The Ordering Problem

Serial dictatorship is the simplest allocation mechanism. Line people up. Each person picks their favorite available item. Move to the next person. It is strategyproof — no one gains by lying about preferences. It is Pareto efficient — no reallocation can improve one person without worsening another. But it is not fair. Someone with higher priority may envy someone who picked earlier and took the item they wanted.

The standard response is to accept this tradeoff — simplicity and strategyproofness come at the cost of fairness. Hamdan (arXiv:2603.05660) shows the tradeoff is less severe than assumed. The fairness of serial dictatorship depends on the ORDER in which people pick. Different orderings produce different amounts of justified envy. There exists an optimal ordering.

Under identical, uniformly distributed preferences with unit-capacity objects, the optimal ordering is the Kemeny ranking — the ordering that minimizes the total pairwise disagreement with agents’ underlying priorities. The Kemeny ranking is a concept from social choice theory, not mechanism design. It was invented to aggregate preferences into a consensus. Here it serves a different purpose: ordering a sequential process to minimize the envy it generates.

Relax any of the simplifying assumptions — allow heterogeneous preferences, non-uniform distributions, or multi-capacity objects — and the Kemeny ranking generalizes to a weighted version. The structure persists: there is always an ordering that minimizes expected justified envy, and it always has the form of an aggregation ranking.

The through-claim: the unfairness of sequential allocation is not intrinsic to the mechanism. It is a property of the ordering. The mechanism is a fixed pipe; the ordering is the variable that controls how much envy flows through it. The same mechanism, reordered, can be substantially fairer — not perfectly fair, but optimally fair within the constraint of sequential choice.