Mathematics Motivated by the Social and Behavioral Sciences (CBMS-NSF Regional Conference Series in Applied Mathematics)

This book considers how mathematics can address issues in social and behavioral sciences in areas like voting, nonparametric statistics, and supply and demand, including using evolutionary game theory to model change, the analysis of voting methods and voting theory, approaches to game theory, and the reductionist approach to complex problems. The book is a slightly expanded version of parts of the author's 10 Conference Board of the Mathematical Sciences lectures presented in August 2012 in West Chester, Pennsylvania. (Ringgold, Inc., Portland, OR) The mathematical challenges coming from the social and behavioral sciences differ significantly from typical applied mathematical concerns. "Change, " for instance, is ubiquitous, but without knowing the fundamental driving force, standard differential and iterative methods are not appropriate. Although differing forms of aggregation are widely used, a general mathematical assessment of potential pitfalls is missing. These realities provide opportunities to create new mathematical approaches. These themes are described in an introductory, expository, and accessible manner by exploring new ways to handle dynamics and evolutionary game theory, to identify subtleties of decision and voting methods, to recognize unexpected modeling concerns, and to introduce new approaches with which to examine game theory. Applications range from avoiding undesired consequences when designing policy to identifying unanticipated voting (where the "wrong" person could win), nonparametric statistical, and economic "supply and demand" properties Front Matter......Page 2 Contents......Page 9 Preface......Page 11 Chapter 1 Evolutionary game Theory......Page 16 Chapter 2 All those puzzling voting mysterie......Page 55 Chapter 3 Voting theory applied elsewhere......Page 82 Chapter 4 Voting Symmetry and decompositions......Page 99 Chapter 5 Game theory A decomposition......Page 122 Chapter 6 The reductionist approach......Page 150 Bibliography......Page 172 Index......Page 180 "The mathematics needed to advance the social and behavioral sciences most surely differs from what has proved to be successful for the physical sciences. This book addresses the need to develop appropriate mathematical tools that, rather than designed for exactness, reflect the current status for much of the social and behavioral science, which requires qualitative predictors"-- Provided by publisher Explores new ways to handle dynamics and evolutionary game theory, to identify subtleties of decision and voting methods, to recognise unexpected modelling concerns, and to introduce new approaches with which to examine game theory. Applications range from avoiding undesired consequences when designing policy to identifying unanticipated voting.