Probability Kinematics And Commutativity*

Iterative Probability Kinematics

Generalized Probability Kinematics

Jeffrey conditionalization is generalized to the case in which new evidence bounds the possible revisions of a prior below by a Dempsterian lower probability. Classical probability kinematics arises within this generalization as the special case in which the evidentiary focal elements of the bounding lower probability are pairwise

Merging of Opinions and Probability kinematics

We explore the question of whether sustained rational disagreement is possible from a broadly Bayesian perspective. The setting is one where agents update on the same information, with special attention being given to the case of uncertain information. The classical merging of opinions theorem of Blackwell and Dubins shows when updated beliefs come and stay closer for Bayesian conditioning. We ...

Maximum Entropy and Probability Kinematics Constrained by Conditionals

Two open questions of inductive reasoning are solved: (1) does the principle of maximum entropy (PME) give a solution to the obverse Majerník problem; and (2) is Wagner correct when he claims that Jeffrey’s updating principle (JUP) contradicts PME? Majerník shows that PME provides unique and plausible marginal probabilities, given conditional probabilities. The obverse problem posed here is whe...

Medial commutativity

It is shown that all the assumptions for symmetric monoidal categories flow out of a unifying principle involving natural isomorphisms of the type (A ∧B) ∧ (C ∧D) → (A ∧ C) ∧ (B ∧D), called medial commutativity. Medial commutativity in the presence of the unit object enables us to define associativity and commutativity natural isomorphisms. In particular, Mac Lane’s pentagonal and hexagonal coh...