# A Cram'er-von Mises Approach to Incentivizing Truthful Data Sharing

arXiv: https://arxiv.org/abs/2506.07272 · HTML: https://mlsanity.com/paper/2506.07272/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Builds on (most cited first, 24 of 24)

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- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Free-rider Attacks on Model Aggregation in Federated Learning](https://mlsanity.com/paper/2006.11901/) (2020)
- [Progressive Knowledge Distillation Of Stable Diffusion XL Using Layer Level Loss](https://mlsanity.com/paper/2401.02677/) (2024)
- [Free-riders in Federated Learning: Attacks and Defenses](https://mlsanity.com/paper/1911.12560/) (2019)
- [One for One, or All for All: Equilibria and Optimality of Collaboration in Federated Learning](https://mlsanity.com/paper/2103.03228/) (2021)
- [Mechanisms that Incentivize Data Sharing in Federated Learning](https://mlsanity.com/paper/2207.04557/) (2022)
- [Crowdsourced Judgement Elicitation with Endogenous Proficiency](https://mlsanity.com/paper/1303.0799/) (2013)
- [Optimum Statistical Estimation with Strategic Data Sources](https://mlsanity.com/paper/1408.2539/) (2014)
- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [Truthful Data Acquisition via Peer Prediction](https://mlsanity.com/paper/2006.03992/) (2020)
- [Water from Two Rocks: Maximizing the Mutual Information](https://mlsanity.com/paper/1802.08887/) (2018)
- [Optimal Data Acquisition for Statistical Estimation](https://mlsanity.com/paper/1711.01295/) (2017)
- [Buying Private Data without Verification](https://mlsanity.com/paper/1404.6003/) (2014)
- [Evaluating and Incentivizing Diverse Data Contributions in Collaborative Learning](https://mlsanity.com/paper/2306.05592/) (2023)
- [Mechanism Design for Collaborative Normal Mean Estimation](https://mlsanity.com/paper/2306.06351/) (2023)
- [Incentivizing Honesty among Competitors in Collaborative Learning and Optimization](https://mlsanity.com/paper/2305.16272/) (2023)
- [Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution](https://mlsanity.com/paper/2407.15881/) (2024)
- [Carrot and Stick: Eliciting Comparison Data and Beyond](https://mlsanity.com/paper/2410.23243/) (2024)
- [Incentivizing Truthful Data Contributions in a Marketplace for Mean Estimation](https://mlsanity.com/paper/2502.16052/) (2025)

## Abstract (arXiv)

Modern data marketplaces and data sharing consortia increasingly rely on incentive mechanisms to encourage agents to contribute data. However, schemes that reward agents based on the quantity of submitted data are vulnerable to manipulation, as agents may submit fabricated or low-quality data to inflate their rewards. Prior work has proposed comparing each agent's data against others' to promote honesty: when others contribute genuine data, the best way to minimize discrepancy is to do the same. Yet prior implementations of this idea rely on very strong assumptions about the data distribution (e.g. Gaussian), limiting their applicability. In this work, we develop reward mechanisms based on a novel, two-sample test inspired by the Cram'er-von Mises statistic. Our methods strictly incentivize agents to submit more genuine data, while disincentivizing data fabrication and other types of untruthful reporting. We establish that truthful reporting constitutes a (possibly approximate) Nash equilibrium in both Bayesian and prior-agnostic settings. We theoretically instantiate our method in three canonical data sharing problems and show that it relaxes key assumptions made by prior work. Empirically, we demonstrate that our mechanism incentivizes truthful data sharing via simulations and on real-world language and image data.