Tight bounds for strategyproof classification

Strategyproof (SP) classification considers situations in which a decision-maker must classify a set of input points with binary labels, minimizing expected error. Labels of input points are reported by self-interested agents, who may lie so as to obtain a classifier more closely matching their own labels. These lies would create a bias in the data, and thus motivate the design of truthful mechanisms that discourage false reporting. We here answer questions left open by previous research on strategyproof classification [12, 13, 14], in particular regarding the best approximation ratio (in terms of social welfare) that an SP mechanism can guarantee for n agents. Our primary result is a lower bound of 3 - ^ on the approximation ratio of SP mechanisms under the shared inputs assumption; this shows that the previously known upper bound (for uniform weights) is tight. The proof relies on a result from Social Choice theory, showing that any SP mechanism must select a dictator at random, according to some fixed distribution. We then show how different randomizations can improve the best known mechanism when agents are weighted, matching the lower bound with a tight upper bound. These results contribute both to a better understanding of the limits of SP classification, as well as to the development of similar tools in other, related domains such as SP facility location. Categories and Subject Descriptors 1.2.11 [Artificial Intelligence]: Distributed Artificial Intelligence- Multiagent Systems General Terms Theory, Algorithms, Economics.