Excedente Escalonado (ExE): a monotone rule for pro-rata ties

the abstract: When several orders tie at the same price and the quantity available is not enough for all of them, some rule must decide who receives each lot. Exchanges usually rely on time priority, which rewards speed, or on pro-rata rules that hand out the leftovers by a second criterion; the latter can show the Alabama paradox, in which one more lot makes someone lose lots. We propose the Excedente Escalonado (Stepwise Excess, ExE) rule, a simple pro-rata rule applied in a single pass through the priority list, which gives priority to the largest demand and uses arrival time only as a tiebreaker. ExE offers three guarantees at once: every order receives at least its proportional share rounded down, the order with the largest demand receives at least its exact share, and no order loses lots when the quantity available increases. Among the exchange, regulatory and parliamentary rules we tested, no other rule combines these three guarantees. Proofs are in the appendix.