Collective discrete optimisation as judgment aggregation

TL;DR

This paper introduces a unified framework for solving various collective decision-making problems modeled as discrete optimisation tasks, using judgment aggregation with weighted issues, and demonstrates its application to collective spanning trees.

Contribution

It proposes a modular, general approach to collective discrete optimisation problems through judgment aggregation, unifying multiple existing methods and providing an ILP implementation.

Findings

Framework generalizes existing CDO procedures

Implementation successfully applied to collective spanning trees

Demonstrates flexibility and effectiveness of the approach

Abstract

Many important collective decision-making problems can be seen as multi-agent versions of discrete optimisation problems. Participatory budgeting, for instance, is the collective version of the knapsack problem; other examples include collective scheduling, and collective spanning trees. Rather than developing a specific model, as well as specific algorithmic techniques, for each of these problems, we propose to represent and solve them in the unifying framework of judgment aggregation with weighted issues. We provide a modular definition of collective discrete optimisation (CDO) rules based on coupling a set scoring function with an operator, and we show how they generalise several existing procedures developed for specific CDO problems. We also give an implementation based on integer linear programming (ILP) and test it on the problem of collective spanning trees.