An Information Theoretic Framework For Designing Information Elicitation Mechanisms That Reward Truth-telling

Kong, Yuqing; Schoenebeck, Grant

doi:10.1145/3296670

Cited by 55 publications

(98 citation statements)

References 26 publications

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“…Definition 2.1 (f -mutual information [20]). The f -mutual information between X and Y is defined as…”

Section: F -Mutual Informationmentioning

confidence: 99%

“…These papers study various settings. In the single-task setting [27,29] agents are asked one multiple-choice question but typically share a common prior over the responses; in the multi-tasks setting [6,20,37] agents are assigned a batch of a priori similar multiple-choice questions. We consider both of these settings.…”

Section: Our Settingmentioning

confidence: 99%

“…The algorithm in the current paper differs in two main aspects: (1) The current paper uses a different expertise model which can successfully capture the possibly hierarchical relationship between different information/expertise as well as the most valuable information; (2) the current paper combines the algorithm with an incentive mechanism that endogenously controls the quality and structure of the input, rather than making exogenous assumptions about the quality of the input. Lemma 2.4 (Convexity of f -mutual information [20]). Let X 1 , X 2 , X, Y, Z, B λ be random variables…”

Section: Related Workmentioning

confidence: 99%

“…We will extend the Mutual Information Paradigm [20] to our Hierarchical Mutual Information Paradigm that handles the hierarchical information structure.…”

Section: Mechanism Design Frameworkmentioning

confidence: 99%

“…If U X,Y equals to V X,Y , the mutual information between X and Y should be zero since X is independent with Y . Intuitively, the "distance" between U X,Y and V X,Y represents the mutual information between them.Definition 2.1 (f -mutual information [20]). The f -mutual information between X and Y is defined aswhere D f is f -divergence.…”

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confidence: 99%

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Eliciting Expertise without Verification

Kong

Schoenebeck

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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A central question 1 of crowdsourcing is how to elicit expertise from agents. This is even more difficult when answers cannot be directly verified. A key challenge is that sophisticated agents may strategically withhold effort or information when they believe their payoff will be based upon comparison with other agents whose reports will likely omit this information due to lack of effort or expertise.Our work defines a natural model for this setting based on the assumption that more sophisticated agents know the beliefs of less sophisticated agents.We then provide a mechanism design framework for this setting. From this framework, we design several novel mechanisms, for both the single and multiple tasks settings, that (1) encourage agents to invest effort and provide their information honestly; (2) output a correct "hierarchy" of the information when agents are rational. arXiv:1802.08312v2 [cs.GT] 22 May 2018 2 Mechanism Design ToolsWe use two key information theory ingredients in designing information elicitation mechanisms. The first ingredient is f -mutual information M I f (X; Y ) which measures the amount of information crossing two random variables X, Y . For example, if X is independent with Y -no information crosses X and Y , M I f (X; Y ) = 0. The second ingredient is proper scoring rule P S(x, p) which measures the accuracy of the prediction p even we only have one sample x of the outcome X.Both two ingredients have the information monotonicity property. If the information is measured by f -mutual information, any "data processing" on either of the random variables will decrease the amount of information crossing them. If the accuracy of a forecast is measured by a proper scoring rule, more information implies a more accurate forecast. f -mutual informationwhere f (⋅) is a convex function and f (1) = 0. Two commonly used f -divergences are KL divergence and total variation distance. Now we start to introduce f -mutual information.Given two random variables X, Y , let U X,Y and V X,Y be two probability measures where U X,Y is the joint distribution of (X, Y ) and V is the product of the marginal distributions of X and Y . Formally, for every pair of (x, y),If U X,Y is very different with V X,Y , the mutual information between X and Y should be high since knowing X changes the belief for Y a lot. If U X,Y equals to V X,Y , the mutual information between X and Y should be zero since X is independent with Y . Intuitively, the "distance" between U X,Y and V X,Y represents the mutual information between them.Definition 2.1 (f -mutual information [20]). The f -mutual information between X and Y is defined aswhere D f is f -divergence. Definition 2.2 (Conditional f -mutual information [20]). Given three random variables X, Y, Z, we define M I f (X; Y Z) as z P r[Z = z]M I f (X; Y Z = z) where M I f (X; Y Z = z) ∶= M I f (X ′ ; Y ′ ) where P r[X ′ = x, Y ′ = y] = P r[X = x, Y = y Z = z].

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“…Definition 2.1 (f -mutual information [20]). The f -mutual information between X and Y is defined as…”

Section: F -Mutual Informationmentioning

confidence: 99%

Section: Our Settingmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…We will extend the Mutual Information Paradigm [20] to our Hierarchical Mutual Information Paradigm that handles the hierarchical information structure.…”

Section: Mechanism Design Frameworkmentioning

confidence: 99%

mentioning

confidence: 99%

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Eliciting Expertise without Verification

Kong

Schoenebeck

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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Eliciting Social Knowledge for Creditworthiness Assessment

York¹,

Dahleh

Parkes³

2022

Web and Internet Economics

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Obtaining costly unverifiable valuations from a single agent

Segal-Halevi

Alkoby

Sharbaf

et al. 2020

Auton Agent Multi-Agent Syst

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We consider the problem of a principal who needs to elicit the true worth of an object she owns from an agent who has a unique ability to compute this information. The correctness of the information cannot be verified by the principal, so it is important to incentivize the agent to report truthfully. Previous works coped with this unverifiability by employing two or more information agents and awarding them according to the correlation between their reports. In this paper we show that even with only one information agent truthful information can be elicited, as long as the object is valuable for the agent too. In particular the paper introduces a mechanism that, under mild realistic assumptions, is proved to elicit the information truthfully, even when computing the information is costly for the agent. Moreover, using this mechanism, the principal obtains the truthful information incurring an arbitrarily small expense beyond whatever unavoidable costs the setting dictates.

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An Information Theoretic Framework For Designing Information Elicitation Mechanisms That Reward Truth-telling

Cited by 55 publications

References 26 publications

Eliciting Expertise without Verification

Eliciting Expertise without Verification

Eliciting Social Knowledge for Creditworthiness Assessment

Obtaining costly unverifiable valuations from a single agent

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