text: We consider crowdsourcing problems where the users are asked to provide evaluations for items; the user evaluations are then used directly, or aggregated into a consensus value. Lacking an incentive scheme, users have no motive in making effort in completing the evaluations, providing inaccurate answers instead. We propose incentive schemes that are truthful and cheap: truthful as the optimal user behavior consists in providing accurate evaluations, and cheap because the truthfulness is achieved with little overhead cost. We consider both discrete evaluation tasks, where an evaluation can be done either correctly, or incorrectly, with no degrees of approximation in between, and quantitative evaluation tasks, where evaluations are real numbers, and the error is measured as distance from the correct value. For both types of tasks, we propose hierarchical incentive schemes that can be effected with a small amount of additional evaluations, and that scale to arbitrarily large crowd sizes: they have the property that the strength of the incentive does not weaken with increasing hierarchy depth. Interestingly, we show that for these schemes to work, the only requisite is that workers know their place in the hierarchy in advance.
  @cite_7: 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.
  @cite_28: 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.
  @cite_1: Agents are asked to rank two objects in a setting where effort is costly and agents differ in quality (which is the probability that they can identify the correct, ground truth, ranking). We study simple output-agreement mechanisms that pay an agent in the case she agrees with the report of another, and potentially penalizes for disagreement through a negative payment. Assuming access to a quality oracle, able to determine whether an agent's quality is above a given threshold, we design a payment scheme that aligns incentives so that agents whose quality is above this threshold participate and invest effort. Precluding negative payments leads the expected cost of this quality-oracle mechanism to increase by a factor of 2 to 5 relative to allowing both positive and negative payments. Dropping the assumption about access to a quality oracle, we further show that negative payments can be used to make agents with quality lower than the quality threshold choose to not to participate, while those above continue to participate and invest effort. Through the appropriate choice of payments, any design threshold can be achieved. This self-selection mechanism has the same expected cost as the cost-minimal quality-oracle mechanism, and thus when using the self-selection mechanism, perfect screening comes for free.
  @cite_6: In this paper, I introduce a class of mechanisms for eliciting private correlated signals from a group of expected score maximizers without external verification or knowledge about the agents’ belief structure. Built on proper scoring rules, these minimum truth serums ask agents to report a signal and a prediction of the signals of others. If two agents with the same signal have the same expectations about the signals of others, the Bayesian incentive compatibility of these mechanisms follows with no further assumptions on the agents’ belief structure. With a slight modification, the mechanism is still feasible and incentive compatible when the prediction portion of the report is optional.
  @cite_19: The elicitation of private information from individuals is crucially important to many real-world tasks. But elicitation is most challenging when it is most useful: when objective (verifiable) truth is inaccessible or unavailable, and there is no answer key" available to verify reports. Prior work has designed mechanisms that truthfully elicit private information without verification for some restricted set of possible information structures of the participants (i.e. the common prior joint distributions of participants' signals). In fact, no mechanism can elicit private information truthfully for all information structures without verification. In this paper, we identify the maximal set of information structures that are truthfully elicitable without verification, and provide a mechanism for such elicitation. This mechanism requires that the designer know the information structure of the participants, which is unavailable in many settings. We then propose a knowledge-free peer prediction mechanism that does not require knowledge of the information structure and can truthfully elicit private information for a set of information structures slightly smaller than the maximal set. This mechanism works for both small and large populations in settings with both binary and non-binary private signals, and is effective on a strict superset of information structures as compared to prior mechanisms that satisfy these properties.
  @cite_23: Peer-prediction is a (meta-)mechanism which, given any proper scoring rule, produces a mechanism to elicit privately-held, non-verifiable information from self-interested agents. Formally, truth-telling is a strict Nash equilibrium of the mechanism. Unfortunately, there may be other equilibria as well (including uninformative equilibria where all players simply report the same fixed signal, regardless of their true signal) and, typically, the truth-telling equilibrium does not have the highest expected payoff. The main result of this paper is to show that, in the symmetric binary setting, by tweaking peer-prediction, in part by carefully selecting the proper scoring rule it is based on, we can make the truth-telling equilibrium focal---that is, truth-telling has higher expected payoff than any other equilibrium. Along the way, we prove the following: in the setting where agents receive binary signals we 1) classify all equilibria of the peer-prediction mechanism; 2) introduce a new technical tool for understanding scoring rules, which allows us to make truth-telling pay better than any other informative equilibrium; 3) leverage this tool to provide an optimal version of the previous result; that is, we optimize the gap between the expected payoff of truth-telling and other informative equilibria; and 4) show that with a slight modification to the peer prediction framework, we can, in general, make the truth-telling equilibrium focal---that is, truth-telling pays more than any other equilibrium (including the uninformative equilibria).
  @cite_15: Subjective judgments, an essential information source for science and policy, are problematic because there are no public criteria for assessing judgmental truthfulness. I present a scoring method for eliciting truthful subjective data in situations where objective truth is unknowable. The method assigns high scores not to the most common answers but to the answers that are more common than collectively predicted, with predictions drawn from the same population. This simple adjustment in the scoring criterion removes all bias in favor of consensus: Truthful answers maximize expected score even for respondents who believe that their answer represents a minority view.
  @cite_34: Many recommendation and decision processes depend on eliciting evaluations of opportunities, products, and vendors. A scoring system is devised that induces honest reporting of feedback. Each rater merely reports a signal, and the system applies proper scoring rules to the implied posterior beliefs about another rater's report. Honest reporting proves to be a Nash equilibrium. The scoring schemes can be scaled to induce appropriate effort by raters and can be extended to handle sequential interaction and continuous signals. We also address a number of practical implementation issues that arise in settings such as academic reviewing and online recommender and reputation systems.
  @cite_17: We consider settings where a collective intelligence is formed by aggregating information contributed from many independent agents, such as product reviews, community sensing, or opinion polls. We propose a novel mechanism that elicits both private signals and beliefs. The mechanism extends the previous versions of the Bayesian Truth Serum (the original BTS, the RBTS, and the multi-valued BTS), by allowing small populations and non-binary private signals, while not requiring additional assumptions on the belief updating process. For priors that are sufficiently smooth, such as Gaussians, the mechanism allows signals to be continuous.
summary: The Bayesian Truth Serum scoring method proposed in @cite_15 elicits truthful subjective answers on multiple choice questions. The author shows that the truthful reporting is a Nash equilibrium with the highest payoff. The model is different from other approaches in that besides the answers, workers need to provide predictions on the final distribution of answers. Workers receive a high score if their answer is surprisingly'' common - the actual percentage of their answer is larger than the predicted fraction. Similarly, incentive mechanisms in @cite_28 @cite_1 @cite_7 @cite_17 @cite_6 require workers provide belief reports along with answers on tasks. Truthful mechanisms in @cite_34 @cite_19 @cite_23 requires knowledge about the distribution from which answers are drawn. Our mechanisms do not rely on worker's beliefs on other workers' responses nor require knowledge about the global answer distribution.