A Robust Bayesian Truth Serum for Small Populations

Peer prediction mechanisms allow the truthful elicitation of private signals (e.g., experiences, or opinions) in regard to a true world state when this ground truth is unobservable. The original peer prediction method is incentive compatible for any number of agents n >= 2, but relies on a common prior, shared by all agents and the mechanism. The Bayesian Truth Serum (BTS) relaxes this assumption. While BTS still assumes that agents share a common prior, this prior need not be known to the mechanism. However, BTS is only incentive compatible for a large enough number of agents, and the particular number of agents required is uncertain because it depends on this private prior. In this paper, we present a robust BTS for the elicitation of binary information which is incentive compatible for every n >= 3, taking advantage of a particularity of the quadratic scoring rule. The robust BTS is the first peer prediction mechanism to provide strict incentive compatibility for every n >= 3 without relying on knowledge of the common prior. Moreover, and in contrast to the original BTS, our mechanism is numerically robust and ex post individually rational.Engineering and Applied Science

A Robust Bayesian Truth Serum for Non-binary Signals

Several mechanisms have been proposed for incentivizing truthful reports of a private signals owned by rational agents, among them the peer prediction method and the Bayesian truth serum. The robust Bayesian truth serum (RBTS) for small populations and binary signals is particularly interesting since it does not require a common prior to be known to the mechanism. We further analyze the problem of the common prior not known to the mechanism and give several results regarding the restrictions that need to be placed in order to have an incentive-compatible mechanism. Moreover, we construct a Bayes-Nash incentive-compatible scheme called multi-valued RBTS that generalizes RBTS to operate on both small populations and non-binary signals. Copyright © 2013, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved

Buying Private Data without Verification

We consider the problem of designing a survey to aggregate non-verifiable information from a privacy-sensitive population: an analyst wants to compute some aggregate statistic from the private bits held by each member of a population, but cannot verify the correctness of the bits reported by participants in his survey. Individuals in the population are strategic agents with a cost for privacy, \ie, they not only account for the payments they expect to receive from the mechanism, but also their privacy costs from any information revealed about them by the mechanism's outcome---the computed statistic as well as the payments---to determine their utilities. How can the analyst design payments to obtain an accurate estimate of the population statistic when individuals strategically decide both whether to participate and whether to truthfully report their sensitive information? We design a differentially private peer-prediction mechanism that supports accurate estimation of the population statistic as a Bayes-Nash equilibrium in settings where agents have explicit preferences for privacy. The mechanism requires knowledge of the marginal prior distribution on bits $b_i$, but does not need full knowledge of the marginal distribution on the costs $c_i$, instead requiring only an approximate upper bound. Our mechanism guarantees $\epsilon$-differential privacy to each agent $i$ against any adversary who can observe the statistical estimate output by the mechanism, as well as the payments made to the $n-1$ other agents $j\neq i$. Finally, we show that with slightly more structured assumptions on the privacy cost functions of each agent, the cost of running the survey goes to $0$ as the number of agents diverges.Comment: Appears in EC 201

Bayesian markets to elicit private information

Financial markets reveal what investors think about the future, and prediction markets are used to forecast election results. Could markets also encourage people to reveal private information, such as subjective judgments (e.g., “Are you satisfied with your life?”) or unverifiable facts? This paper shows how to design such markets, called Bayesian markets. People trade an asset whose value represents the proportion of affirmative answers to a question. Their trading position then reveals their own answer to the question. The results of this paper are based on a Bayesian setup in which people use their private information (their “type”) as a signal. Hence, beliefs about others’ types are correlated with one’s own type. Bayes