mlsanityData to 7 Oct 2026

Optimization of Scoring Rules

arXiv 2007.02905 ↗First posted 6 Jul 2020cs.GTcited by 28

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Abstract (arXiv)

We characterize the optimal reward functions (scoring rules) that incentivize an agent to acquire information and report it truthfully to the principal. The optimal scoring rules let the agent make a simple binary bet in single-dimensional problems, and choose the dimension with the most surprising signal to be scored on in symmetric multi-dimensional problems. This scoring rule format remains approximately optimal for asymmetric distributions. These results demonstrate the importance of linking incentives to obtain high-quality information in multi-dimensional problems. In contrast, standard scoring rules like the quadratic scoring rule, or averages of single-dimensional scoring rules can be far from optimal.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jul 2020.

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Citing papers per year: 2021: 1; 2022: 1; 2023: 3; 2024: 7; 2025: 10; 2026: 6.

28 papers.

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  1. 2023U-Calibration: Forecasting for an Unknown Agentcited by 46
  2. 2024Contracting with a Learning Agentcited by 22
  3. 2024Eliciting Informative Text Evaluations with Large Language Modelscited by 14
  4. 2024Calibration Error for Decision Makingcited by 11
  5. 2025Can a calibration metric be both testable and actionable?cited by 10
  6. 2023Incentivizing honest performative predictions with proper scoring rulescited by 9
  7. 2024ElicitationGPT: Text Elicitation Mechanisms via Language Modelscited by 9
  8. 2023Learning to Incentivize Information Acquisition: Proper Scoring Rules Meet Principal-Agent Modelcited by 7
  9. 2025Explaining and Improving Information Complementarities in Multi-Agent Decision-makingcited by 6
  10. 2021Optimal Scoring Rule Design under Partial Knowledgecited by 4
  11. 2024Spot Check Equivalence: an Interpretable Metric for Information Elicitation Mechanismscited by 4
  12. 2025Improved Bounds for Swap Multicalibration and Swap Omnipredictioncited by 4
16 more
  1. 2025A Perfectly Truthful Calibration Measurecited by 4
  2. 2025Calibration through the Lens of Indistinguishabilitycited by 4
  3. 2025Aligned Textual Scoring Rulescited by 2
  4. 2026Near-optimal Swap Regret Minimization for Convex Lossescited by 2
  5. 2022Better Peer Grading through Bayesian Inferencecited by 1
  6. 2025Explanations are a Means to an End: Decision Theoretic Explanation Evaluationcited by 1
  7. 2026The Endogeneity of Miscalibration: Impossibility and Escape in Scored Reportingcited by 1
  8. 2024Underspecified Human Decision Experiments Considered Harmfulcited by 0
  9. 2024Score Design for Multi-Criteria Incentivizationcited by 0
  10. 2025Provably Efficient Algorithm for Best Scoring Rule Identification in Online Principal-Agent Information Acquisitioncited by 0
  11. 2025Designing DSIC Mechanisms for Data Sharing in the Era of Large Language Modelscited by 0
  12. 2025Choice of Scoring Rules for Indirect Elicitation of Properties with Parametric Assumptionscited by 0
  13. 2026Next-Token Prediction and Regret Minimizationcited by 0
  14. 2026When do prophets profit in prediction markets?cited by 0
  15. 2026Fast Rates for Swap-Agnostic Learning of Proper Lossescited by 0
  16. 2026Scoring Rules! Statistical and Strategic Alignment for Text Evaluation Metricscited by 0