Group Decision Making via Weighted Propositional Logic: Complexity and Islands of Tractability.

Greco Gianluigi (1) , Jérôme Lang (2)

1 Unical - Università della Calabria [Arcavacata di Rende]
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

We study a general class of multiagent optimization problems, together with a compact representation language of utilities based on weighted propositional formulas. We seek solutions maximizing utilitarian social welfare as well as fair solutions maximizing the utility of the least happy agent. We show that many problems can be expressed in this setting, such as fair division of indivisible goods, some multiwinner elections, or multifacility location. We focus on the complexity of finding optimal solutions, and we identify the tractability boarder between polynomial and NP-hard settings, along several parameters: the syntax of formulas, the allowed weights, as well as the number of agents, propositional symbols, and formulas per agent.

Mots clés: knowledge representation; social choice

Domaines: Informatique [cs]

Greco Gianluigi, Jérôme Lang. Group Decision Making via Weighted Propositional Logic: Complexity and Islands of Tractability.. 24th International Joint Conference on Artificial Intelligence (IJCAI 2015), Jul 2015, Buenos Aires, Argentina. pp.3008-3014. ⟨hal-01498923⟩