Pareto-Optimal Allocations Unveiled: Efficiency and Sequenceability in Fair Division
The article explores how to fairly divide indivisible goods among people with different preferences. It focuses on using sequences of choices to allocate objects, where each person picks one item at a time. The researchers found that any fair allocation under numerical preferences can be done in a sequence, but not all sequences are fair. They also discovered a three-step efficiency scale: Pareto-optimality, sequenceability without fairness, and non-sequenceability. Additionally, they found that some fair allocations may not be in sequence, but all competitive equilibriums with equal incomes can be.