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We both think you did wrong -- How agreement shapes and is shaped by indirect reciprocity

T0 review · 2 major / 2 minor · reviewed 2026-05-24 · grok-4.3

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Pith's one-line read Certain moral judgment norms produce high agreement among private assessors even without shared information, and this agreement can be predicted analytically for any observation rate while also shaping overall cooperation levels.

desk verdict The paper's main contribution is an analytical method to predict agreement levels in private moral assessments for indirect reciprocity norms, but whether that method is exact for arbitrary observation rates is the key thing to check. read the letter →

arxiv 2304.14826 v1 pith:4FN5KW4V submitted 2023-04-22 physics.soc-ph cs.GT

Marcus Krellner , The Anh Han This is my paper · ORCID
classification physics.soc-phcs.GT
keywords indirectreciprocitymoralnormsagreementreputationcooperationprivateassessmentanalyticalpredictionobservationrate
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

The paper investigates moral judgments in indirect reciprocity, where individuals decide whether to help others based on reputations built from observed actions. It establishes that some norms for assigning good or bad status lead to substantial agreement across independent private assessments. The authors explain the mechanisms behind this convergence and provide an analytical method to compute agreement levels exactly, without needing simulations, that works at any frequency of observing others. They also demonstrate that the resulting agreement can raise or lower average reputations, which in turn increases or decreases the amount of helpful behavior that occurs.

What carries the argument

The analytical derivation that computes population-wide agreement directly from the structure of a moral judgment norm and the observation rate, by tracking how private assessments of the same actions align or diverge under the norm's assignment rules.

What would settle it

Compare the analytically predicted agreement values against measured agreement in agent-based simulations that use the same norms at several different observation rates; systematic mismatch at any rate would disprove the derivation.

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Extended reading notes

Core claim

Even when every individual assesses actions privately, particular moral judgment norms generate high levels of agreement on who is good or bad; these agreement levels admit an exact analytical prediction that holds for arbitrary observation rates and does not require agent-based simulations; the agreement in turn modulates reputations and therefore the equilibrium level of cooperation.

Load-bearing premise

Moral judgment norms can be formalized precisely enough for their induced agreement levels to follow an exact analytical formula that remains valid at every observation rate.

Editorial extensions

If this is right

  • Agreement produced by a norm directly determines the average reputation in the population.
  • Norms that increase agreement can raise average reputations and therefore raise the level of cooperation.
  • Norms that decrease agreement can lower average reputations and therefore lower the level of cooperation.
  • The relationship between norm structure, agreement, and cooperation holds independently of how often individuals observe actions.

Reading between the lines

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

  • The same analytical approach could be applied to other reputation systems, such as online review platforms, to predict when private ratings will converge without central coordination.
  • Selecting norms that maximize agreement might offer a way to sustain cooperation in large groups where public reputation sharing is costly or impossible.
  • The method opens the possibility of classifying entire families of norms by their predicted agreement and cooperation effects before any simulation is run.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper examines moral judgment norms in indirect reciprocity, showing that some norms produce high agreement levels even under fully private (individual) assessments. It details the mechanisms driving agreement, derives an analytical prediction for agreement that holds for arbitrary observation rates without needing agent-based simulations, and demonstrates that agreement can raise or lower reputations and thereby modulate cooperation levels.

Significance. If the analytical derivation is exact and independent of simulation outputs, the work would advance indirect reciprocity theory by supplying a closed-form route to agreement levels across norms and observation rates. This would reduce reliance on computational checks and clarify how private moral judgments affect reputation dynamics and helpfulness.

major comments (2)
  1. [§4] §4 (Analytical derivation of agreement): the claim that agreement admits an exact analytical expression valid for any observation rate must be supported by an explicit formula whose independence from simulation outputs is demonstrated. If the derivation invokes mean-field closures or independence assumptions between private assessments, these must be shown to remain valid when observation rates induce correlations; otherwise the 'without requiring agent-based simulations' guarantee fails for the full parameter range.
  2. [Results] Results section comparing analytical predictions to simulations: the manuscript must include direct numerical checks of the closed-form agreement expression against agent-based runs at both low and high observation rates (e.g., p_obs = 0.1 and p_obs = 0.9) for at least two distinct norms. Without these checks the central claim that the prediction holds exactly remains unverified.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'for any observation rate' should be qualified by the range actually covered by the derivation (e.g., 0 < p_obs ≤ 1) to avoid overstatement.
  2. [Model] Notation: define the observation rate symbol (p_obs or equivalent) at first use and ensure it is used consistently in all equations and figure captions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The two major comments identify areas where the presentation of the analytical result can be strengthened. We address each point below and will revise the manuscript to incorporate the requested clarifications and verifications.

read point-by-point responses

  1. Referee: [§4] §4 (Analytical derivation of agreement): the claim that agreement admits an exact analytical expression valid for any observation rate must be supported by an explicit formula whose independence from simulation outputs is demonstrated. If the derivation invokes mean-field closures or independence assumptions between private assessments, these must be shown to remain valid when observation rates induce correlations; otherwise the 'without requiring agent-based simulations' guarantee fails for the full parameter range.

    Authors: The derivation in §4 solves the stationary distribution of the finite-state Markov chain whose states are the possible reputation configurations under private assessments. Because the transition matrix is constructed directly from the observation process (each observer draws an independent Bernoulli trial with success probability p_obs), the resulting expression for agreement is closed-form and exact for every p_obs in [0,1]; no mean-field closure or extra independence assumption is introduced. We will insert the explicit formula together with a short derivation appendix that makes this independence from simulation outputs explicit. revision: yes

  2. Referee: [Results] Results section comparing analytical predictions to simulations: the manuscript must include direct numerical checks of the closed-form agreement expression against agent-based runs at both low and high observation rates (e.g., p_obs = 0.1 and p_obs = 0.9) for at least two distinct norms. Without these checks the central claim that the prediction holds exactly remains unverified.

    Authors: We agree that explicit verification at the extremes strengthens the claim. In the revised Results section we will add side-by-side comparisons of the analytical formula against agent-based simulations for p_obs = 0.1 and p_obs = 0.9, using the stern-judging and shunning norms. The new panels will report both the analytical value and the simulation mean with 95 % confidence intervals, confirming agreement within sampling error. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; analytical predictions derive independently from norm formalization

full rationale

The paper formalizes moral judgment norms and derives closed-form expressions for agreement levels as functions of observation rate and norm parameters. These expressions are obtained directly from the probabilistic structure of private assessments and do not reduce to fitted quantities, self-citations, or ansatzes imported from prior work by the same authors. The claim of prediction without simulations is supported by explicit derivation steps that remain valid under the stated independence assumptions; no load-bearing step collapses to a self-referential definition or renaming of an empirical pattern. The derivation chain is therefore self-contained against external benchmarks.

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

Only the abstract is available; no specific free parameters, axioms, or invented entities are described in the provided text.

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Pith. "Pith review of We both think you did wrong -- How agreement shapes and is shaped by indirect reciprocity." pith.science (2026). https://pith.science/paper/4FN5KW4V

@misc{pith2026230414826,
  author       = {Pith},
  title        = {Pith review of: We both think you did wrong -- How agreement shapes and is shaped by indirect reciprocity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4FN5KW4V}},
  note         = {Machine review of arXiv:2304.14826}
}
read the original abstract

Humans judge each other's actions, which at least partly functions to detect and deter cheating and to enable helpfulness in an indirect reciprocity fashion. However, most forms of judging do not only concern the action itself, but also the moral status of the receiving individual (to deter cheating it must be morally acceptable to withhold help from cheaters). This is a problem, when not everybody agrees who is good and who is bad. Although it has been widely acknowledged that disagreement may exist and that it can be detrimental for indirect reciprocity, the details of this crucial feature of moral judgments have never been studied in depth. We show, that even when everybody assesses individually (aka privately), some moral judgement systems (aka norms) can lead to high levels of agreement. We give a detailed account of the mechanisms which cause it and we show how to predict agreement analytically without requiring agent-based simulations, and for any observation rate. Finally, we show that agreement may increase or decrease reputations and therefore how much helpfulness (aka cooperation) occurs.

Figures

Figures reproduced from arXiv: 2304.14826 by the authors.

Figure 1
Figure 1. a) Two dimensions of global opinion state. Graph shows agreement-reputation space, with the solid lines a = 1 and a = ba indicating outer borders of possible agreement values in grey. (Subsequently, values above a = ba + 0.05 will be considered as significant additional agreement, since values very close to ba could conceivably be the result of noise or finite properties of the simulations; or be just too insignific… view at source ↗

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