Set-Theoretic Methods

Advanced methods
Course Description: 

This is an advanced methodological course on set-theoretic methods for the social sciences. While the spectrum of a set-theoretic methods is broad, including techniques such as Mill's methods or typological theory, this course primarily focuses on the crisp-set and fuzzy-set versions of Qualitative Comparative Analysis (QCA). Invented by Charles Ragin [1987], this technique has undergone various modications, improvements, and ramications [Ragin, 2000, 2008]. These methods are applied in fields as diverse as political science, public policy, international relations, sociology, business and management studies, or even musicology (see This course aims at enabling students to produce a publishable QCA of their own. In order to achieve this, this course provides both the formal set theoretical underpinnings of QCA and the technical and research practical skills necessary for performing a QCA.

The course is structured as follows. We start with some basics of formal logic and set theory. Then we introduce the notions of sets and how they are calibrated. After this, we move on to the concepts of causal complexity and of necessity and sufficiency, show how the latter denote subset relations, and then learn how such subset relations can be analyzed with so-called truth tables. All concepts and analytic steps are first introduced based on crisp sets and then it is shown how they apply to fuzzy sets. Once students master the current standard analysis practice, we discuss several extensions and possible improvements of QCA. Depending on the needs and interests of participants, we choose several topics from the following list: set-theoretic multi-method research, i.e. the combination of QCA with follow-up within-case analyses; the integration of time into QCA; or theory-evaluation in set-theoretic methods. The course is split into three blocks of two weeks each. During these blocks, we will meet twice a week. 

Since this is an advanced PhD course, students who plan to attend should rst check for themselves and, in case of doubt, with me whether they fulll the following requirements: Participants should have (a) some practical experience in empirical comparative social research; (b) undergone some thorough courses in basic research methodology; and (c) preferably some basic statistical training, or at least hands-on knowledge with some sort of spreadsheet programs (even if it is just Excel). The core reading of the course is Schneider and Wagemann [2012]. Students who wish to take the course and need more information as to what the course is about are invited to read the first chapters of the book.

From the beginning, we will use specialized software for performing the analytic steps learned in class. We will use R (and RStudio) and within it, the packages QCA [Dusa, 2007] and SetMethods [Medzihorsky et al., 2016]. A desired (and very likely) side effect of this course will be that we engage into discussions on more general methodological issues of good comparative research, such as principles and practices of case selection, concept formation, measurement validity, and forms of causal relations.

Learning Outcomes: 

The learning outcomes of the doctoral program are supported and measured by the present course in the following ways: The ability to reflect on some of the major methodological schools in the discipline; to deploy elective oral presentation and discussion skills as measured primarily by the in-class participation. The skills to employ cutting-edge methods are reflected by the mid-term exam and the final paper.


The overall grade will primarily indicate the ability of the students to comprehend two things:
(a) to understand the distinct logic of social inquiry that one is buying into when applying set-theoretic methods such as QCA and
(b) to master the practical tricks of the trade when performing a QCA.