Friend-based Ranking
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We analyze the design of mechanisms to rank individuals in communities where individuals only have local, ordinal information on the characteristics of their neighbors. In completely informative communities, we show that the planner can construct an ex-post incentive compatible and ex-post efficient mechanism if and only if all pair of individuals are observed by a third individual---every pair of individuals in the social network has a common friend. We use this insight to characterize the sparsest social network for which a complete ranking exists as the "friendship network" of Erdős, Rényi, and Sós (1966). When the social network is not completely informative, we show that any self-report which is not supported by a third party must be discarded. We provide two sufficient conditions on the social network under which an ex-post incentive compatible and ex-post efficient mechanism may be constructed: when the social network is bipartite or only formed of triangles. We use data on social networks from India and Indonesia to illustrate the results of the theoretical analysis. We measure information provided by the social network as the share of unique comparisons which can be obtained by friend-based comparisons (the density of the comparison network) and show that information varies greatly even for given density, across triangle comparisons are important at low densities, and information is close to an upper bound when degree is capped at a small value relative to the community size.
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