Computational and Mathematical Modeling in the Social Sciences
Mathematical models in the social sciences have become increasingly sophisticated and widespread in the last decade. This period has also seen many critiques, most lamenting the sacrifices incurred in pursuit of mathematical rigor. If, as critics argue, our ability to understand the world has not improved during the mathematization of the social sciences, we might want to adopt a different paradigm. This book examines the three main fields of mathematical modeling - game theory, statistics, and computational methods - and proposes a new framework for modeling. Unlike previous treatments which view each field separately, the treatment provides a framework that spans and incorporates the different methodological approaches. The goal is to arrive at a new vision of modeling that allows researchers to solve more complex problems in the social sciences. Additionally, a special emphasis is placed upon the role of computational modeling in the social sciences.
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agents alliance game allow approach argue argument artiﬁcial assumptions beneﬁt candidate Chapter choices choose complex component games computational model conﬁdence conﬂict currency game curse of dimensionality data set deductive models deﬁned dependent derive difﬁcult dyad electorate empirical models empirical referent encoding equivalence classes Euclidean evaluation example existing Fearon’s feature space FEDERAL SPENDING ﬁeld ﬁnal ﬁnd ﬁnding ﬁrst ﬁt ﬁtness Friedman game theoretic models game theory genetic algorithm given goal graph ideal point idiosyncratic utility functions independent variables linear logical implications machine chess mathematical modeling measure methodology methods Nash equilibrium neighborhood neural networks normal form game noted observations one’s optimization out-of-sample testing overﬁt parameter space parameter values payoffs Perl player political population POSITION 7PT possible predictive problem qualitative question regime shifts regression ROC curves sample social sciences speciﬁc statistical model strategies survey data territory tions underﬁtting units utility function variance voters