Subjectivity, Bayesianism, and Causality

TL;DR

This paper explores the subjective nature of Bayesian probability and introduces a formal model incorporating causal interventions to better represent agency, using a game-theoretic approach.

Contribution

It presents an abstract, measure-theoretic model of subjectivity that integrates causal interventions within Bayesian reasoning via a game-theoretic framework.

Findings

Model accommodates causal interventions in Bayesian probability

Formalizes subjectivity with a measure-theoretic approach

Demonstrates causal induction within the proposed framework

Abstract

Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by drawing parallels between Lacanian theory and Bayesian probability theory, and concludes that the latter must be enriched with causal interventions to model agency. The central contribution of this work is an abstract model of the subject that accommodates causal interventions in a measure-theoretic formalisation. This formalisation is obtained through a game-theoretic Ansatz based on modelling the inside and outside of the subject as an extensive-form game with imperfect information between two players. Finally, I illustrate the expressiveness of this model with an example of causal induction.