Abstract
Strictly proper scoring rules (SPSR) are widely used when designing incentive mechanisms to elicit private information from strategic agents using realized ground truth signals, and they can help quantify the value of elicited information. In this paper, we extend such scoring rules to settings where a mechanism designer does not have access to ground truth. We consider two such settings: (i) a setting when the mechanism designer has access to a noisy proxy version of the ground truth, with {\em known} biases; and (ii) the standard peer prediction setting where agents’ reports, and possibly some limited prior knowledge of ground truth, are the only source of information that the mechanism designer has. We introduce {\em surrogate scoring rules} (SSR) for the first setting, which use the noisy ground truth to evaluate quality of elicited information. We show that SSR preserves the strict properness of SPSR. Using SSR, we then develop a multi-task scoring mechanism – called \emph{uniform dominant truth serum} (DTS) – to achieve strict properness when there are sufficiently many tasks and agents, and when the mechanism designer only has access to agents’ reports and one bit information about the marginal of the entire set of tasks’ ground truth. In comparison to standard equilibrium concepts in peer prediction, we show that DTS can achieve truthfulness in \emph{uniform dominant strategy} in a multi-task setting when agents adopt the same strategy for all the tasks that they are assigned (hence the term uniform). A salient feature of SSR and DTS is that they quantify the quality of information despite lack of ground truth, just as proper scoring rules do for the {\em with} verification setting. Our method is verified both theoretically and empirically using data collected from real human participants.
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URL
http://arxiv.org/abs/1802.09158