In Ellsberg paradox, decision makers that are partially informed about the actual probability distribution violate the expected utility paradigm. This paper develops a theory of decision making with a partially specified probability. The paper takes an axiomatic approach using Anscombe-Aumann's...

To allow conditioning on counterfactual events, zero probabilities can be replaced by infinitesimal probabilities that range over a non-Archimedean ordered field. This paper considers a suitable minimal field that is a complete metric space. Axioms similar to those in Anscombe and Aumann (1963)...

Introduction -- Set functions, capacities and games -- The core and the selectope of games -- Integrals -- Decision under risk and uncertainty -- Decisions with multiple criteria -- Dempster-Shafer and possibility theory.

We suggest that one individual holds multiple degrees of belief about an outcome, given the evidence. We then investigate the implications of such noisy probabilities for a buyer and a seller of binary options and find the odds agreed upon to ensure zero-expectation betting, differ from those...