How large language models judge and influence human cooperation

Alexandre S. Pires; Fernando P. Santos; Laurens Samson; Sennay Ghebreab

REVIEW 3 major objections 5 minor 1 cited by

How large language models judge and influence human cooperation

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper argues that the social norms people would absorb from LLM judges differ from model to model and version to version, and that these differences are large enough to shift whether cooperation persists in an evolving population.

desk verdict A genuinely new integration of LLM norm extraction with indirect reciprocity; the invalid-answer filtering deserves scrutiny but the modeling core holds up. read the letter →

arxiv 2507.00088 v1 pith:XLE4QJSA submitted 2025-06-30 physics.soc-ph cs.AIcs.SI

Alexandre S. Pires , Laurens Samson , Sennay Ghebreab , Fernando P. Santos This is my paper

classification physics.soc-phcs.AIcs.SI MSC 91A2291A80

keywords indirectreciprocitylargelanguagemodelssocialnormscooperationreputationdynamicsevolutionarygametheorypromptengineeringdonation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Large language models are increasingly consulted for judgments about other people, and such judgments are the engine of indirect reciprocity: we tend to cooperate with people who have good reputations. This paper extracts the implicit rule each of 21 LLMs uses to assign reputations in a donation game, then feeds those rules into an evolutionary model of a population deciding whether to cooperate. It finds that models nearly all agree on one thing, cooperating with a good person is good and defecting against one is bad, but they split sharply on how to treat defectors of already bad reputation. Because of that split, different LLM norms support very different long-run cooperation levels, from near-collapse under norms like Shunning to near-maximum cooperation under Stern-Judging. The authors also show that simple prompt instructions aimed at maximizing cooperation can push models toward the Image Score norm, which is robust when reputations are private.

What carries the argument

The load-bearing object is the second-order social norm, written as $d=(d_{GC},d_{GD},d_{BC},d_{BD})$, with each probability in $[0,1]$, representing the chance that an observer assigns a good reputation to a donor after observing cooperation (C) or defection (D) with a recipient whose reputation is good (G) or bad (B). The paper extracts such a norm from each LLM by prompting it with 43,200 donation-game vignettes and averaging parsed 'good' and 'bad' answers. It then inserts the norm into a finite-population evolutionary model in which ALLC, ALLD, and DISC strategies compete through mutation and Fermi imitation, with a gossip parameter interpolating between private and public reputation sharing, and measures the resulting cooperation index $I$. The formalism extends classical indirect reciprocity norms such as Image Score, Simple Standing, Shunning, and Stern-Judging to probabilistic values, which is what lets measured LLM behavior, including its variance, be evaluated directly.

What would settle it

A behavioral experiment would settle it: have participants play a repeated donation game while receiving reputation labels from a specific LLM, for example GPT-4o versus Llama 3.3 70B, and record whether their own subsequent judgments move toward that LLM's norm. If participants' reputation assignments barely change, or if the two advisory models produce indistinguishable judgments, then the between-model differences in the cooperation index would not be observed in human societies.

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Extended reading notes

Core claim

The central claim is that the social norms LLMs reveal when asked to judge donation interactions are not interchangeable: the probabilities they assign to 'good' after each combination of donor action and recipient reputation form a norm vector $d = (d_{GC},d_{GD},d_{BC},d_{BD})$, and the position of that vector in norm space determines the cooperation index of a population that adopts it. Most tested models cluster near Image Score or Simple Standing, and most families move from Image Score toward Simple Standing as versions and parameter counts increase, yet only Llama 3.3 70B Instruct approximates Stern-Judging. Under public reputations that norm is the one that maximizes cooperation, whereas under private reputations Image Score-like norms, common in earlier models, sustain the most cooperation. The authors conclude that subtle differences between model versions and prompting decisions significantly affect long-term cooperation dynamics, and that targeted goal-oriented prompts can steer LLM norms in a cooperation-supporting direction.

Load-bearing premise

People will actually take the LLM's reputation judgments as their own, and everyone has access to the same single LLM; if humans resist the advice or use different models, the predicted long-term cooperation levels do not follow.

Editorial extensions

If this is right

If human populations adopt LLM reputation judgments, different model versions of the same family can produce materially different levels of cooperation, so model choice becomes a design decision for social infrastructure.
The observed drift from Image Score toward Simple Standing improves cooperation when reputations are public but reduces it when reputations are private, so the same model upgrade helps or harms prosociality depending on information sharing.
Only Llama 3.3 70B Instruct among the 21 models uses a Stern-Judging-like norm that maximizes cooperation under public reputations; no other tested model reaches that maximum.
Goal-oriented prompts such as 'motivation' and 'signalling' shift norms across models toward Image Score, which is the norm that keeps cooperation viable under private reputations, suggesting a cheap alignment lever.
LLM norms vary with actor names and interaction contexts, so a single averaged norm hides uncertainty that can push the predicted cooperation index up or down.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An untested consequence is fragmentation: if different people consult different LLMs, the population would mix incompatible norms, and the disagreement could suppress cooperation more than any single extracted norm does; the paper's single-LLM assumption is the optimistic endpoint.
The consistent effect of motivation prompts hints that LLMs have a latent cooperative prior that explicit goals can surface; whether that holds under adversarial phrasings or fine-tuned models is a testable extension.
The norm map could serve as a monitor: periodically re-extracting these four probabilities for each new model release would give a cheap early warning of whether LLM judges are drifting toward norms known to collapse cooperation.
Because the model treats LLMs only as observers, an extension would let LLMs act as donors; the same norm might then change their own behavior and create feedback loops that the current cooperation index does not capture.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This paper does something genuinely new: it takes the second-order social norm formalism from indirect reciprocity and uses it to measure what 21 LLMs think about cooperation and defection, then feeds those measured norms into a standard evolutionary model to see which norms sustain cooperation. The bridge from LLM judgments to evolutionary outcomes is the contribution, and it works as a modeling exercise. The prompt dataset is large, the model is clearly specified, and the supplementary analysis of biases and invalid answers is more transparent than most.

The headline finding — that most LLM families drift from Image Score toward Simple Standing, with only Llama 3.3 70B near Stern-Judging — is interesting and not something I had seen before. The prompt-intervention results are also plausible and well presented.

The soft spots are real but not fatal. The stress-test concern about invalid-answer filtering lands. S3 shows refusals are concentrated in "not help" prompts and non-explicit benefit/cost contexts. That means the aggregated norm entries are conditional on willingness to answer, not estimates of the unconditional judgment distribution. For dBD in particular, if refusals correlate with the judgment itself — e.g., the model declines precisely when it would have said "bad" — the coordinates shift, potentially toward more lenient, Simple-Standing-like positions. The paper reports invalid rates but doesn't check whether the filtering biases the norm averages. This is an internal validity issue, not just an external one. The direction and magnitude are speculative, and the cross-model variation is large enough that I doubt it reverses the main conclusion that LLMs differ. But it could affect the specific claim that Llama 3.3 is uniquely Stern-Judging, and that claim is load-bearing for Figure 3.

The lack of code and data is also a real reproducibility gap. Temperature zero makes the LLM responses deterministic, but without the prompt datasets and parsing scripts, exact reproduction is impossible. The authors' stated limitation about full adoption of LLM reputations by humans is a genuine external validity concern, but at least they name it explicitly.

Overall, this is a solid, honest paper. The central modeling result — that measured LLM norms differ and those differences matter for cooperation — holds up under the model's assumptions. The invalid-answer filtering deserves a robustness check, and the authors should release their artifacts. I'd send it to a serious referee with a request for those additions, not desk-reject it.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes a two-step pipeline: it extracts second-order social norms from 21 LLMs by prompting them with 43,200 donation-game scenarios, and then feeds the extracted probabilistic norms into a standard evolutionary indirect-reciprocity model with ALLC/ALLD/DISC strategies, public or private reputations, execution and assessment errors, mutation, and selection. The main empirical findings are that models largely agree when judging interactions with good recipients but disagree when the recipient is bad; that LLM families tend to move from Image Score toward Simple Standing with version and parameter scale; that Llama 3.3 70B Instruct is the only tested model near Stern-Judging, which maximizes cooperation under public reputations; and that goal-oriented prompt interventions can shift norms, with motivation moving models toward Image Score. The evolutionary model is clearly specified and the paper is transparent about its central simplifying assumption that agents fully adopt LLM reputation judgments.

Significance. If the extracted norms are accurate, the paper provides a useful bridge between LLM evaluation and evolutionary social science, with a large prompt corpus and a standard, well-documented indirect-reciprocity model. The quantitative conclusions about which norms maximize cooperation under public versus private information are grounded in established theory, and the authors are explicit about the strong assumption that humans adopt LLM judgments. The main risk is not the evolutionary machinery but the reliability of the norm-extraction step, because several high-error-rate models contribute to the headline cross-model trend and because the point estimates are sensitive to the prompt design choices.

major comments (3)

[Methods, 'LLM social norm assessment'; Supplementary S3] The norm entries in Eq. (11) are computed as averages over valid answers only, but the invalid-answer rate is strongly correlated with prompt content: Supplementary S3 shows that Claude 3.7 Sonnet, Llama 2 13B, and Phi-4 refuse or fail to parse disproportionately in prompts where the donor does not help and where the benefit/cost is not explicit. Because willingness to answer is therefore not independent of the judgment being elicited, the entries dGD and dBD are conditional on the model's willingness to answer rather than unbiased estimates of the underlying judgment distribution. This matters for the headline trend: Llama 2 13B and Claude 3.7 Sonnet are among the models displayed in Figure 3, and their positions on the Image-Score/Simple-Standing edge could shift if refusals were imputed differently. I ask the authors to report the extracted norms under at least two bounding treatments of invalid answers (for example, all refusals coded as 'bad' versus all coded as 'good', plus a multiple-imputation check) and to state whether the cross-model trends and the uniqueness of Llama 3.3 70B survive.
[Figure 3; Table S4] The cooperation map in Figure 3 is computed under the restriction dGC = 1 and dGD = 0, as stated in the caption, yet the overlaid LLM norms are plotted using only their (dBC, dBD) coordinates. For models with dGD appreciably above zero—GPT-4o (dGD = 0.197), Llama 2 13B (0.158), and Claude 3.7 Sonnet (0.145) in Table S4—the cooperation index read from the map is not the cooperation index that their full four-dimensional norm would produce. The text's statement that 'most models adopt the SS-IS edge leading to I in [0.5, 0.75]' is therefore partly an artifact of the projection for those models, and the later discussion of GPT-4o in Figure 4 confirms that its actual cooperation is lower. I ask the authors to compute model-specific cooperation indices using the full norms for all models overlaid in Figure 3, or to annotate the overlay explicitly as a two-dimensional projection that does not correspond to each model's true cooperation index.
[LLM social norm assessment; Supplementary Fig. S9] The point-estimate norm dD' is an unweighted average over the prompt corpus, whose topic distribution is a design choice. The paper's own Figure S9 reports that dBD differs by almost 40 percentage points between non-neutral explicit topics and neutral non-explicit topics. Because the topic mix is arbitrary, the coordinates in Figure 2B and the model ranking in Figure 3 are not invariant to prompt-design choices. The uncertainty ellipses partially address this concern, but the headline comparisons and the 'only Llama 3.3 70B' claim are based on point estimates. Please add a sensitivity analysis that reweights or restricts the topic categories (for example, explicit cost/benefit prompts only, which correspond most closely to the donation game) and report whether the cross-model ordering and the Stern-Judging identification survive.

minor comments (5)

[Methods, model list] In the model enumeration, Claude 3.7 Sonnet is cited as reference [47], but [47] is the Claude 3.5 Haiku announcement; the citation should be [48].
[Throughout] The number 43200 should be written as 43,200 for readability, and the same applies to the abstract and introduction.
[Supplementary Table S5] The table caption mentions red and green coloring, but the plain-text table does not show colors; please add explicit plus/minus signs or numeric deltas instead of relying on color.
[Discussion, limitations] The self-identified assumptions that humans fully adopt LLM reputation assignments and that a single LLM is universally accessible are important external-validity constraints. They are stated clearly in the Discussion, but the abstract and title could be read as making unconditional claims about human cooperation; I suggest adding wording such as 'if adopted' or 'under the assumption that LLM judgments are followed' in the abstract.
[Reproducibility] The manuscript does not state whether the prompt dataset and analysis code will be made available; given the emphasis on reproducibility and temperature-zero queries, a data/code availability statement would strengthen the paper.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: LLM social norms are measured independently and evaluated through a fixed forward cooperation model; self-citations are background formalism only.

full rationale

Derivation chain: (1) each LLM is prompted with 43,200 donation-game vignettes and its four norm entries dGC, dGD, dBC, dBD are measured as means of parsed answers (Eq. 11); (2) those measured norms are inserted as d = dL into a finite-population indirect-reciprocity model whose equations (1)-(10) and parameters (Z=100, b/c=5, ee=ea=0.01, gamma=0.01, beta=1) are fixed in advance; (3) the stationary distribution of the strategy Markov chain yields a cooperation index I that is compared across models and reputation-sharing regimes. No parameter of the evolutionary model is fit to any target cooperation level, and the norm coordinates are measured before and independently of the cooperation computation, so the claim that Llama 3.3 70B IT sits near Stern-Judging and thereby maximizes cooperation under public reputations (Figs. 3-4) is a forward evaluation, not an identity. The four classical norms used for labeling (IS, SS, SH, SJ) are cited to external works (Nowak & Sigmund 1998; Milinski et al. 2001; Panchanathan & Boyd 2004; Pacheco et al. 2006), and the model machinery is traceable to external sources (Hilbe et al. 2018; Ohtsuki & Iwasa 2006/2007; Kawakatsu et al. 2024; Perret et al. 2021; Traulsen et al. 2006). The few self-citations (Santos et al. 2016, 2018, 2021) support only background formalism that the paper also states in its own equations and that is independently established, so they are not load-bearing. The stated limitations, that humans fully adopt LLM reputation assignments and that only one equally accessible LLM is considered (Discussion), are external-validity caveats rather than circularity. The supplementary exclusion of unparsable answers (S3, Fig. S1), which for Claude 3.7 Sonnet, Llama 2 13B, and Phi-4 concentrates in non-help and non-explicit-cost prompts, means the affected norm entries are conditional on willingness to answer; this is a measurement-bias risk for the input coordinates, not a case of the prediction being equivalent to its input by construction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The model uses standard IR machinery with hand-set simulation parameters rather than fitted parameters. The only substantive postulate is that humans adopt LLM reputational judgments, which the paper explicitly flags as an assumption. No new physical or social entities are introduced.

free parameters (5)

Population size Z = 100
Standard simulation size from IR literature; not fitted to data.
Benefit-to-cost ratio b/c = 5.0 in main figures, varied 1-8 in Fig 4
Chosen from prior IR studies; cooperation index depends on this value.
Execution and assessment error rates ee, ea = 0.01 each
Standard error values; not fitted.
Mutation rate gamma = 0.01
Chosen to allow rare strategy exploration; not fitted.
Selection strength beta = 1
Standard weak-to-moderate selection value from the pairwise comparison rule.

assumptions (5)

domain assumption A second-order social norm d in [0,1]^4 fully describes LLM judgments of cooperation and defection against good and bad recipients.
Invoked in Methods, LLM social norm assessment; reduces rich LLM outputs to four probabilities.
domain assumption Reputation dynamics converge on a faster timescale than strategy dynamics.
Standard in IR models, cited to refs [39,71]; allows the ODE approximation in Eq (2).
domain assumption The gossip aggregation formula in Eq (5) correctly describes how private reputations become public.
Taken from Kawakatsu et al. [75]; not independently derived in this paper.
ad hoc to paper All agents consult one LLM and fully adopt its reputation assignment.
Acknowledged in Discussion as a limitation; central to the human-impact claim.
standard math The strategy Markov chain is irreducible and has a unique stationary distribution.
Used to compute the cooperation index; follows from finite irreducible chain properties.

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Cite this review

Pith. "Pith review of How large language models judge and influence human cooperation." pith.science (2026). https://pith.science/paper/XLE4QJSA

@misc{pith2026250700088,
  author       = {Pith},
  title        = {Pith review of: How large language models judge and influence human cooperation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XLE4QJSA}},
  note         = {Machine review of arXiv:2507.00088}
}

read the original abstract

Humans increasingly rely on large language models (LLMs) to support decisions in social settings. Previous work suggests that such tools shape people's moral and political judgements. However, the long-term implications of LLM-based social decision-making remain unknown. How will human cooperation be affected when the assessment of social interactions relies on language models? This is a pressing question, as human cooperation is often driven by indirect reciprocity, reputations, and the capacity to judge interactions of others. Here, we assess how state-of-the-art LLMs judge cooperative actions. We provide 21 different LLMs with an extensive set of examples where individuals cooperate -- or refuse cooperating -- in a range of social contexts, and ask how these interactions should be judged. Furthermore, through an evolutionary game-theoretical model, we evaluate cooperation dynamics in populations where the extracted LLM-driven judgements prevail, assessing the long-term impact of LLMs on human prosociality. We observe a remarkable agreement in evaluating cooperation against good opponents. On the other hand, we notice within- and between-model variance when judging cooperation with ill-reputed individuals. We show that the differences revealed between models can significantly impact the prevalence of cooperation. Finally, we test prompts to steer LLM norms, showing that such interventions can shape LLM judgements, particularly through goal-oriented prompts. Our research connects LLM-based advices and long-term social dynamics, and highlights the need to carefully align LLM norms in order to preserve human cooperation.

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Payoff scaling shapes cooperation in LLM agents across languages
cs.AI 2026-01 reject novelty 5.0 of 10

LLM agents are inferred to switch from always-defect toward conditional and cooperative strategies as payoff stakes rise, with language also shifting the inferred strategy distributions.

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