---
title: "Group Decision Making via Weighted Propositional Logic: Complexity and Islands of Tractability"
authors:
  - "Gianluigi Greco"
  - "Jérôme Lang"
doi: ""
url: "https://ijcai.org/proceedings/2015/425"
pdf: "https://ijcai.org/proceedings/2015/0425.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "3008-3013"
track: "Special Track on Knowledge Representation and Reasoning"
keywords:
---

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

Gianluigi Greco, Jérôme Lang

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 3008-3013.

## Abstract

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.