Logic, Probability, and Games
The seminar is concerned with applying formal methods to fundamental issues, with an emphasis on probabilistic reasoning, decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different disciplines, including philosophy, statistics, economics, and computer science. The seminar is intended to bring together scholars from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year, meetings are regularly presented by the members of the seminar and distinguished guest speakers. In the spring of 2014, the seminar also became an integral part of the University Seminars at Columbia University .
Past speakers: Arif Ahmed, Juliet Floyd, Haim Gaifman, Stephan Hartmann, Daniel Kahneman, Edi Karni, Hannes Leitgeb, Bud Mishra, Eric Pacuit, Rohit Parikh, Teddy Seidenfeld, Gregory Wheeler.
2015 – 2016 Meetings
Abstract. It is often assumed that a natural way to aggregate utility over multiple agents is by addition. When there are infinitely many agents, this leads to various problems. Vallentyne and Kagan approach this problem by providing a partial ordering over outcomes, rather than a numerical aggregate value. Bostrom and Arntzenius both argue that without a numerical value, it is difficult to integrate this aggregation into our best method for considering acts with risky outcomes: expected value.
My 2014 paper, “Decision Theory without Representation Theorems”, describes a project for evaluating risky acts that extends expected value to cases where it is infinite or undefined. The project of this paper is to extend this methodology in a way that deals with risk and aggregation across agents simultaneously, instead of giving priority to one or the other as Bostrom and Arntzenius require. The result is still merely a partial ordering, but since it already includes all considerations of risk and aggregation, there is no further need for particular numerical representations.
Abstract. In this paper, we compare and contrast two methods for revising qualitative (viz., “full”) beliefs. The first method is a (broadly) Bayesian one, which operates (in its most naive form) via conditionalization and the minimization of expected inaccuracy. The second method is the AGM approach to belief revision. Our aim here is to provide the most straightforward explanation of the ways in which these two methods agree and disagree with each other. Ultimately, we conclude that AGM may be seen as more epistemically risk-seeking (in a sense to be made precise in the talk) than EUT (from the Bayesian perspective).
This talk is based on a joint work with Ted Shear.
Abstract. This talk will focus on a set of game theoretic ideas with applications to Computer, Biological and Social Sciences. We will primarily rely on a realistic formulation of classical information-asymmetric signaling games, in a repeated form, while allowing the agents to dynamically vary their utility functions. We will also explore the design and creolization of a new natural language system (“InTuit”) specifically designed for the web.
The talk will build on our earlier experience in the areas of systems biology (evolutionary models), game theory, data science, model checking, causality analysis, cyber security, insider threat, virtualization and data markets.
Abstract. In the wake of growing awareness, decision makers anticipate that they might acquire knowledge that, in their current state of ignorance, is unimaginable. Supposedly, this anticipation manifests itself in the decision makers’ choice behavior. In this paper we model the anticipation of growing awareness, lay choice-based axiomatic foundations to subjective expected utility representation of beliefs about the likelihood of discovering unknown consequences, and assign utility to consequences that are not only unimaginable but may also be nonexistent. In so doing, we maintain the flavor of reverse Bayesianism of Karni and Vierø (2013, 2015).