Solving sequential collective decision problems under qualitative uncertainty

Abstract

This paper addresses the question of sequential collective decision making under qualitative uncertainty. It resumes the criteria introduced in previous works [4–6] by Ben Amor et al. and extends them to a more general context where every decision maker is free to have an optimistic or a pessimistic attitude w.r.t. uncertainty. These criteria are then considered for the optimization of possibilistic decision trees and an algorithmic study is performed for each of them. When the global utility does satisfy the monotonicity property, a classical possibilistic Dynamic Programming can be applied. Otherwise, two cases are possible: either the criterion is max oriented (the more is the satisfaction of any agent, the greater is the global satisfaction), and a dedicated algorithm can be proposed, that relies on as many calls to Dynamic Programming as the number of decision makers; or the criterion is min oriented (all the agents must like the common decision) and the optimal strategy can be provided by a Branch and Bound Algorithm. The paper concludes by an experimental study that shows the feasibility of the approaches, and details to what extent simple Dynamic programming algorithms can be used as approximation procedures for the non monotonic criteria.