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We consider the problem of fairly dividing a set of items. Much of the fairdivision literature assumes that the items are `goods' i.e., they yieldpositive utility for the agents. There is also some work where the items are`chores' that yield negative utility for the agents. In this paper, we considera more general scenario where an agent may have negative or positive utilityfor each item. This framework captures, e.g., fair task assignment, whereagents can have both positive and negative utilities for each task. We showthat whereas some of the positive axiomatic and computational results extend tothis more general setting, others do not. We present several new and efficientalgorithms for finding fair allocations in this general setting. We also pointout several gaps in the literature regarding the existence of allocationssatisfying certain fairness and efficiency properties and further study thecomplexity of computing such allocations.

Fair allocation of combinations of indivisible goods and chores