Collective discrete optimisation as judgment aggregation

Abstract

Many important collective decision-making problems can be seen as multiagent 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.

The (Computational) Social Choice Take on Indivisible Participatory Budgeting

“…As we have seen already PB can be seen as a collective variant of the knapsack problem (see e.g., Fluschnik, Skowron, Triphaus and Wilker, 2019). e idea of looking at collective variants of optimisation problems is a growing field in which PB fits nicely (Boes, Colley, Grandi, Lang and Novaro, 2021). Other optimisation problems for which their collective variants have been studied include finding spanning trees or scheduling jobs on machines Pferschy, 2009, 2011;Pascual, Rzadca and Skowron, 2018).…”