Peer prediction mechanisms incentivize self-interested agents to truthfully report their signals even in the absence of verification by comparing agents’ reports with their peers. We propose two new mechanisms, Source and Target Differential Peer Prediction, and prove very strong guarantees for a very general setting.
Our Differential Peer Prediction mechanisms are strongly truthful: Truth-telling is a strict Bayesian Nash equilibrium. Also, truth-telling pays strictly higher than any other equilibria, excluding permutation equilibria, which pays the same amount as truth-telling. The guarantees hold for asymmetric priors among agents, which the mechanisms need not know (detail-free) in the single question setting. Moreover, they only require three agents, each of which submits a single item report: two report their signals (answers), and the other reports her forecast (prediction of one of the other agent’s reports). Our proof technique is straightforward, conceptually motivated, and turns on the logarithmic scoring rule’s special properties.
Moreover, we can recast the Bayesian Truth Serum mechanism into our framework. We can also extend our results to the setting of continuous signals with a slightly weaker guarantee on the optimality of the truthful equilibrium.
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Surrogate Scoring Rules
Strictly proper scoring rules (SPSR) are incentive compatible for eliciting information about random variables from strategic agents when the principal can reward agents after the realization of the random variables. They also quantify the quality of elicited information, with more accurate predictions receiving higher scores in expectation. In this paper, we extend such scoring rules to settings where a principal elicits private probabilistic beliefs but only has access to agents’ reports. We name our solution Surrogate Scoring Rules (SSR). SSR is built on a bias correction step and an error rate estimation procedure for a reference answer defined using agents’ reports. We show that, with a little information about the prior distribution of the random variables, SSR in a multi-task setting recover SPSR in expectation, as if having access to the ground truth. Therefore, a salient feature of SSR is that they quantify the quality of information despite the lack of ground truth, just as SPSR do for the setting with ground truth. As a by-product, SSR induce dominant uniform strategy truthfulness in reporting. Our method is verified both theoretically and empirically using data collected from real human forecasters.
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- PAR ID:
- 10391557
- Date Published:
- Journal Name:
- ACM Transactions on Economics and Computation
- ISSN:
- 2167-8375
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)Peer prediction mechanisms incentivize agents to truthfully report their signals even in the absence of verification by comparing agents’ reports with those of their peers. In the detail-free multi-task setting, agents are asked to respond to multiple independent and identically distributed tasks, and the mechanism does not know the prior distribution of agents’ signals. The goal is to provide an epsilon-strongly truthful mechanism where truth-telling rewards agents “strictly” more than any other strategy profile (with epsilon additive error) even for heterogeneous agents, and to do so while requiring as few tasks as possible. We design a family of mechanisms with a scoring function that maps a pair of reports to a score. The mechanism is strongly truthful if the scoring function is “prior ideal”. Moreover, the mechanism is epsilon-strongly truthful as long as the scoring function used is sufficiently close to the ideal scoring function. This reduces the above mechanism design problem to a learning problem – specifically learning an ideal scoring function. Because learning the prior distribution is sufficient (but not necessary) to learn the scoring function, we can apply standard learning theory techniques that leverage side information about the prior (e.g., that it is close to some parametric model). Furthermore, we derive a variational representation of an ideal scoring function and reduce the learning problem into an empirical risk minimization. We leverage this reduction to obtain very general results for peer prediction in the multi-task setting. Specifically, Sample Complexity. We show how to derive good bounds on the number of tasks required for different types of priors–in some cases exponentially improving previous results. In particular, we can upper bound the required number of tasks for parametric models with bounded learning complexity. Furthermore, our reduction applies to myriad continuous signal space settings. To the best of our knowledge, this is the first peer-prediction mechanism on continuous signals designed for the multi-task setting. Connection to Machine Learning. We show how to turn a soft-predictor of an agent’s signals (given the other agents’ signals) into a mechanism. This allows the practical use of machine learning algorithms that give good results even when many agents provide noisy information. Stronger Properties. In the finite setting, we obtain -strongly truthful mechanisms for any stochastically relevant prior. Prior works either only apply to more restrictive settings, or achieve a weaker notion of truthfulness (informed truthfulness).more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3565559
