PMLR 147:320-330 (2021)

Arthur Van Camp
University of Bristol
Kevin Blackwell
University of Michigan, Ann Arbor
Jason Konek
University of Bristol
We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1] have called S-independence. We show that neither is more general than the other.
Keywords choice function  set of desirable gamble sets  epistemic independence  S-independence  natural extension
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Choosers as Extension Axioms.Bora Erdamar & M. Remzi Sanver - 2009 - Theory and Decision 67 (4):375-384.
The Rationalizability of Two-Step Choices.Ruth Poproski - 2010 - Journal of Philosophical Logic 39 (6):713 - 743.
Extending Independent Sets to Bases and the Axiom of Choice.Kyriakos Keremedis - 1998 - Mathematical Logic Quarterly 44 (1):92-98.
Linear Independence Without Choice.Douglas Bridges, Fred Richman & Peter Schuster - 1999 - Annals of Pure and Applied Logic 101 (1):95-102.
Independence of Irrelevant Alternatives Revisited.Susumu Cato - 2014 - Theory and Decision 76 (4):511-527.
The Computational Complexity of Choice Sets.Felix Brandt, Felix Fischer & Paul Harrenstein - 2009 - Mathematical Logic Quarterly 55 (4):444-459.
Discourse, Diversity, and Free Choice.Wolfgang Schwarz - 2021 - Australasian Journal of Philosophy 99 (1):48-67.
Weak Pseudo-Rationalizability.Rush T. Stewart - 2020 - Mathematical Social Sciences 104:23-28.


Added to PP index

Total views
41 ( #274,243 of 2,498,579 )

Recent downloads (6 months)
20 ( #42,703 of 2,498,579 )

How can I increase my downloads?


My notes