2007, © Verlag Barbara Budrich 2007.
First published in English by Cambridge University Press 2012 as SetTheoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis © Cambridge University Press 2012.
This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.
Printed and bound in the United Kingdom by the MPG Books Group
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
ISBN 9781107013520 Hardback
ISBN 9781107601130 Paperback
Additional resources for this publication at www.cambridge.org/schneiderwagemann
Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or thirdparty internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
In honor of Philippe Schmitter, wise advisor, generous colleague, and good friend.
Dedicated to Sheila, Giulia, and Leo, without whom this book would have been finished much sooner.
Contents
List of figures

xii 
List of tables

xiv 
Acknowledgements

xvi 
Introduction

1 
Settheoretic approaches in the social sciences

1 
Qualitative Comparative Analysis as a settheoretic approach and technique

8 
Variants of QCA

13 
Plan of the book

16 
How to use this book

19 
Part I Settheoretic methods: the basics

21 
1 Sets, set membership, and calibration

23 
1.1 The notion of sets

24 
1.1.1 Sets and concepts

24 
1.1.2 The pros and cons of crisp sets

24 
1.1.3 Properties of fuzzy sets

27 
1.1.4 What fuzzy sets are not

30 
1.2 The calibration of set membership

32 
1.2.1 Principles of calibration

32 
1.2.2 The use of quantitative scales for calibration

33 
1.2.3 The “direct” and “indirect” methods of calibration

35 
1.2.4 Does the choice of calibration strategy matter much?

38 
1.2.5 Assessing calibration

40 
2 Notions and operations in set theory

42 
2.1 Conjunctions, Boolean and fuzzy multiplication, intersection, logical AND

42 
2.2 Disjunctions, Boolean and fuzzy addition, union, logical OR

45 
2.3 Negations, complements, logical NOT

47 
2.4 Operations on complex expressions

47 
2.4.1 Rules for combining logical operators

48 
2.4.2 Negation, intersection, and union of complex sets

49 
2.4.3 Calculating membership in complex sets

51 
2.5 Relations between sets

52 
2.6 Notational systems in settheoretic methods

54 
3 Set relations

56 
3.1 Sufficient conditions

57 
3.1.1 Crisp sets

57 
3.1.2 Fuzzy sets

65 
3.2 Necessary conditions

69 
3.2.1 Crisp sets

69 
3.2.2 Fuzzy sets

75 
3.3 Causal complexity in settheoretic methods

76 
3.3.1 Defining causal complexity

78 
3.3.2 INUS and SUIN conditions

79 
3.3.3 The notion of asymmetry

81 
3.3.4 Settheoretic methods and standard quantitative approaches

83 
4 Truth tables

91 
4.1 What is a truth table?

92 
4.2 How to get from a data matrix to a truth table

93 
4.2.1 Crisp sets

93 
4.2.2 Fuzzy sets

96 
4.3 Analyzing truth tables

104 
4.3.1 Matching similar conjunctions

105 
4.3.2 Logically redundant prime implicants

108 
4.3.3 Issues related to the analysis of the nonoccurrence of the outcome

112 
Part II Neat formal logic meets noisy social science data

117 
5 Parameters of fit

119 
5.1 Defining and dealing with contradictory truth table rows

120 
5.2 Consistency of sufficient conditions

123 
5.3 Coverage of sufficient conditions

129 
5.4 Consistency of necessary conditions

139 
5.5 Coverage of necessary conditions

144 
5.6 Issues related to consistency and coverage

148 
6 Limited diversity and logical remainders

151 
6.1 Limited diversity in settheoretic methods: how to see it when it is there

152 
6.2 Sources of limited diversity

153 
6.2.1 Arithmetic remainders

154 
6.2.2 Clustered remainders

154 
6.2.3 Impossible remainders

155 
6.3 What limited diversity is not

157 
6.4 The Standard Analysis procedure: identifying logical remainders for crafting plausible solution terms

160 
6.4.1 The dimension of set relations

161 
6.4.2 The dimension of complexity

165 
6.4.3 The dimension of types of counterfactuals

167 
6.4.4 The Standard Analysis procedure in a nutshell

175 
7 The Truth Table Algorithm

178 
7.1 From the data matrix to truth table

179 
7.2 Attributing an outcome value to each truth table row

182 
7.3 Logically minimizing the truth table

186 
7.4 Implications of the Truth Table Algorithm

190 
Part III Potential pitfalls and suggestions for solutions

195 
8 Potential pitfalls in the Standard Analysis procedure and suggestions for improvement

197 
8.1 Beyond the Standard Analysis: expanding the types of counterfactuals

198 
8.2 The Enhanced Standard Analysis: forms of untenable assumptions and how to avoid them

200 
8.2.1 Incoherent counterfactuals I: contradicting the statement of necessity

201 
8.2.2 Incoherent counterfactuals II: contradictory assumptions

203 
8.2.3 Implausible counterfactuals: contradicting common sense

206 
8.2.4 Putting the Enhanced Standard Analysis procedure into practice

209 
8.3 TheoryGuided Enhanced Standard Analysis: complementary strategies for dealing with logical remainders

211 
8.3.1 Choosing entire truth table rows as good counterfactuals

212 
8.3.2 Formulating conjunctural directional expectations

215 
8.4 Comparing the different strategies for the treatment of logical remainders

217 
9 Potential pitfalls in the analysis of necessity and sufficiency and suggestions for avoiding them

220 
9.1 Pitfalls in inferring necessity from sufficiency solution terms

221 
9.1.1 Hidden necessary conditions

221 
9.1.2 The appearance of false necessary conditions

227 
9.2 The analytic consequences of skewed setmembership scores

232 
9.2.1 The coverage of necessary conditions and the problem of trivialness

233 
9.2.2 The consistency of sufficient conditions and the problem of simultaneous subset relations

237 
9.2.3 A general treatment of skewed set membership in fuzzyset analyses

244 
Part IV Variants of QCA as a technique meet QCA as an approach

251 
10 Variants of QCA

253 
10.1 The twostep approach

253 
10.2 Multivalue QCA

255 
10.2.1 Principles of mvQCA: notation and logical minimization

256 
10.2.2 An assessment of mvQCA

258 
10.3 Settheoretic methods and time

263 
10.3.1 Forms of causally relevant notions of time

264 
10.3.2 Informal ways of integrating notions of time into settheoretic methods

265 
10.3.3 Sequence elaboration

266 
10.3.4 Temporal QCA

269 
11 Data analysis technique meets settheoretic approach

275 
11.1 Recipe for a good QCA

275 
11.1.1 The appropriateness of settheoretic methods

276 
11.1.2 The choice of the conditions and the outcome

276 
11.1.3 The choice of the QCA variant

277 
11.1.4 Calibration of setmembership scores

277 
11.1.5 Analysis of necessary conditions

278 
11.1.6 Analysis of sufficient conditions

278 
11.1.7 Presentation of results

280 
11.1.8 Interpretation of results

280 
11.1.9 Reiteration of the research cycle

281 
11.1.10 The use of software

282 
11.2 Robustness and uncertainty in QCA

284 
11.2.1 How do we see robustness in settheoretic methods when it is there?

285 
11.2.2 The effects of changing calibration

287 
11.2.3 The effects of changing consistency levels

291 
11.2.4 The effect of dropping or adding cases

293 
11.3 The evaluation of theories in settheoretic methods

295 
11.3.1 Why standard hypothesis testing does not fit into settheoretic methods

296 
11.3.2 The basics of theory evaluation in settheoretic methods

297 
11.3.3 Extending theory evaluation by integrating consistency and coverage

300 
11.3.4 Summarizing settheoretic theory evaluation

304 
11.4 Settheoretic methods and case selection

305 
11.4.1 Types of cases after a QCA

306 
11.4.2 Forms and aims of (comparative) withincase studies after a QCA

308 
11.4.3 PostQCA case selection principles

310 
12 Looking back, looking ahead

313 
12.1 Looking back: the main topics of this book

313 
12.2 Myths and misunderstandings

316 
12.3 Looking ahead: tasks and developments in the coming years

318 
Glossary

322 
Bibliography

336 
Index

346 
© Cambridge University Press