7 research outputs found
Exchangeable choice functions
We investigate how to model exchangeability with choice functions.
Exchangeability is a structural assessment on a sequence of uncertain
variables. We show how such assessments are a special indifference assessment,
and how that leads to a counterpart of de Finetti's Representation Theorem,
both in a finite and a countable context
Natural extension of choice functions
International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU (17 th, 2018, Cádiz, Spain
Coherent and Archimedean choice in general Banach spaces
I introduce and study a new notion of Archimedeanity for binary and
non-binary choice between options that live in an abstract Banach space,
through a very general class of choice models, called sets of desirable option
sets. In order to be able to bring an important diversity of contexts into the
fold, amongst which choice between horse lottery options, I pay special
attention to the case where these linear spaces don't include all `constant'
options.I consider the frameworks of conservative inference associated with
Archimedean (and coherent) choice models, and also pay quite a lot of attention
to representation of general (non-binary) choice models in terms of the
simpler, binary ones.The representation theorems proved here provide an
axiomatic characterisation for, amongst many other choice methods, Levi's
E-admissibility and Walley-Sen maximality.Comment: 34 pages, 7 figure
Coherent choice functions without Archimedeanity
We study whether it is possible to generalise Seidenfeld et al.’s representation result for coherent choice functions in terms of sets of probability/utility pairs when we let go of Archimedeanity. We show that the convexity property is necessary but not sufficient for a choice function to be an infimum of a class of lexicographic ones. For the special case of two-dimensional option spaces, we determine the necessary and sufficient conditions by weakening the Archimedean axiom