Designing information to improve welfare in matching markets

In matching markets, objects are allocated to agents without monetary transfers, based on agents’ preferences. However, agents may not have enough information to determine their preferences over the objects precisely. How should a benevolent planner optimally reveal information to maximize social welfare in this context? I show that when agents are symmetric and there are just two options, letting each agent know his rank in the realized distribution of preferences – but not his actual preferences – always improves social welfare over providing no information. When there are more objects, this rank-based information policy generalizes to the Object Recommendation (OR) Signal, which consists of simply recommending each agent to pick his socially-optimal choice. Under a mild regularity condition, I show that, when agents’ a priori relative preferences over the objects are “not too strong”, the OR Signal, used together with any standard ordinal mechanism, not only maximizes welfare, but achieves the unconstrained social optimum — formalizing the intuition that when people do not have strong opinions over several options, it is easy to sway them.