Exchangeability and sets of desirable gambles

Abstract

Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments for them, and prove counterparts of de Finetti's finite and infinite representation theorems. We show that the finite representation in terms of count vectors has a very nice geometrical interpretation, and that the representation in terms of frequency vectors is tied up with multivariate Bernstein (basis) polynomials. We also lay bare the relationships between the representations of updated exchangeable models, and discuss conservative inference (natural extension) under exchangeability and the extension of exchangeable sequences.

40 pages

References in corpus (1)

• Exchangeable lower previsions

Cited by in corpus (10)

• Accept & Reject Statement-Based Uncertainty Models
• Irrelevant and independent natural extension for sets of desirable gambles
• Desirability and the birth of incomplete preferences
• A polarity theory for sets of desirable gambles
• Interpreting, axiomatising and representing coherent choice functions in terms of desirability
• A Desirability-Based Axiomatisation for Coherent Choice Functions
• Information algebras of coherent sets of gambles in general possibility spaces
• Bernstein's socks and polynomial-time provable coherence
• Quantum indistinguishability through exchangeable desirable gambles
• Algebras of Sets and Coherent Sets of Gambles