Independent Natural Extension for Infinite Spaces: Williams-Coherence to the Rescue

TL;DR

This paper introduces a new method for defining independent natural extensions in infinite spaces using Williams-coherence, ensuring existence and desirable properties unlike previous approaches.

Contribution

It proposes a novel independent natural extension framework based on Williams-coherence, guaranteeing existence and key properties in infinite spaces.

Findings

Independent natural extension always exists under Williams-coherence.

The new extension satisfies factorisation and external additivity.

It contrasts with previous methods that lack guaranteed existence.

Abstract

We define the independent natural extension of two local models for the general case of infinite spaces, using both sets of desirable gambles and conditional lower previsions. In contrast to Miranda and Zaffalon (2015), we adopt Williams-coherence instead of Walley-coherence. We show that our notion of independent natural extension always exists - whereas theirs does not - and that it satisfies various convenient properties, including factorisation and external additivity.