Summary
Contents
Subject index
Via 99 entries or "mini-chapters," the SAGE 21st Century Reference Series volumes on political science highlight the most important topics, issues, questions, and debates any student obtaining a degree in this field ought to have mastered for effectiveness in the 21st century. 21st Century Political Science: A Reference Handbook serves as an authoritative reference source that meets students' research needs with more detailed information than encyclopedia entries but not so much jargon, detail, or density as a journal article or a research handbook chapter. An editorial advisory board comprised of eminent scholars from various subfields, many of whom are also award-winning teachers, selected the most important general topics in the discipline. The two volumes are divided into six major parts: 1) General Approaches of Political Science; 2) Comparative Politics; 3) International Relations; 4) Political Science Methodology; 5) Political Thought; and 6) American Politics. A section on identity politics includes chapters on topics such as Race, Ethnicity, and Politics; Gender and Politics; Religion and Politics; and LGBT Issues/ Queer Theory. This two-volume resource makes fairly complex approaches in political science accessible to advanced undergraduate and beginning graduate students.
Formal Theory and Spatial Modeling
Formal Theory and Spatial Modeling
In Greek mythology, Hercules is tasked with 12 impossible labors to regain honor and thus ascend to Mount Olympus as a god. The job of explaining formal theory and spatial theory in a brief, nontechnical essay is a labor of sufficient difficulty to make the search for the Golden Fleece pale in comparison. Given that this author has no transcendental gifts (though Hippolyta's belt may be around here somewhere), aspirations, or pretentions, this chapter eschews the impossible task of summarizing and explaining the entirety of formal and spatial theory. Instead, this chapter settles for the daunting yet mortal goal of a thorough yet concise introduction to some of the classical and contemporary works of the formal and spatial theories on politics and the concepts, definitions, and models on which those works rest (for a more complete treatment of formal theory and its contribution as a field of political inquiry, see Morton, 1999; Ordeshook, 1992; and Shepsle & Bonchek, 1997). Although Duncan Black (1958) may have understated the mathematical underpinnings of spatial theory as “simple arithmetic,” it is as true today as it was then that the fundamental assumptions, intuitions, and predictions of formal and spatial theory can be grasped with a relatively basic foundation in mathematics such as algebra and geometry. Formal theorists employ a range of advanced mathematical concepts (i.e., integral calculus, matrix algebra, etc.) in their models. However, one does not need these to understand what formal theory is, what the foundational principles of formal theory are, and the gamut of its predictions and conclusions regarding political institutions and behavior. To the extent possible without compromising the material, this chapter keeps the discussion broad and descriptive and thus accessible to the undergraduate reader.
What is Formal Theory?
Formal theory is a field of inquiry that uses mathematical techniques to explicitly and precisely define theoretical concepts and the relationships between those concepts. Formal mathematics permits the systemizing of theory and thus permits precise deductions and synthesis and enhances the decidability of scientific propositions. Although the term formal theory is common parlance, it is also known as rational choice theory, public choice, positive political theory, political economy, the economic theory of politics, and a variety of other synonyms. Two of the primary branches of formal theory used frequently in political science are game theory and spatial theory. Game theory is concerned primarily with the strategic interaction of utility-maximizing actors in competitive and cooperative settings (see Chapter 64, “Game Theory,” in this volume, for more information). Spatial theory, as the reader will see, examines the behavior of actors by representing beliefs, positions, choices, and institutional contexts in terms of spatial distance (most commonly as points on the Cartesian plane). Although formal theory shares a foundation in mathematics and logic with quantitative methods, it is distinct from the traditional empirical inquiry of standard statistical methods. Formal theory seeks to explicitly define political concepts and derive logical implications from their interrelations. Traditional empirical methods assess the relationships between political concepts through direct statistical analysis. Nonformal theory underpins much of the empirical work in political science. A nonformal model suggests relationships between actors and institutions in the real world of politics using general and sometimes ambiguous terminology. This is not to suggest that traditional theorizing is necessarily bad or unrelated to that of formal theorizing. Indeed, there may be an underlying formal model in a generally stated theory of politics that, as Arrow (1963) notes, has not been expressed formally because of mathematical or linguistic limitations. A model is formalized when we use abstract and symbolic representations to explicitly state the assumptions of the model and from which can be derived equilibrium and comparative statics predictions (Binamore, 1990; Elster, 1986; Morton, 1999).
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