# Mechanism Design for Collaborative Normal Mean Estimation

arXiv: https://arxiv.org/abs/2306.06351 · HTML: https://mlsanity.com/paper/2306.06351/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2023.

## Built on by (most cited first, 7 of 7)

- [Online Learning from Strategic Human Feedback in LLM Fine-Tuning](https://mlsanity.com/paper/2412.16834/) (2024)
- [Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution](https://mlsanity.com/paper/2407.15881/) (2024)
- [Revisiting Active Sequential Prediction-Powered Mean Estimation](https://mlsanity.com/paper/2604.18569/) (2026)
- [Designing DSIC Mechanisms for Data Sharing in the Era of Large Language Models](https://mlsanity.com/paper/2506.05379/) (2025)
- [A Cram'er-von Mises Approach to Incentivizing Truthful Data Sharing](https://mlsanity.com/paper/2506.07272/) (2025)
- [Gradient Manipulation in Distributed Stochastic Gradient Descent with Strategic Agents: Truthful Incentives with Convergence Guarantees](https://mlsanity.com/paper/2603.27962/) (2026)
- [Truthful Online Preference Aggregation for LLM Fine-Tuning in Mobile Crowdsourcing](https://mlsanity.com/paper/2605.24052/) (2026)

## Abstract (arXiv)

We study collaborative normal mean estimation, where m strategic agents collect i.i.d samples from a normal distribution N(μ, σ2) at a cost. They all wish to estimate the mean μ. By sharing data with each other, agents can obtain better estimates while keeping the cost of data collection small. To facilitate this collaboration, we wish to design mechanisms that encourage agents to collect a sufficient amount of data and share it truthfully, so that they are all better off than working alone. In naive mechanisms, such as simply pooling and sharing all the data, an individual agent might find it beneficial to under-collect and/or fabricate data, which can lead to poor social outcomes. We design a novel mechanism that overcomes these challenges via two key techniques: first, when sharing the others' data with an agent, the mechanism corrupts this dataset proportional to how much the data reported by the agent differs from the others; second, we design minimax optimal estimators for the corrupted dataset. Our mechanism, which is Nash incentive compatible and individually rational, achieves a social penalty (sum of all agents' estimation errors and data collection costs) that is at most a factor 2 of the global minimum. When applied to high dimensional (non-Gaussian) distributions with bounded variance, this mechanism retains these three properties, but with slightly weaker results. Finally, in two special cases where we restrict the strategy space of the agents, we design mechanisms that essentially achieve the global minimum.