Comparing Algorithms for Fair Allocation of Indivisible Items with Limited Information

In studies of collective decision-making, the problem of allocating indivisible items fairly and efficiently is now recognized as the most difficult. Here, various algorithms for finding allocations are assessed on their ability to achieve the desirable properties of envy-freeness, Pareto-optimality, maximin, maximum Borda sum, and Borda maximin. Two players with additive preferences allocate an even number of indivisible items when their only information is the other’s strict preference ordering. Algorithms under study include both naive and sophisticated versions of sequential selection, bottom-up sequential selection (or sequential rejection), balanced alternation, bottom-up balanced alternation, and fallback bargaining. The results suggest that fallback bargaining, the only simultaneous algorithm, satisfies most fairness and efficiency criteria but has some distinctive drawbacks.