Inferences concerning interpersonal choices given anonymously

It may be difficult or impossible to make a reliable empirical investigation of an unknown network of interpersonal choices or contacts if these are in some respect sensitive for the individuals involved. We consider how choice data given anonymously can be used to reveal various features of the network. Using tools from statistical decision theory and information theory we can determine risks and capacities of disclosing choice data, the graph structure of choice data and its numbers of loops and mutuals. We give some general results, illustrate the combinatorial complexity of the problem and comment upon the computational difficulties.