Mathematical Modeling with Multidisciplinary Applications

CHAPTER 12

DECISION THEORY UNDER RISK AND APPLICATIONS IN SOCIAL SCIENCES: I. INDIVIDUAL DECISION MAKING

E. V. PETRACOU¹ AND A. N. YANNACOPOULOS²

¹Department of Geography, University of the Aegean, Greece

²Department of Statistics, Athens University of Economics and Business, Greece

If the facts do not fit the theory change the facts—A. Einstein

12.1 INTRODUCTION

It is the aim of this chapter to provide a very brief and first encounter with mathematical modeling in the social sciences. This is a very exciting field, combining solid mathematics (ranging from pure to the applied) with fundamental concepts from philosophy, political and social theory, in an attempt to provide benchmarks for human behavior and understanding motives and patterns for human actions. A large part of this field has been developed into an independent discipline, that of decision theory in mathematical economics, and is now the dominant tool in understanding the phenomena of the economy. On the other hand, there is a lot of interest in developing these techniques to understand social phenomena not directly related to the economy, such as human action and institutions, voting patterns etc. This is now a very active field, blending techniques from mathematics and statistics (e.g., game theory, decision analysis, probability models, optimization techniques, differential equations, etc.), physics and engineering (e.g., particle systems, mean field theory, etc.) and social sciences (e.g., economics, political ...