REVIEW 3 major objections 5 minor 29 references
Exploring the Potential for Large Language Models to Demonstrate Rational Probabilistic Beliefs
T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash
Pith's one-line read The paper shows that current large language models frequently violate the standard probability axioms of complementarity and monotonicity when assigning confidence to natural-language claims, and that uncertainty-quantification prompts do…
desk verdict Useful dataset and broad evaluation of LLM probabilistic coherence, but the headline claim overreaches and the monotonicity metric needs a tie analysis before the numbers are trustworthy. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The paper's machinery is a consistency test built from three corollaries of the standard probability axioms: complementarity, $P(A)+P(A^c)=1$; specialisation monotonicity, $P(A')<P(A)$ whenever $A' \subset A$; and generalisation monotonicity, $P(A)<P(A')$ whenever $A \subset A'$. The Rational Probabilistic Beliefs dataset instantiates these patterns in natural language: 517 base claims, each with a complement, a more specific variant, and a more general variant (2068 samples in total). The evaluation elicits a probability for each variant using four methods, namely direct prompting, chain-of-thought prompting, a structured argumentative LLM, and top-k logit sampling, and then checks whether the elicited numbers satisfy the equalities and strict inequalities. This turns abstract axiomatic constraints into a measurable benchmark.
What would settle it
Have independent human annotators label a random sample of the RPB specialised and generalised pairs as strictly more probable, strictly less probable, or roughly equal, and recompute the monotonicity violation rates using only pairs where the strict inequality is uncontested; if the rates fall to near zero the central result would collapse, and if they stay high the result would survive.
Extended reading notes
Core claim
On the paper's own terms, the central discovery is a negative one: state-of-the-art LLMs do not maintain rational probabilistic beliefs about claims with indeterminate truth values. Accuracies on the specialisation monotonicity task range from roughly 45% to 69% across models and elicitation methods, and on generalisation from roughly 51% to 84%, so a large share of elicited probability triples are internally inconsistent. Complementarity scores show similar trouble: for most models, over 70% of responses deviate from $P(\text{claim}) + P(\text{negation}) = 1$ by more than 5 points, and the deviations are not eliminated by chain-of-thought, argumentative scaffolding, or top-k logit sampling. The paper reads these results as evidence that capability at language and even calibration at the level of single questions do not imply coherent probabilistic reasoning, and it points to neurosymbolic systems, with a symbolic module enforcing consistency, as the more promising route.
Load-bearing premise
The monotonicity result assumes that every GPT-4o-generated 'more specific' or 'more general' variant is strictly less or strictly more probable than the base claim, an assumption the paper supports only by manual inspection of the generated variants.
Editorial extensions
If this is right
- Any automated decision system that consumes LLM confidence scores as probabilities will inherit the incoherence: a more specific version of a claim can receive a higher probability than the claim it implies.
- Uncertainty-quantification add-ons such as chain-of-thought prompting, argumentative scaffolding, and logit averaging do not restore axiom compliance, so prompt engineering alone is not a fix.
- The pattern across model sizes suggests that scaling alone will not make LLMs reliable probabilistic reasoners.
- Systems that need coherent probabilities should combine LLM natural-language processing with a symbolic module that enforces constraints such as $P(A)+P(A^c)=1$, as the paper itself suggests.
Reading between the lines
- The paper does not test whether rephrasing the same claim in different wording changes the elicited probability; measuring that gap would separate genuine axiom violations from sensitivity to surface phrasing.
- Because the dataset was generated by GPT-4o and the same model family is among the tested systems, evaluating on independently human-authored claims would show whether the failures are intrinsic to current LLMs or partly an artefact of self-generation.
- If the result holds across human-authored claims, a practical consequence is that asking an LLM for a single number is the wrong interface: better to have it produce structured evidence and let a symbolic probabilistic reasoner combine it into a coherent distribution.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript introduces the Rational Probabilistic Belief (RPB) dataset of 517 base claims with indeterminate truth values, each accompanied by a complement, a more specific version, and a more general version. It then evaluates seven LLMs with several uncertainty-quantification methods, including direct prompting, chain-of-thought, an argumentative LLM approach, and top-k logit sampling, measuring how often the models violate complementarity and monotonicity. The authors report high violation rates across models and conclude that current LLMs frequently fail to provide rational, coherent probabilistic beliefs even when enhanced with uncertainty-quantification techniques.
Significance. If the central finding holds, the paper provides a useful negative result for a community that increasingly relies on LLM-generated probability estimates in decision-support systems. The contribution is strengthened by the public release of code and data, by the evaluation of multiple open- and closed-source models, and by the use of simple, externally motivated normative constraints rather than a fitted benchmark. The paper also explicitly separates objective uncertainty from subjective model uncertainty, which is a helpful conceptual clarification. The main risk is that the monotonicity metric treats strictness in a way that may inflate violation rates, and this needs to be addressed before the quantitative claims can be taken at face value.
major comments (3)
- [§3.1, §2] The monotonicity evaluation defines violations via the strict inequalities P(original) > P(specialised) and P(original) < P(generalised), so an exact equality in the estimated probabilities is counted as a violation. The justification given in Section 3.1, that the dataset's practical instantiation ensures the difference is always non-zero, rests on manual inspection rather than on a formal guarantee. The problem is amplified by two design choices: Section 2 states that specialised and generalised claims are deliberately generated to be not too distant probabilistically from the original, and the models output integer percentage scores whose final estimate is the mean of only five samples. A rational model facing a true gap of a fraction of a percent can therefore easily produce equal rounded means. The paper does not report how often the estimated probabilities are exactly equal for a pair, so the contribution of these ties to the 50-70% monotonicity violation rates is unknown. The authors should report the tie rate and either recompute violation rates treating ties as non-violations, or provide independent evidence, such as a documented annotation study or adjustment log, that every specialised claim is strictly less probable and every generalised claim strictly more probable than its base claim. This is load-bearing because the monotonicity violation rates are a central pillar of the paper's conclusion.
- [Table 2 caption, §3.2] The complementarity deviation is printed as |1 - P(original statement) + P(negated statement)| * 100. The intended quantity is clearly |1 - (P(original statement) + P(negated statement))| * 100. As written, the formula would measure |1 - P(original) + P(negated)|, which is not the deviation from P(A)+P(A^c)=1. Please correct the formula and verify that the values reported in Table 2 are computed from the intended expression. Because complementarity is one of the two main empirical claims, this ambiguity is a reproducibility issue that must be fixed.
- [§2] The construction of the RPB dataset relies on a manual check in which the authors state, 'We adjust any samples that were found to violate either of these requirements.' The paper does not specify the adjustment criteria, the number or fraction of samples adjusted, or whether the adjustments were performed by more than one annotator. Since the validity of the specialised and generalised variants is what makes the monotonicity comparisons meaningful, this step should be documented in detail, and the final data, including an adjustment log if possible, should accompany the released dataset.
minor comments (5)
- [§3, first paragraph] The words 'former' and 'latter' appear to be swapped relative to the listed principles complementarity and monotonicity: the sentence beginning 'For the former' describes specialisation and generalisation, which belong to monotonicity, while the sentence beginning 'For the latter' describes the negated claim, which belongs to complementarity.
- [Tables 1-3] The tables report proportions without confidence intervals or significance tests. Given that each estimate is the mean of only five samples, the precision of the violation rates should be quantified, for example with bootstrap confidence intervals.
- [§4.1] The validation set and prompt-selection procedure are described, but no validation results are reported, so the reader cannot assess whether the chosen direct-prompting candidate is indeed best among the four candidates.
- [§4.4] The top-k logit method discards probability mass outside the top five tokens; the possible bias from this truncation should be acknowledged or quantified in the discussion of the method's results.
- [§2, §5.1] The dataset was generated by GPT-4o, which is also one of the evaluated models. Manual filtering mitigates some concerns, but the potential dependence of the results on the generator's own biases should be discussed as a limitation.
Circularity Check
No circularity: violations are measured against external Kolmogorov axioms; the only self-citations are non-load-bearing methodological tools.
full rationale
The paper's central claim — that state-of-the-art LLMs frequently violate complementarity and monotonicity — is an empirical measurement against an external normative standard (Kolmogorov's axioms). The monotonicity and complementarity scores are computed directly from the models' elicited probability estimates; no parameter is fitted to those estimates and then renamed as a prediction. The RPB dataset is generated with GPT-4o, one of the evaluated models, and variants are manually filtered, but this does not force a violation rate: generation is based on n%-probability prompts and specificity/generality transformations, not on the axioms being tested. The strict-inequality convention in Section 3.1 is an assumption about non-zero probability gaps justified by manual inspection; if wrong it would inflate violation rates, but it is not a construction that makes the conclusion equal to the input. The only references to the authors' prior work (Freedman et al. 2024) appear in Section 4.1 for a prompting template and Section 4.3 for the ArgLLM method; these are methodological tools, and the main result is reproduced across direct prompting, chain-of-thought, ArgLLM, and top-k logit sampling, so the self-citation is not load-bearing. I find no equation or predicted quantity that reduces by definition to a fitted input or to an unverified self-citation.
Assumptions & free parameters
assumptions (4)
- standard math Kolmogorov probability axioms define rational probabilistic beliefs
- domain assumption The generated specialised and generalised claims are true subset and superset events of the base claims
- ad hoc to paper Every specialised claim is strictly less probable than its base claim, and every generalised claim is strictly more probable
- domain assumption The elicited numeric scores represent the model's probabilistic belief
Cite this review
Pith. "Pith review of Exploring the Potential for Large Language Models to Demonstrate Rational Probabilistic Beliefs." pith.science (2026). https://pith.science/paper/JGKA7VNE
@misc{pith2026250413644,
author = {Pith},
title = {Pith review of: Exploring the Potential for Large Language Models to Demonstrate Rational Probabilistic Beliefs},
year = {2026},
howpublished = {\url{https://pith.science/paper/JGKA7VNE}},
note = {Machine review of arXiv:2504.13644}
}
read the original abstract
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may be essential to ensure trustworthy, explainable and effective performance in these tasks. Despite previous work suggesting that LLMs can perform complex reasoning and well-calibrated uncertainty quantification, we find that current versions of this class of model lack the ability to provide rational and coherent representations of probabilistic beliefs. To demonstrate this, we introduce a novel dataset of claims with indeterminate truth values and apply a number of well-established techniques for uncertainty quantification to measure the ability of LLM's to adhere to fundamental properties of probabilistic reasoning.
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