Glenn Shafer (Rutgers): "Using Game Theory to Reunify Subjective and Objective Probability.” Abstract. Belief and frequency co-existed in the calculus of games of chance as it was taught in Europe beginning in the 13th century. They still co-existed in the theory of mathematical probability that Jacob Bernoulli based on that calculus. But they came apart in the middle of the 19th century. In this talk, I show how game theory can bring them back together. My new book with Volodya Vovk (Game-Theoretic Foundations for Probability and Finance, Wiley, May 2019) bases mathematical probability on a game with three players: Forecaster (who offers bets), Skeptic (who decides which offers to take), and Reality (who decides the outcomes). Forecaster is the Bayesian. Skeptic is the frequentist. See the working papers at www.probabilityandfinance.com.

• "The Language of Betting as a Strategy for Statistical and Scientific Communication" (Shafer, Working Paper #54, October 22, 2019).
• "Let’s replace p-values with betting outcomes!" (Shafer, AMASES 2019).

"The Permissible and the Forbidden" (Richter, Rubinstein), November 2019.

"Formal Approaches to Social Procedures" (van Eijck, Verbrugge), Winter 2019. cf. "Formal Approaches to Social Procedures," Spring 2017.

Adam Elga (Princeton): "Causal Decision Theory does not Exist.” Abstract. The box is either empty or contains $1 million (you can't see which). You will either receive (1) just the contents of the box, or (2) the contents of the box plus an extra $1,000. You get to choose (1) or (2). The catch is that a reliable predictor put the $1 million in the box if and only if he predicted you would refuse the extra $1,000. Should you take the $1,000?

This is Newcomb's Problem, which has divided philosophers since it was described by Nozick (1969). Those who favor taking the $1,000 are called "two-boxers" and are typically moved by the sort of "causal dominance reasoning" exemplified by the following speech: "I have no present control over the contents of the box. Whether the box is empty or not, I prefer having an extra $1,000. So I should take the $1,000."

It is often thought that various so-called "causal decision theories" (such as theories described by Stalnaker, Lewis, Gibbard & Harper, Joyce, and others) vindicate causal dominance reasoning, and so are attractive theories for two-boxers. Adapting observations due to Ahmed, Dorr, and Joyce, I argue that those theories do not vindicate causal dominance reasoning in general. Indeed, for each such theory there are Newcomb problems in which the theory recommends *one-boxing*. So none of those theories deserve the name "causal decision theory". I conclude that a true causal decision theory does not exist---or at least, does not exist yet.

Attendees interested in a playful introduction to disputes about Newcomb's problem may optionally wish to look at "Newcomb University: A Play in One Act." (The talk will be self-contained and no advance reading will be presupposed.)

Arthur Paul Pedersen (The City University of New York): "Bayesian Aggregation under Severe Uncertainty and Unresolved Conflict.” Abstract. This is the second part of a two-part talk treating the problem of aggregating judgments of a group of individuals.

What criteria are to serve as normative standards for reaching Bayesian consensus? The first part of this talk examined (i) external Bayesianism and other proposed normative criteria (with regard to, e.g., update then aggregate vs. aggregate then update) and (ii) Bayesian extensions of Arrow-like impossibility theorems and their counterpart possibility theorems. Do the purported normative standards extend to conditions of severe uncertainty or unresolved conflict? Do normative standards appropriate to common conditions such as these avoid Arrow-like impossibility theorems?

For the second part of this talk, I'll turn to discuss (iii) incompleteness vs. indeterminacy in probability and utility judgment (tentative vs. assertive incompleteness) and then (iv) advance an account of set-valued judgment aggregation under conditions of contradictory or incomplete information or unresolved conflict, (v) recount the problem of dilation, and (vi) report results I've established within this general account which demonstrate not only some encouraging possibility theorems but also the weak conditions under which Arrow-like impossibility theorems nonetheless return.

Arthur Paul Pedersen (The City University of New York): "Bayesian Aggregation under Severe Uncertainty and Unresolved Conflict.” Abstract. I'll examine the problem of aggregating judgments of a group of individuals. What criteria are to serve as normative standards for reaching Bayesian consensus? This talk has two parts. As background, for the first of this talk I'll discuss (i) external Bayesianism and other proposed normative criteria (with regard to, e.g., update then aggregate vs. aggregate then update) and (ii) Bayesian extensions of Arrow-like impossibility theorems and their counterpart possibility theorems. Do the purported normative standards extend to conditions of severe uncertainty or unresolved conflict? Do normative standards appropriate to common conditions such as these avoid Arrow-like impossibility theorems?

For the second part of this talk, I'll turn to discuss (iii) incompleteness vs. indeterminacy in probability and utility judgment (tentative vs. assertive incompleteness) and then (iv) advance an account of set-valued judgment aggregation under conditions of contradictory or incomplete information or unresolved conflict, (v) recount the problem of dilation, and (vi) report results I've established within this general account which demonstrate not only some encouraging possibility theorems but also the weak conditions under which Arrow-like impossibility theorems nonetheless return.

The goal for Friday's seminar meeting is to work through background material --- namely, topics (i) and (ii). I'll resume discussion of material I cannot cover this Friday during our our next seminar meeting.

Jia Xu (Hunter College): "New Directions in Neural Machine Translation.”

Ignacio Ojea Quintana: "Segregating and Integrating Dynamics in Social Networks.”

Arthur Paul Pedersen (The City University of New York): "Amartya Sen: Welfare Aggregation and Measurability.”

• Collective Choice and Social Welfare (Sen).
• "On Weights and Measures: Informational Constraints in Social Welfare Analysis" (Sen).

Ron van der Meyden (University of New South Wales): "Social Software on the Blockchain.”

• "On the Specification and Verification of Atomic Swap Smart Contracts" (van der Meyden).
• "Token-Curated Registries 1.0" (Goldin).
• "Token Curated Registries - A Game Theoretic Approach" (Asgaonkar, Krishnamachari).
• "Solving the Buyer and Seller's Dilemma" (Asgaonkar, Krishnamachari).

"Social Choice Theory" (List), Winter 2013.

Eric Pacuit (University of Maryland): "Voting Methods."

"Voting Methods" (Pacuit), Fall 2019. cf. "Voting Methods" (Pacuit), Fall 2017.

Arthur Paul Pedersen (The City University of New York): "Arrow's Impossibility Theorem."

"Arrow's Theorem" (Morreau), Winter 2016.

• Social Choice and Individual Values (Arrow), 1951.
• "A Difficulty in the Concept of Social Welfare" (Arrow), 1950.

"Voting" (Easley, Kleinberg).

"The Power Of Knowledge in Games" (Parikh, Tasdemir, Witzel).

"Cheap Talk" (Farrell, Rabin).

"The Use of Knowledge in Society" (Hajek).

"The Logic of Non-Persons" (Parikh).