# From Model Choice to Model Belief: Establishing a New Measure for LLM-Based Research

arXiv: https://arxiv.org/abs/2512.23184 · HTML: https://mlsanity.com/paper/2512.23184/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Out of One, Many: Using Language Models to Simulate Human Samples](https://mlsanity.com/paper/2209.06899/) (2022)
- [Large Language Models: A Survey](https://mlsanity.com/paper/2402.06196/) (2024)
- [Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies](https://mlsanity.com/paper/2208.10264/) (2022)
- [The Challenge of Using LLMs to Simulate Human Behavior: A Causal Inference Perspective](https://mlsanity.com/paper/2312.15524/) (2023)
- [Large Language Models: An Applied Econometric Framework](https://mlsanity.com/paper/2412.07031/) (2024)
- [LOLA: LLM-Assisted Online Learning Algorithm for Content Experiments](https://mlsanity.com/paper/2406.02611/) (2024)
- [Transforming the Voice of the Customer: Large Language Models for Identifying Customer Needs](https://mlsanity.com/paper/2503.01870/) (2025)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used to simulate human behavior, but common practices to use LLM-generated data are inefficient. Treating an LLM's output ("model choice") as a single data point underutilizes the information inherent to the probabilistic nature of LLMs. This paper introduces and formalizes "model belief," a measure derived from an LLM's token-level probabilities that captures the model's belief distribution over choice alternatives in a single generation run. The authors prove that model belief is asymptotically equivalent to the mean of model choices (a non-trivial property) but forms a more statistically efficient estimator, with lower variance and a faster convergence rate. Analogous properties are shown to hold for smooth functions of model belief and model choice often used in downstream applications. The authors demonstrate the performance of model belief through a demand estimation study, where an LLM simulates consumer responses to different prices. In practical settings with limited numbers of runs, model belief explains and predicts ground-truth model choice better than model choice itself, and reduces the computation needed to reach sufficiently accurate estimates by roughly a factor of 20. The findings support using model belief as the default measure to extract more information from LLM-generated data.