Consistency and the sequential equal contributions rule for airport problems

We consider the problem of sharing the cost of a public facility among agents who have different needs for it. We base two characterizations of the sequential equal contributions rule on smallest-cost consistency. Namely, (i) the rule is the only rule satisfying equal treatment of equals, independence of all but the smallest-cost, and smallest-cost consistency, and (ii) it is the only rule satisfying equal share lower bound, cost monotonicity, and smallest-cost consistency.