The Elgar Companion to Recent Economic Methodology
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The Elgar Companion to Recent Economic Methodology

Edited by John B. Davis and D. Wade Hands

Bringing together a collection of leading contributors to this new methodological thinking, the authors explain how it differs from the past and point towards further concerns and future issues. The recent research programs explored include behavioral and experimental economics, neuroeconomics, new welfare theory, happiness and subjective well-being research, geographical economics, complexity and computational economics, agent-based modeling, evolutionary thinking, macroeconomics and Keynesianism after the crisis, and new thinking about the status of the economics profession and the role of the media in economics.
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Chapter 11: Agent-based Modeling: The Right Mathematics for the Social Sciences?

Paul L. Borrill and Leigh Tesfatsion


Paul L. Borrill and Leigh Tesfatsion 11.1 INTRODUCTION As in the physical sciences, theoretical modeling in the social sciences typically entails the specification and analysis of parameterized systems of differential equations. Many critical insights have been obtained by social scientists using this powerful classical mathematics approach. Nevertheless, it is extremely difficult to capture physical, institutional and behavioral aspects of social systems with empirical fidelity and still retain analytical tractability. Entities in social systems are neither infinitesimally small nor infinitely many, nor are their identities or behaviors necessarily indistinguishable from one another. Common simplifications, such as assumed homogeneous behaviors or the existence of single representative agents, are thus problematic. Moreover, the social sciences cannot separate observers from ‘the real world out there’. Rather, social scientists must consider multiple observers in a continual co-evolving interaction with each other and with their environment. This leads us to question whether other forms of traditional mathematics, or even new forms of mathematics, might better serve the purposes of social scientists. In short, what is the ‘right’ mathematics for the social sciences? Moreover, if a ‘right’ mathematics exists for the social sciences, what are the implications for the physical sciences? And what can the social and physical sciences learn from each other? As elaborated in Bridges (2009), constructive mathematics is distinguished from classical mathematics by the strict interpretation of ‘there exists’ (E) as ‘we can construct’, classical mathematicans accept the law of the excluded middle (LEM): for any proposition P, either P is true or its...

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