Manuscripts available on request.

Belief Revision

Consensus Does Not Justify Contraction (with Isaac Levi)

Unanimous Consensus against AGM? [Preprint] [Journal]

Decision Theory

Conditional Choice with a Vacuous Second Tier [Preprint] [Journal]

Rationalizability: Pseudo, Sub, and Weak

Social Choice Theory for Deliberative Democrats


Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence (with Michael Nielsen) [Preprint] [Journal]

Counterexamples to Some Characterizations of Dilation (with Michael Nielsen) [Preprint] [Journal]

Distention for Sets of Probabilities (with Michael Nielsen)

Learning and Pooling, Pooling and Learning (with Ignacio Ojea Quintana) [Preprint] [Journal]

Obligation, Permission, and Bayesian Orgulity (with Michael Nielsen) [Preprint] [Journal]

On a Disanalogy between Measure and Algebra (with Michael Nielsen)

On the Possibility of Testimonial Justice (with Michael Nielsen)

Persistent Disagreement and Polarization in a Bayesian Setting (with Michael Nielsen) [Preprint] [Journal]

Probabilistic Opinion Pooling with Imprecise Probabilities (with Ignacio Ojea Quintana) [Preprint] [Journal]

Support for Geometric Pooling (with Jean Baccelli)

What’s Hot in Mathematical Philosophy Column in The Reasoner 12(10) (with Michael Nielsen) [Gazette]


Mathematical aggregation frameworks are general and precise settings in which to study ways of forming a consensus or group point of view from a set of potentially diverse points of view. Yet the standard frameworks have significant limitations. A number of results show that certain sets of desirable aggregation properties cannot be simultaneously satisfied. Drawing on work in the theory of imprecise probabilities, I propose philosophically-motivated generalizations of the standard aggregation frameworks (for probability, preference, full belief) that I prove can satisfy the desired properties. I then look at some applications and consequences of these proposals in decision theory, epistemology, and the social sciences. [Short Abstract] [Extended Abstract]