# How Proper Scoring Rules Shape LLM Forecasting

arXiv: https://arxiv.org/abs/2608.28482 · HTML: https://mlsanity.com/paper/2608.28482/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [ForecastBench: A Dynamic Benchmark of AI Forecasting Capabilities](https://mlsanity.com/paper/2409.19839/) (2024)
- [Approaching Human-Level Forecasting with Language Models](https://mlsanity.com/paper/2402.18563/) (2024)
- [Confronting Reward Model Overoptimization with Constrained RLHF](https://mlsanity.com/paper/2310.04373/) (2023)
- [Forecasting Future World Events with Neural Networks](https://mlsanity.com/paper/2206.15474/) (2022)
- [Future-as-Label: Scalable Supervision from Real-World Outcomes](https://mlsanity.com/paper/2601.06336/) (2026)

## Abstract (arXiv)

This paper evaluates how reward function choice shapes the performance and behavior of LLM forecasters. We compare five proper scoring rules as training objectives for binary forecasts of resolved real-world events. Although the rules share the same theoretical incentive for truthful probability reporting, the resulting models differ in calibration, probability use, and estimated profiles of bias, information, and noise, with smaller differences in aggregate accuracy and discrimination. The Brier-trained model has the lowest observed Brier score and highest AUC-ROC, while the log-trained model has the highest observed log score and lowest calibration error. Models with similar aggregate performance also reach that performance through different combinations of bias, information, and noise. Proper scoring rules therefore need not behave interchangeably as training objectives. Reward choice may shape not only how well an LLM forecasts, but how its forecasting errors are structured.