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We examine general decision problems with loss functions that are bounded below. We allow the loss function to assume the value ∞. No other assumptions are made about the action space, the types of data available, the types of non-randomized decision rules allowed, or the parameter space. By allowing prior distributions and the randomizations in randomized rules to be finitely-additive, we find very general complete class and minimax theorems. Specifically, under the sole assumption that the loss function is bounded below, every decision problem has a minimal complete class and all admissible rules are Bayes rules. Also, every decision problem has a minimax rule and a least-favorable distribution and every minimax rule is Bayes with respect to the least-favorable distribution. Some special care is required to deal properly with infinite-valued risk functions and integrals taking infinite values. This talk will focus on some examples and the major differences between finitely-additive and countably-additive decision theory. This is joint work with Teddy Seidenfeld, Jay Kadane, and Rafael Stern.

UNIVERSITY SEMINAR ON LOGIC, PROBABILITY, AND GAMES
Finitely-Additive Decision Theory
Mark Schervish (Carnegie Mellon)
4:10 pm, Friday, February 16th, 2018
Faculty House, Columbia University

Psychopathy is a mental disorder closely associated with marked emotional dysfunctions, limited capacity for moral judgments, recidivistic offending, and poor treatment outcome. Considering its peculiar characteristics, the status of psychopathy in the field of law raises several disputes. While current criminal law holds psychopaths fully responsible and punishable for their misbehavior, some scholars argue that psychopathy is a condition that may severely compromise an individual’s moral agency and capacity for rationality. As such, it should be included among the potential excusing or mitigating factors for criminal responsibility and punishment. This argument finds additional support in the body of studies from neurocriminology showing that people who suffer from psychopathy exhibit (often severe) reduced functioning in the socio-emotional brain regions that are now known to be significantly involved in moral decision-making and prosocial behavior. The insights into the neurobiological roots of psychopathy seem to challenge even more the perennial dilemmas that have occupied the minds of legal scholars and philosophers for many years: Are psychopaths “bad” or “mad” (or both)? And how should criminal law and the justice system deal with them? This seminar aims to examine these issues and explore other contentious arguments about the status of psychopathy in the field law.

Three leading experts in neurocriminology, law, and philosophy will discuss recent neuroscientific findings in psychopathy research. The speakers will consider how these findings might contribute to the reconsideration of the responsibility of psychopathic offenders and how criminal justice should optimally respond to individuals suffering from such a controversial disorder.

Speakers:
Stephen J. Morse; Ferdinand Wakeman Hubbell Professor of Law; Professor of Psychology and Law in Psychiatry; Associate Director, Center for Neuroscience & Society; University of Pennsylvania Law School
Adrian Raine; Richard Perry University Professor, University of Pennsylvania
Katrina L. Sifferd; Professor and Chair of Philosophy, Elmhurst College

Free and open to the public, but RSVP is required via Eventbrite. This event is part of the Seminars in Society and Neuroscience series.

Randomized acts play a marginal role in traditional Bayesian decision theory, essentially only one of tie-breaking. Meanwhile, rationales for randomized decisions have been offered in a number of areas, including game theory, experimental design, and machine learning. A common and plausible way of accommodating some (but not all) of these ideas from a Bayesian perspective is by appeal to a decision maker’s bounded computational resources. Making this suggestion both precise and compelling is surprisingly difficult. We propose a distinction between interesting and uninteresting cases where randomization can help a decision maker, with the eventual aim of achieving a unified story about the rational role of randomization. The interesting cases, we claim, all arise from constraints on memory.

UNIVERSITY SEMINAR ON LOGIC, PROBABILITY, AND GAMES
On the Rational Role of Randomization
Thomas Icard (Stanford)

Speakers:
Amanda Pustilnik, Professor of Law, University of Maryland
Tor Wager, Professor of Psychology and Neuroscience, University of Colorado Boulder

Moderators:
Federica Coppola, Presidential Scholar in Society and Neuroscience, Columbia University
Lan Li, Presidential Scholar in Society and Neuroscience, Columbia University

We will provide additional information as soon as possible.

Free and open to the public, but RSVP is required via Eventbrite. This event is part of the Seminars in Society and Neuroscience series.

A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run. This is joint work with Eric Wofsey.

Michael Nielsen (Columbia University).
4:10 pm, Friday, November 16th, 2018
Faculty House, Columbia University

What does it mean that an event C “actually caused” event E? The problem of defining actual causation goes beyond mere philosophical speculation.  For example, in many legal arguments, it is precisely what needs to be established in order to determine responsibility.   (What exactly was the actual cause of the car accident or the medical problem?) The philosophy literature has been struggling with the problem of defining causality since the days of Hume, in the 1700s. Many of the definitions have been couched in terms of counterfactuals. (C is a cause of E if, had C not happened, then E would not have happened.) In 2001, Judea Pearl and I introduced a new definition of actual cause, using Pearl’s notion of structural equations to model counterfactuals.  The definition has been revised twice since then, extended to deal with notions like “responsibility” and “blame”, and applied in databases and program verification.  I survey the last 15 years of work here, including joint work with Judea Pearl, Hana Chockler, and Chris Hitchcock. The talk will be completely self-contained.

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 (logic and epistemology), 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.

details tba

02/08/2019 Faculty House, Columbia University
4:00 PM

03/22/2019 Faculty House, Columbia University
4:00 PM

04/19/2018 Faculty House, Columbia University
4:00 PM

There are two approaches to life. The first one, which we are identifying with Sir Karl Popper, is to think before we act and to let our hypotheses die in our stead when the overall outcome is likely to be negative. We act now for a better future, and we think now which action will bring the best future. Both decision theory and backward induction are technical versions of this train of thought.  The second approach, which we will identify with the Buddha, is to live in the present and not allow the future to pull us away from living in the ever present  Now. The Buddha’s approach is echoed in many others who came after him, Jelaluddin Rumi, Kahlil Gibran, and even perhaps Jesus.  It occurs in many contemporary teachers like Eckhart Tolle and Thich Nhat Hanh.  We may call Popper’s approach “futurism” and the Buddha’s approach “presentism.”

In this talk, we will discuss various aspects of the discourse on presentism and futurism. The purpose is to contrast one with the other. We will not attempt to side with one against the other, and instead leave it as a future project to find a prescriptive action-guiding choice between the two. We merely conjecture that a better optimal choice between these two positions may be somewhere in between. (This is joint work with Jongjin Kim.)