Calendar

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)

State-dependent utility is a problem for decision theory under uncertainty. It questions the very possibility that beliefs be revealed by choice data. According to the current literature, all models of beliefs are equally exposed to the problem. Moreover, the problem is solvable only when the decision-maker can influence the resolution of uncertainty. This paper shows that these two views must be abandoned. The various models of beliefs are unequally exposed to the problem of state-dependent utility. The problem is solvable even when the decision-maker has no influence over the resolution of uncertainty. The implications of such reappraisal for a philosophical appreciation of the revealed preference methodology are discussed.

Jean Baccelli (Munich Center for Mathematical Philosophy).

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

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.)