Extending choice assessments to choice functions: An algorithm for computing the natural extension
This work addresses decision-making under uncertainty for researchers in AI and operations research, but it appears incremental as it extends existing mathematical frameworks.
The paper tackles the problem of inferring new choices from prior choices within the choice functions framework by defining and computing the natural extension, and it presents a practical algorithm with scalability improvements tested on various choice assessments.
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.