Dear all,
We will have our next LIRa session on Thursday, May 27th. Our speaker is Francesca Zaffora Blando. You can find the details of the talk below. We will use our recurring zoom link: https://uva-live.zoom.us/j/92907704256?pwd=anY3WkFmQVhLZGhjT2JXMlhjQVl1dz09 (Meeting ID: 929 0770 4256, Passcode: 036024)
Speaker: Francesca Zaffora Blando
Date and Time: Thursday, May 27th 2021, 16:30-18:00, Amsterdam time.
Venue: online.
Title: Weak merging of opinions for computationally limited agents.
Abstract. A standard objection to subjective Bayesianism is that appealing to subjective probabilities threatens the objectivity of scientific inquiry. A standard Bayesian response to this charge relies on merging-of-opinions theorems: a family of results which establish that, as long as their respective priors are sufficiently compatible, two Bayesian agents with differing initial beliefs are guaranteed to almost surely reach a consensus with increasing evidence. So, objectivity can be recovered in the form of intersubjective agreement. One of the most well-known such results is the Blackwell-Dubins Theorem, which shows that Bayesian conditioning leads to a strong form of merging of opinions, provided that the agents agree on probability zero events to begin with—i.e., provided that their priors are mutually absolutely continuous. Since absolute continuity is a rather strong form of compatibility between priors, it is natural to wonder whether merging of opinions—and what type of merging of opinions—can be achieved with weaker assumptions. In this talk, I will address this question from the perspective of computationally limited Bayesian agents: agents whose priors are computable. I will argue that, for computable Bayesian learners, it is natural to appeal to the theory of algorithmic randomness—a branch of computability theory aimed at characterizing the concept of effective measure-theoretic typicality—to define notions of compatibility between priors. We will see that the proposed notions of compatibility induced by algorithmic randomness naturally correspond to restricted forms of absolute continuity. Then, I will show that some of these notions, while too weak to ensure merging of opinions in the strong sense of Blackwell and Dubins, nonetheless suffice to attain a weaker type of merging, first studied by Kalai and Lehrer, which only requires reaching a consensus over finite-horizon events.
Hope to see you there!
The LIRa team