Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a semester-long or yearlong course to acquire the necessary skills. Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social sciences and a handy reference for seasoned researchers. The book begins with the fundamental building blocks of mathematics and basic algebra, then goes on to cover essential subjects such as calculus in one and more than one variable, including optimization, constrained optimization, and implicit functions; linear algebra, including Markov chains and eigenvectors; and probability. It describes the intermediate steps most other textbooks leave out, features numerous exercises throughout, and grounds all concepts by illustrating their use and importance in political science and sociology. * Uniquely designed and ideal for students and researchers in political science and sociology * Uses practical examples from political science and sociology * Features "Why Do I Care?" sections that explain why concepts are useful * Includes numerous exercises * Complete online solutions manual (available only to professors, email david.siegel at duke.edu, subject line "Solution Set") * Selected solutions available online to students

Most theories of elections assume that voters and political actors are fully rational. While these formulations produce many insights, they also generate anomalies--most famously, about turnout. The rise of behavioral economics has posed new challenges to the premise of rationality. This groundbreaking book provides a behavioral theory of elections based on the notion that all actors--politicians as well as voters--are only boundedly rational. The theory posits learning via trial and error: actions that surpass an actor's aspiration level are more likely to be used in the future, while those that fall short are less likely to be tried later.

Based on this idea of adaptation, the authors construct formal models of party competition, turnout, and voters' choices of candidates. These models predict substantial turnout levels, voters sorting into parties, and winning parties adopting centrist platforms. In multiparty elections, voters are able to coordinate vote choices on majority-preferred candidates, while all candidates garner significant vote shares. Overall, the behavioral theory and its models produce macroimplications consistent with the data on elections, and they use plausible microassumptions about the cognitive capacities of politicians and voters. A computational model accompanies the book and can be used as a tool for further research.