When agents'allocations are one-dimensional and preferences are convex, the three perenial goals of mechanism design, efficiency, prior-free incentive compatibility and fairness (horizontal equity) are compatible. This has been known for decades in the cases of voting and of division of a non disposable commodity. We show that it is in fact true when the range of allocation profiles is an arbitrary convex and compact set.
Examples include: load balancing with arbitrary flow graph constraints;!coordinating joint work inside a team or across teams, when individual contributions are substitutable or complementary; and any joint venture with a convex technology where each agent provides a single input or consumes a single output. The set of efficient, incentive compatible and fair mechanisms is very rich, and additional requirement such as consistency are needed to identify reasonable candidates.