题  目：Great Expectations: Introducing a Surreal Decision Theory

主  讲：陈科名(Eddy Keming Chen), Rutgers University

简 介：He is a graduate student at the Rutgers Philosophy Department. As his interests lie in the intersections of science, mathematics, language, and philosophy, he is pursuing a PhD degree in philosophy, a Master's degree in mathematical physics, and a graduate certificate in cognitive science. Currently, he is most interested in the metaphysical and epistemological issues in the foundation of physics. Before coming to Rutgers, he did his undergraduate work in math, physics, and philosophy at the National University of Singapore, the University of Oxford, and finished at Calvin College. He also dabbled in membrane engineering (at the biomedical engineering department at NUS), marketing research (at Magnity Electronics), and journalism (at the New York Times).

主  持：王彦晶副教授

时  间：12月22日星期二15:10-18:00

地  点：北京大学三教506

摘  要：Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to include infinite utilities and infinite state spaces have resulted in many paradoxes. Nevertheless, some of the most venerable decision problems such as the St. Petersburg Game and Pascal’s Wager employ exactly these things. In this paper, we argue that the use of John Conway’s surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem, show that surreal decision theory respects dominance reasoning even in the infinite case, and bring our new resources to bear on one of the most puzzling and oft-discussed problems in the literature: Hajek and Nover’s Pasadena Game. We show how to use the "surreal toolbox" to capture our rational preferences among the Pasadena Game and its nearby cousins. Thus, we provide a fruitful new framework for thinking about infinite decision problems.