# Incentivizing honest performative predictions with proper scoring rules

arXiv: https://arxiv.org/abs/2305.17601 · HTML: https://mlsanity.com/paper/2305.17601/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 57 references that are in the map.
- First posted on arXiv 28 May 2023.

## Builds on (most cited first, 21 of 21)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Risks from Learned Optimization in Advanced Machine Learning Systems](https://mlsanity.com/paper/1906.01820/) (2019)
- [The Alignment Problem from a Deep Learning Perspective](https://mlsanity.com/paper/2209.00626/) (2022)
- [Optimal Policies Tend to Seek Power](https://mlsanity.com/paper/1912.01683/) (2019)
- [Truthful AI: Developing and governing AI that does not lie](https://mlsanity.com/paper/2110.06674/) (2021)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Stable Opponent Shaping in Differentiable Games](https://mlsanity.com/paper/1811.08469/) (2018)
- [DiCE: The Infinitely Differentiable Monte-Carlo Estimator](https://mlsanity.com/paper/1802.05098/) (2018)
- [Hidden Incentives for Auto-Induced Distributional Shift](https://mlsanity.com/paper/2009.09153/) (2020)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [Optimization of Scoring Rules](https://mlsanity.com/paper/2007.02905/) (2020)
- [Good and safe uses of AI Oracles](https://mlsanity.com/paper/1711.05541/) (2017)
- [Binary Scoring Rules that Incentivize Precision](https://mlsanity.com/paper/2002.10669/) (2020)
- [Avoiding Tampering Incentives in Deep RL via Decoupled Approval](https://mlsanity.com/paper/2011.08827/) (2020)
- [Informational Substitutes](https://mlsanity.com/paper/1703.08636/) (2017)
- [Scoring Rules for Performative Binary Prediction](https://mlsanity.com/paper/2207.02847/) (2022)

## Built on by (most cited first, 9 of 9)

- [Evaluating Superhuman Models with Consistency Checks](https://mlsanity.com/paper/2306.09983/) (2023)
- [Human Expertise in Algorithmic Prediction](https://mlsanity.com/paper/2402.00793/) (2024)
- [Revisiting the Predictability of Performative, Social Events](https://mlsanity.com/paper/2503.11713/) (2025)
- [Statistical Inference under Performativity](https://mlsanity.com/paper/2505.18493/) (2025)
- [Dissecting Performative Prediction: A Comprehensive Survey](https://mlsanity.com/paper/2602.10176/) (2026)
- [Joint Scoring Rules: Zero-Sum Competition Avoids Performative Prediction](https://mlsanity.com/paper/2412.20732/) (2024)
- [Conditional Forecasts and Proper Scoring Rules for Reliable and Accurate Performative Predictions](https://mlsanity.com/paper/2510.21335/) (2025)
- [Evolutionary Prediction Games](https://mlsanity.com/paper/2503.03401/) (2025)
- [The Behavioral Credibility Trilemma: When Calibrated Autonomy Becomes Impossible](https://mlsanity.com/paper/2605.25739/) (2026)

## Abstract (arXiv)

Proper scoring rules incentivize experts to accurately report beliefs, assuming predictions cannot influence outcomes. We relax this assumption and investigate incentives when predictions are performative, i.e., when they can influence the outcome of the prediction, such as when making public predictions about the stock market. We say a prediction is a fixed point if it accurately reflects the expert's beliefs after that prediction has been made. We show that in this setting, reports maximizing expected score generally do not reflect an expert's beliefs, and we give bounds on the inaccuracy of such reports. We show that, for binary predictions, if the influence of the expert's prediction on outcomes is bounded, it is possible to define scoring rules under which optimal reports are arbitrarily close to fixed points. However, this is impossible for predictions over more than two outcomes. We also perform numerical simulations in a toy setting, showing that our bounds are tight in some situations and that prediction error is often substantial (greater than 5-10%). Lastly, we discuss alternative notions of optimality, including performative stability, and show that they incentivize reporting fixed points.