# Knowing Your Uncertainty -- On the application of LLM in social sciences

arXiv: https://arxiv.org/abs/2512.05461 · HTML: https://mlsanity.com/paper/2512.05461/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 75 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [BERTopic: Neural topic modeling with a class-based TF-IDF procedure](https://mlsanity.com/paper/2203.05794/) (2022)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Large Language Models Empowered Agent-based Modeling and Simulation: A Survey and Perspectives](https://mlsanity.com/paper/2312.11970/) (2023)
- [Can Large Language Models Transform Computational Social Science?](https://mlsanity.com/paper/2305.03514/) (2023)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [SemEval-2017 Task 4: Sentiment Analysis in Twitter](https://mlsanity.com/paper/1912.00741/) (2019)
- [Simulating Opinion Dynamics with Networks of LLM-based Agents](https://mlsanity.com/paper/2311.09618/) (2023)
- [Controlling Linguistic Style Aspects in Neural Language Generation](https://mlsanity.com/paper/1707.02633/) (2017)
- [Analyzing Transformers in Embedding Space](https://mlsanity.com/paper/2209.02535/) (2022)
- [Emergent social conventions and collective bias in LLM populations](https://mlsanity.com/paper/2410.08948/) (2024)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [LLM Social Simulations Are a Promising Research Method](https://mlsanity.com/paper/2504.02234/) (2025)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [LUQ: Long-text Uncertainty Quantification for LLMs](https://mlsanity.com/paper/2403.20279/) (2024)
- [Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach](https://mlsanity.com/paper/2404.15993/) (2024)
- [Beyond prompt brittleness: Evaluating the reliability and consistency of political worldviews in LLMs](https://mlsanity.com/paper/2402.17649/) (2024)
- [Changing Answer Order Can Decrease MMLU Accuracy](https://mlsanity.com/paper/2406.19470/) (2024)
- [Take Caution in Using LLMs as Human Surrogates: Scylla Ex Machina](https://mlsanity.com/paper/2410.19599/) (2024)
- [Social Science Meets LLMs: How Reliable Are Large Language Models in Social Simulations?](https://mlsanity.com/paper/2410.23426/) (2024)

## Abstract (arXiv)

Large language models (LLMs) are rapidly being integrated into computational social science research, yet their blackboxed training and designed stochastic elements in inference pose unique challenges for scientific inquiry. This article argues that applying LLMs to social scientific tasks requires explicit assessment of uncertainty -- an expectation long established in both quantitative methodology in the social sciences and machine learning. We introduce a unified framework for evaluating LLM uncertainty based on Hill numbers, a family of diversity measures. By transforming existing uncertainty quantification (UQ) metrics into Hill numbers, the framework provides a common and intuitive scale for interpreting variation in LLM outputs while accommodating different notions of semantic similarity and different sensitivities to output distributions. We show how it might help the application of LLMs in social sciences through four empirical applications.