Collective combinatorial optimisation as judgment aggregation

Boes, L., Colley, R. , Grandi, U., Lang, J. and Novaro, A. (2023) Collective combinatorial optimisation as judgment aggregation. Annals of Mathematics and Artificial Intelligence, (doi: 10.1007/s10472-023-09910-w) (Early Online Publication)

Abstract

In many settings, a collective decision has to be made over a set of alternatives that has a combinatorial structure: important examples are multi-winner elections, participatory budgeting, collective scheduling, and collective network design. A further common point of these settings is that agents generally submit preferences over issues (e.g., projects to be funded), each having a cost, and the goal is to find a feasible solution maximising the agents’ satisfaction under problem-specific constraints. We propose the use of judgment aggregation as a unifying framework to model these situations, which we refer to as collective combinatorial optimisation problems. Despite their shared underlying structure, collective combinatorial optimisation problems have so far been studied independently. Our formulation into judgment aggregation connects them, and we identify their shared structure via five case studies of well-known collective combinatorial optimisation problems, proving how popular rules independently defined for each problem actually coincide. We also chart the computational complexity gap that may arise when using a general judgment aggregation framework instead of a specific problem-dependent model.

• Item Type: Articles
• Keywords: Computational social choice, judgment aggregation, combinatorial optimisation, computational complexity.
• Status: Early Online Publication
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Colley, Dr Rachael
• Authors: Boes, L., Colley, R., Grandi, U., Lang, J., and Novaro, A.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Annals of Mathematics and Artificial Intelligence
• Publisher: Springer
• ISSN: 1012-2443
• ISSN (Online): 1573-7470
• Published Online: 15 December 2023
• Copyright Holders: Copyright © The Author(s) 2023
• First Published: First published in Annals of Mathematics and Artificial Intelligence 2023
• Publisher Policy: Reproduced under a Creative Commons license