Extending choice assessments to choice functions: An algorithm for computing the natural extension

TL;DR

This paper introduces an algorithm to compute the natural extension of choice assessments to choice functions, enabling the inference of new choices while ensuring coherence, with practical improvements for scalability tested across various assessments.

Contribution

It presents a novel algorithm for extending choice assessments to choice functions, enhancing decision-making capabilities with scalable computational methods.

Findings

The algorithm effectively computes the natural extension in various scenarios.

Scalability improvements enable practical application to large choice assessments.

Experimental results demonstrate the method's accuracy and efficiency.

Abstract

We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natural (most conservative) extension of a given choice assessment to a coherent choice function -- whenever possible -- and use this natural extension to make new choices. We provide a practical algorithm for computing this natural extension and various ways to improve scalability. Finally, we test these algorithms for different types of choice assessments.