Can we reach Pareto optimal outcomes using bottom-up approaches?
  Traditionally, researchers in decision making have focused on attempting to reach Pareto Optimality using horizontal approaches, where optimality is calculated taking into account every participant at the same time. Sometimes, this may prove to be a difficult task (e.g., conflict, mistrust, no information sharing, etc.). In this paper, we explore the possibility of achieving Pareto Optimal outcomes in a group by using a bottom-up approach: discovering Pareto optimal outcomes by interacting in subgroups. We analytically show that Pareto optimal outcomes in a subgroup are also Pareto optimal in a supergroup of those agents in the case of strict, transitive, and complete preferences. Then, we empirically analyze the prospective usability and practicality of bottom-up approaches in a variety of decision making domains. 
Victor Sanchez-Anguix and Reyhan Aydogan and Tim Baarslag and   Catholijn M. Jonker
cs.MA cs.AI cs.GT