Hearsay or Fact? How Framing and Elicitation Shape LLM Probability Updates

An-Sheng Jhang

cs.CLOct 20, 2026

Hearsay or Fact? How Framing and Elicitation Shape LLM Probability Updates

Authors: An-Sheng Jhang

Organizations: Dongguan University of Technology

Abstract

Large language models (LLMs) are increasingly used as judgment assistants and as stand-in participants in psychology experiments, yet little is known about how much their probability estimates move in response to a single new piece of information. We pair premise-hypothesis items from $δ$ -SNLI with one strengthener and one weakener each, elicit the prior and the posteriors in separate calls, and measure the directional movement s: the mean posterior change signed by the annotated direction, so that the prior cancels out. We vary whether the update is stated ("Here is something else you learned") or reported ("Someone said that"), and whether the model gives one probability or five weighted estimates. We test seven configurations: two local models (Qwen3-8B, OLMo-2-7B; 240 pairs) and five configurations run through agent command-line harnesses (120 pairs), with hypotheses and analysis rules fixed before the formal runs (not publicly registered). Under stated, direct elicitation all seven move in the annotated direction (s = 18-28 percentage points). Reporting lowers s in all seven point estimates (significantly in six, by 2-5 points) and raises the share of reverse movements in all seven: the effect is consistent but small. Five weighted estimates lower the share of responses at $\leq$ 5% or $\geq$ 95% in all seven, but in the two local models they also reduce s by 43% and 68%, whereas in the harnessed configurations the point estimates of the change lie between -3.7 and +0.5 points. An elicitation format that reduces extreme values thus need not preserve sensitivity to evidence; the two should be tested separately. Because $δ$ -NLI annotates only direction, we make no claim about how large an update should be. Code, data and the frozen plan: https://github.com/asj252/llm-judgment-studies

Probability Elicitation from Language Models

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Feb 26, 2026

Empirical Characterization of Inference-Time Elicited Probability Transformations in Large Language Models

Large language models increasingly rely on inference-time procedures such as chain-of-thought reasoning, self-refinement, retrieval augmentation, and verifier-guided revision, yet the structure of elicited probability transformations under these procedures remains poorly understood. We study externally elicited probability assignments over candidate answers and observe recurring approximate log-ratio relationships:

\log \tilde q_t(i) = α_t \left( \log q_t(i) + \log b_t(i) \right) + c_t,

where

q_t

and

\tilde q_t

are pre- and post-elicitation probabilities,

b_t

is an externally constructed evidence signal, and

α_t

is an empirical descriptor of the prompting configuration. Across 4,975 reasoning problems from GPQA Diamond, TheoremQA, MMLU-Pro, and ARC-Challenge, evaluated on multiple instruction-tuned model families, we observe approximate log-ratio relationships with mean

R^2 \approx 0.76

over about

1.3 \times 10^5

candidate-level observations. Coefficients vary across elicitation settings, but qualitatively similar relationships persist across evaluated conditions. Robustness analyses using alternative statistical representations, prompting configurations, held-out evaluation, and token-level log-probabilities suggest that the observed structure is not tied to one prompting procedure or probability estimation method. The main contribution is not the algebraic form itself, which is related to generalized Bayesian updating and probability-transformation frameworks, but the empirical observation that diverse inference-time prompting pipelines repeatedly exhibit reproducible log-ratio structure under controlled conditions. The framework provides a protocol-sensitive perspective for analyzing calibration, evidence amplification, uncertainty propagation, and interaction sensitivity in inference-time LLM pipelines.

Mike Farmer, Abhinav Kochar, Yugyung Lee

Bloch School of Management, Regnier Institute for Entrepreneurship & Innovation, University of Missouri–Kansas City. · Department of Computer Science, School of Science and Engineering, University of Missouri–Kansas City.

LLM Inference Belief Updating in LLMs Confidence Estimation in Language Models Language Model Calibration

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Apr 2, 2026

Bayesian Elicitation with LLMs: Model Size Helps, Extra "Reasoning" Doesn't Always

Large language models (LLMs) have been proposed as alternatives to human experts for estimating unknown quantities with associated uncertainty, a process known as Bayesian elicitation. We test this by asking eleven LLMs to estimate population statistics, such as health prevalence rates, personality trait distributions, and labor market figures, and to express their uncertainty as 95% credible intervals. We vary each model's reasoning effort (low, medium, high) to test whether more "thinking" improves results. Our findings reveal three key results. First, larger, more capable models produce more accurate estimates, but increasing reasoning effort provides no consistent benefit. Second, all models are severely overconfident: their 95% intervals contain the true value only 9--44% of the time, far below the expected 95%. Third, a statistical recalibration technique called conformal prediction can correct this overconfidence, expanding the intervals to achieve the intended coverage. In a preliminary experiment, giving models web search access degraded predictions for already-accurate models, while modestly improving predictions for weaker ones. Models performed well on commonly discussed topics but struggled with specialized health data. These results indicate that LLM uncertainty estimates require statistical correction before they can be used in decision-making.

Luka Hobor, Mario Brcic, Mihael Kovac +1

University of Zagreb Faculty of Electrical Engineering and Computing, Zagreb, Croatia

Probability Elicitation from Language Models LLM Uncertainty Estimation LLM Reliability Confidence Estimation

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May 7, 2026

LLMs are not (consistently) Bayesian: Quantifying internal (in)consistencies of LLMs' probabilistic beliefs

Modern AI systems are being deployed in complex domains such as medicine, science, and law, where it is important that they not only produce correct answers, but also represent and update uncertain beliefs about the world as new evidence arrives. We introduce the novel technique of studying LLMs as information processing rules and utilize the information processing gap to study the internal (in)consistencies of how LLMs update their probabilistic beliefs from evidence. Our extensive experiments evaluate multiple approaches in which LLMs can incorporate evidence into their beliefs. Some of these approaches produce (nearly) Bayesian updates; others seem to use a learned heuristic. Surprisingly, the non-Bayesian heuristic updates often outperform exact Bayesian computation in terms of downstream task performance -- indicating the LLMs' probabilistic models of the world are misspecified. Lastly, we show how our measure can provide diagnostics to identify issues with LLM-powered inferential systems.

Chacha Chen, Matthew Jörke, Adam Goliński +4

1Apple · 2Stanford University · †Work done while an intern at Apple. +1

Belief Revision LLM Auditing Bayesian Inference LLM Uncertainty Estimation Belief Updating in LLMs

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Abstract

Probability Elicitation from Language Models

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Empirical Characterization of Inference-Time Elicited Probability Transformations in Large Language Models

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