Results about sets of desirable gamble sets

TL;DR

This paper investigates the axioms and representations of coherent sets of desirable gamble sets, providing new insights into their structure and how they can be extended and represented mathematically.

Contribution

It introduces results on the axioms for coherence, natural extension, and a representation via proper filters of coherent sets of desirable gambles.

Findings

Characterization of axioms for coherence

Method for natural extension of gamble sets

Representation of coherent sets by proper filters

Abstract

Coherent sets of desirable gamble sets is used as a model for representing an agents opinions and choice preferences under uncertainty. In this paper we provide some results about the axioms required for coherence and the natural extension of a given set of desirable gamble sets. We also show that coherent sets of desirable gamble sets can be represented by a proper filter of coherent sets of desirable gambles.