Bayesian Argumentation

In this essay, we present an account of argumentation as the exchange of information between Bayesian rational agents. The basic idea of the Bayesian view of probability is that probabilities represent subjective degrees of belief. So if we know the beliefs of some rational “subject”, we can precisely define and measure various concepts relating to the quality of an argument in the mind of the subject. In other words we can objectively measure the subjective quality of an argument.

Argument and Information In the previous essay in this series, we introduced the idea of relevance, and said that a premise is relevant to the conclusion iff $P(A \vert B) > P(A \vert \bar{B})$. Consider the argument (𝐴) this is a good candidate for the job because (𝐵) he has a pulse. Having a pulse may not be a very persuasive reason to hire somebody, but it is probably quite relevant, because if the candidate did not have a pulse, the subject would probably be much less likely to want to hire him.

Why Accept the Premise? In the previous essay in this series, we defined the ideas of necessity and sufficiency from the perspective of a Bayesian rational agent. If an argument is necessary, then if the subject were to reject the premise, they would decrease their acceptance of the conclusion. And if an argument is sufficient, then if the subject were to accept the premise, they would increase their acceptance of the conclusion.