`Why didn't you allocate this task to them?' Negotiation-Aware Task Allocation and Contrastive Explanation Generation

Task-allocation is an important problem in multi-agent systems. It becomes more challenging when the team-members are humans with imperfect knowledge about their teammates' costs and the overall performance metric. While distributed task-allocation methods let the team-members engage in iterative dialog to reach a consensus, the process can take a considerable amount of time and communication. On the other hand, a centralized method that simply outputs an allocation may result in discontented human team-members who, due to their imperfect knowledge and limited computation capabilities, perceive the allocation to be unfair. To address these challenges, we propose a centralized Artificial Intelligence Task Allocation (AITA) that simulates a negotiation and produces a negotiation-aware task allocation that is fair. If a team-member is unhappy with the proposed allocation, we allow them to question the proposed allocation using a counterfactual. By using parts of the simulated negotiation, we are able to provide contrastive explanations that providing minimum information about other's costs to refute their foil. With human studies, we show that (1) the allocation proposed using our method does indeed appear fair to the majority, and (2) when a counterfactual is raised, explanations generated are easy to comprehend and convincing. Finally, we empirically study the effect of different kinds of incompleteness on the explanation-length and find that underestimation of a teammate's costs often increases it.