Abstract
Reputations are critical to human societies, as individuals are treated differently based on their social standing1,2. For instance, those who garner a good reputation by helping others are more likely to be rewarded by third parties3,4,5. Achieving widespread cooperation in this way requires that reputations accurately reflect behaviour6 and that individuals agree about each other’s standings7. With few exceptions8,9,10, theoretical work has assumed that information is limited, which hinders consensus7,11 unless there are mechanisms to enforce agreement, such as empathy12, gossip13,14,15 or public institutions16. Such mechanisms face challenges in a world where empathy, effective communication and institutional trust are compromised17,18,19. However, information about others is now abundant and readily available, particularly through social media. Here we demonstrate that assigning private reputations by aggregating several observations of an individual can accurately capture behaviour, foster emergent agreement without enforcement mechanisms and maintain cooperation, provided individuals exhibit some tolerance for bad actions. This finding holds for both first- and second-order norms of judgement and is robust even when norms vary within a population. When the aggregation rule itself can evolve, selection indeed favours the use of several observations and tolerant judgements. Nonetheless, even when information is freely accessible, individuals do not typically evolve to use all of it. This method of assessing reputations—‘look twice, forgive once’, in a nutshell—is simple enough to have arisen early in human culture and powerful enough to persist as a fundamental component of social heuristics.
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Data availability
There are no empirical data associated with this study.
Code availability
The code for generating the numerical calculations in this study is freely available at Zenodo (https://doi.org/10.5281/zenodo.12795781)49 and through GitHub at github.com/michel-mata/IRMO.jl.
References
Roberts, G. et al. The benefits of being seen to help others: indirect reciprocity and reputation-based partner choice. Philos. Trans. R. Soc. B 376, 20200290 (2021).
Raihani, N. The Social Instinct: How Cooperation Shaped the World (Random House, 2021).
Alexander, R. D. The Biology of Moral Systems (Routledge, 2017).
Nowak, M. A. & Sigmund, K. Evolution of indirect reciprocity. Nature 437, 1291–1298 (2005).
Okada, I. A review of theoretical studies on indirect reciprocity. Games 11, 27 (2020).
Ohtsuki, H. & Iwasa, Y. How should we define goodness?–reputation dynamics in indirect reciprocity. J. Theor. Biol. 231, 107–120 (2004).
Hilbe, C., Schmid, L., Tkadlec, J., Chatterjee, K. & Nowak, M. A. Indirect reciprocity with private, noisy, and incomplete information. Proc. Natl Acad. Sci. USA 115, 12241–12246 (2018).
Berger, U. Learning to cooperate via indirect reciprocity. Games Econ. Behav. 72, 30–37 (2011).
Berger, U. & Grune, A. On the stability of cooperation under indirect reciprocity with first-order information. Games Econ. Behav. 98, 19–33 (2016).
Schmid, L., Ekbatani, F., Hilbe, C. & Chatterjee, K. Quantitative assessment can stabilize indirect reciprocity under imperfect information. Nat. Commun. 14, 2086 (2023).
Fujimoto, Y. & Ohtsuki, H. Evolutionary stability of cooperation in indirect reciprocity under noisy and private assessment. Proc. Natl Acad. Sci. USA 120, e2300544120 (2023).
Radzvilavicius, A. L., Stewart, A. J. & Plotkin, J. B. Evolution of empathetic moral evaluation. eLife 8, e44269 (2019).
Nakamaru, M. & Kawata, M. Evolution of rumours that discriminate lying defectors. Evol. Ecol. Res. 6, 261–283 (2004).
Sommerfeld, R. D., Krambeck, H.-J., Semmann, D. & Milinski, M. Gossip as an alternative for direct observation in games of indirect reciprocity. Proc. Natl Acad. Sci. USA 104, 17435–17440 (2007).
Seki, M. & Nakamaru, M. A model for gossip-mediated evolution of altruism with various types of false information by speakers and assessment by listeners. J. Theor. Biol. 407, 90–105 (2016).
Radzvilavicius, A. L., Kessinger, T. A. & Plotkin, J. B. Adherence to public institutions that foster cooperation. Nat. Commun. 12, 3567 (2021).
Iyengar, S., Lelkes, Y., Levendusky, M., Malhotra, N. & Westwood, S. J. The origins and consequences of affective polarization in the United States. Annu. Rev. Political Sci. 22, 129–146 (2019).
Newton, K. & Norris, P. in Disaffected Democracies: What’s Troubling the Trilateral Countries (eds Pharr, S. J. & Putnam, R. D.) 52–73 (Cambridge Univ. Press, 2000).
Public Trust in Government: 1958–2024. Pew Research Center www.pewresearch.org/politics/2024/06/24/public-trust-in-government-1958-2024/ (2024).
Boyd, R. & Richerson, P. J. The evolution of indirect reciprocity. Soc. Netw. 11, 213–236 (1989).
Nowak, M. A. & Sigmund, K. The dynamics of indirect reciprocity. J. Theor. Biol. 194, 561–574 (1998).
Manrique, H. M. et al. The psychological foundations of reputation-based cooperation. Philos. Trans. R. Soc. B 376, 20200287 (2021).
Panchanathan, K. & Boyd, R. A tale of two defectors: the importance of standing for evolution of indirect reciprocity. J. Theor. Biol. 224, 115–126 (2003).
Nowak, M. A. & Sigmund, K. Evolution of indirect reciprocity by image scoring. Nature 393, 573–577 (1998).
Wedekind, C. & Milinski, M. Cooperation through image scoring in humans. Science 288, 850–852 (2000).
Milinski, M., Semmann, D., Bakker, T. C. & Krambeck, H.-J. Cooperation through indirect reciprocity: image scoring or standing strategy? Proc. R. Soc. B: Biol. Sci. 268, 2495–2501 (2001).
Okada, I. Two ways to overcome the three social dilemmas of indirect reciprocity. Sci. Rep. 10, 16799 (2020).
Brandt, H. & Sigmund, K. The logic of reprobation: assessment and action rules for indirect reciprocation. J. Theor. Biol. 231, 475–486 (2004).
Santos, F. P., Santos, F. C. & Pacheco, J. M. Social norm complexity and past reputations in the evolution of cooperation. Nature 555, 242–245 (2018).
Raihani, N. J. & Bshary, R. The reputation of punishers. Trends Ecol. Evol. 30, 98–103 (2015).
Pacheco, J. M., Santos, F. C. & Chalub, F. A. C. Stern-judging: a simple, successful norm which promotes cooperation under indirect reciprocity. PLoS Comput. Biol. 2, e178 (2006).
Ohtsuki, H. & Iwasa, Y. The leading eight: social norms that can maintain cooperation by indirect reciprocity. J. Theor. Biol. 239, 435–444 (2006).
Takahashi, N. & Mashima, R. The importance of subjectivity in perceptual errors on the emergence of indirect reciprocity. J. Theor. Biol. 243, 418–436 (2006).
Uchida, S. & Sasaki, T. Effect of assessment error and private information on stern-judging in indirect reciprocity. Chaos Solitons Fractals 56, 175–180 (2013).
Uchida, S. Effect of private information on indirect reciprocity. Phys. Rev. E 82, 036111 (2010).
Nowak, M. A. Evolutionary Dynamics: Exploring the Equations of Life (Harvard Univ. Press, 2006).
Sasaki, T., Okada, I. & Nakai, Y. The evolution of conditional moral assessment in indirect reciprocity. Sci. Rep. 7, 41870 (2017).
Taylor, P. D. & Jonker, L. B. Evolutionary stable strategies and game dynamics. Math. Biosci. 40, 145–156 (1978).
Boyd, R. & Richerson, P. J. Culture and the Evolutionary Process (Univ. of Chicago Press, 1985).
Morin, O., Jacquet, P. O., Vaesen, K. & Acerbi, A. Social information use and social information waste. Philos. Trans. R. Soc. B 376, 20200052 (2021).
Henrich, J. & Gil-White, F. J. The evolution of prestige: freely conferred deference as a mechanism for enhancing the benefits of cultural transmission. Evol. Hum. Behav. 22, 165–196 (2001).
Kessinger, T. A., Tarnita, C. E. & Plotkin, J. B. Evolution of norms for judging social behavior. Proc. Natl Acad. Sci. USA 120, e2219480120 (2023).
Okada, I., Sasaki, T. & Nakai, Y. A solution for private assessment in indirect reciprocity using solitary observation. J. Theor. Biol. 455, 7–15 (2018).
Kandori, M. Social norms and community enforcement. Rev. Econ. Stud. 59, 63–80 (1992).
Santos, F. P., Pacheco, J. M. & Santos, F. C. Evolution of cooperation under indirect reciprocity and arbitrary exploration rates. Sci. Rep. 6, 37517 (2016).
Sugden, R. et al. The Economics of Rights, Co-operation and Welfare (Springer, 2004).
Perret, C., Krellner, M. & Han, T. A. The evolution of moral rules in a model of indirect reciprocity with private assessment. Sci. Rep. 11, 23581 (2021).
Axelrod, R. & Hamilton, W. D. The evolution of cooperation. Science 211, 1390–1396 (1981).
Michel-Mata, S. The evolution of private reputations in information-abundant landscapes. Zenodo https://doi.org/10.5281/zenodo.12795781 (2024).
Acknowledgements
We thank members of the Tarnita and Plotkin labs and D. Ocampo for productive discussions. We thank J. Chisausky for testing the code for reproducibility. We are grateful to the anonymous reviewers for much constructive feedback. We acknowledge support from the James S. McDonnell Foundation, a Postdoctoral Fellowship Award in Understanding Dynamic and Multi-scale Systems (https://doi.org/10.37717/2021-3209 to M.K.), the Simons Foundation Math+X Grant to the University of Pennsylvania (J.B.P.) and the John Templeton Foundation (Grant No. 62281 to J.B.P. and T.A.K.).
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S.M.M., M.K., J.S., T.A.K., J.B.P. and C.E.T. conceived the study and developed and analysed the mathematical model. S.M.M., J.B.P. and C.E.T. wrote the paper with input from M.K., J.S. and T.A.K.
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Extended data figures and tables
Extended Data Fig. 1 ‘Look twice, forgive once’ is stable and facilitates cooperative outcomes regardless of the social norm.
We show the dynamics between ALLC, ALLD, and a discriminator strategy using M = 1 or M = 2. The classical DISC (M = 1) is unstable for all norms, and the cooperative outcomes for scoring and simple-standing are vulnerable to invasion by ALLD. When DISCq,M uses M = 2 observations and is strict (q = 2/2), the outcomes of the dynamics are worse than with a single observation. But when DISCq,M is tolerant (q = 1/2), it is stable regardless of the social norm. The rate of cooperation at the ‘look twice, forgive once’ equilibrium is > 99.8% for all norms. For all panels, the benefit-to-cost ratio is b/c = 5, with error rates of assessment and execution α = 0.02 and ε = 0.02, respectively.
Extended Data Fig. 2 For M = 2, aggregating discriminators evolve versus unconditional strategies.
We estimated the volume of the basins of attraction towards aggregating discriminators, for a strategy space containing either strict (DISC2/2,2) or tolerant (DISC1/2,2) aggregating discriminators in the presence of ALLC and ALLD (left of dashed lines); and for the full strategy space with unconditional strategies and both aggregating discriminators (right of dashed lines). Each panel corresponds to a fixed, shared social norm. We estimated the basins by numerically integrating trajectories from evenly distributed initial frequencies in the interior of the simplex (171 for triplets and 975 for quartets; see Methods). The bars concatenate the steady states of all these trajectories. Regardless of the norm, tolerant discriminators are stable against unconditional strategies, while strict discriminators are not. When the full strategy space is considered, aggregating discriminators always have a basin of attraction. Under scoring or simple-standing, the stable equilibrium is a mix, with a large fraction of ‘look twice, forgive once’ coexisting with a small fraction of strict discriminators. Under stern-judging or shunning, we find a pure ‘look twice, forgive once’ stable equilibrium. The rate of cooperation at the discriminating equilibrium is 99.5% for scoring, 99.8% for stern-judging, 99.4% for simple-standing, and 99.8% for shunning. For all panels, the benefit-to-cost ratio is b/c = 5, with error rates of assessment and execution α = 0.02 and ε = 0.02, respectively.
Extended Data Fig. 3 Robustness of the evolution of tolerance thresholds under scoring.
Panels show the competition of aggregating discriminators using all possible thresholds q for a fixed number of observations M in the presence of the unconditional strategies, for varying values of the benefit-to-cost ratio (b/c) and of the assessment (α) and execution (ε) error rates (with α = ε). Each bar concatenates the steady states reached by numerical integration from 100 different initial conditions. White labels indicate the aggregating discriminators (pure or mixed) that are stable against invasion by unconditional strategies. The rates of cooperation at the discriminating equilibria range from 69.2% to 99.9%. Of the 99 steady states shown in this plot, only 11 are below a rate of cooperation of 90%.
Extended Data Fig. 4 Robustness of the evolution of tolerance thresholds under stern-judging.
Panels show the competition of aggregating discriminators using all possible thresholds q for a fixed number of observations M in the presence of the unconditional strategies, for varying values of the benefit-to-cost ratio (b/c) and of the assessment (α) and execution (ε) error rates (with α = ε). Each bar concatenates the steady states reached by numerical integration from 100 different initial conditions. White labels indicate the aggregating discriminators (pure or mixed) that are stable against invasion by unconditional strategies. The rates of cooperation at the discriminating equilibria range from 30.1% to 99.9%. Of the 76 steady states shown in this plot, only 5 are below a rate of cooperation of 90%.
Extended Data Fig. 5 An unconditional strategy probCp can invade classical DISC and pure DISCq,M, but not mixed equilibria.
a-c, Competition between probabilistic unconditional cooperator (probCp), classic discriminators (DISC), and aggregating discriminators (DISCq,M) under scoring. The horizontal axis shows multiple values of probCp’s probability of cooperation (p = 0 being ALLD and p = 1 being ALLC). The vertical axes represent the frequency of discriminators. Arrows show the flow of the evolutionary dynamics along the vertical axis. Filled-in circles represent stable equilibria; open circles represent unstable equilibria. a, probCp can invade and coexist with the classic single-observation discriminator (DISC) when the probability of cooperating is large enough (p > 0.3). At low values of p ≤ 0.3, coexistence becomes bistability. b, When competing against ‘look twice, forgive once’, only a narrow range of high probabilities (0.8 < p < 1.0) allows probCp to invade. At lower p ≤ 0.8, we find bistability. c, probCp is also able to invade strict discriminators and coexist with them for p > 0.1, with a larger fraction of probCp at this mixed equilibrium as p increases. d-e, Effects of probCp when more strategies are present. The bars show the results of the competition between probCp, ALLD, and DISC (for M = 1); and the competition between probCp, ALLD, tolerant aggregating discriminator (q = 1/2), and strict aggregating discriminator (q = 2/2) (for M = 2). d, When discriminators use a single observation, the outcomes are very similar to the classic scenario with ALLC: if p is large enough (p > 0.3), there is coexistence between probCp and DISC with the same weakness of the ‘scoring dilemma’ (i.e. ALLD can invade and take over). e, With multiple observations, for all values of p we tested, a mixture of tolerant and strict discriminators can coexist, have a non-trivial basin of attraction, and resist invasion by probCp and ALLD. This is because having a few strict discriminators in the mix effectively increases the overall strictness of the population compared to a scenario where only DISC1/2,2 is present. As a result, the overall ‘effective population tolerance’ becomes qe > 1/2. This higher level of strictness enables the population to more successfully identify and punish probCp when rare. As p increases, the basin of attraction towards such mixed discriminating equilibrium decreases. For all panels, the benefit-to-cost ratio is b/c = 5, with error rates of assessment and execution α = 0.02 and ε = 0.02, respectively.
Extended Data Fig. 6 Robustness of the evolution of the number of observations under scoring.
Panels show the competition of all possible numbers of observations (2 ≤ M ≤ 10) for a fixed strictness threshold q in the presence of unconditional strategies, for varying values of the benefit-to-cost ratio (b/c) and of the assessment (α) and execution (ε) error rates (with α = ε). Each bar concatenates the steady states reached by numerical integration from 100 different initial conditions. The rates of cooperation at the discriminating equilibria range from 79.2% to 100%. Of the 88 steady states shown in this plot, only 3 are below a rate of cooperation of 90% (marked with a dashed line).
Extended Data Fig. 7 Robustness of the evolution of the number of observations under stern-judging.
Panels show the competition of all possible numbers of observations (2 ≤ M ≤ 10) for a fixed strictness threshold q in the presence of unconditional strategies, for varying values of the benefit-to-cost ratio (b/c) and of the assessment (α) and execution (ε) error rates (with α = ε). Each bar concatenates the steady states reached by numerical integration from 100 different initial conditions. The rates of cooperation at all 76 discriminating equilibria in this plot range from 92.4% to 100%.
Extended Data Fig. 8 Conditions for the evolution of a number of observations M under a fixed strictness threshold q.
a, The panel illustrates the criteria determining how a resident discriminator, which aggregates MR observations, can resist invasion by a discriminator that aggregates a larger number of observations (MI > MR). The criterion for each resident type is shown by distinct curves. Below each curve are the conditions where the resident discriminator successfully resists invasion, while above the curves indicates vulnerability to invasion by discriminators aggregating a larger number of observation. The space between adjacent curves is a coexistence zone, where both resident and invading discriminators can stably exist together. Lower numbers of observations are favored by lower benefit-to-cost ratios. As error rates increase, the benefit-to-cost ratio required by a resident to resist invasion decreases exponentially. The dashed line shows b/c = 10 as an example, with different markers indicating specific values of the error rates. b, Panel shows the outcomes of the competition between multiple aggregating discriminators using M ∈ {2,4,6,8,10} in the presence of the unconditional strategies. Each bar correspond to each of the markers of panel a, showing the steady states reached by numerical integration from 100 different initial conditions. The steady states confirm the criteria of panel a and show that, as error rates increase with a fixed benefit-to-cost ratio, larger numbers of observations evolve. For all panels, we set q = 1/2 and fixed scoring as the social norm.
Extended Data Fig. 9 Coevolution of the number of observations M and the strictness threshold q under scoring.
a, Estimated basins of attraction after competition of all possible thresholds for M ∈ {4,6,8} and the two unconditional strategies. The mix between two moderately tolerant discriminators has the largest basin of attraction regardless of M. b, Estimated basins of attraction after competition of all possible thresholds for M = 2, with a large basin of attraction towards the ‘look twice, forgive once’ and strict discriminator mix. c, Competition between the mix of M = 2 and the mixes that evolve in larger M ∈ {4,6,8} in the presence of unconditional strategies. Such dynamics result in new mixed equilibria, which always contain ‘look twice, forgive once’ and an aggregating discriminator from larger M. Specifically, the strict discriminator with M = 2 is outcompeted by less strict discriminators but with larger M ∈ {4,6,8}. The rates of cooperation at the discriminating equilibria are all > 99.5%. For all panels, the benefit-to-cost ratio is b/c = 5, with error rates of assessment and execution α = 0.02 and ε = 0.02, respectively.
Extended Data Fig. 10 Coevolution of strategies and social norms, for all pairs of norms.
Each table cell shows the outcome of the competition among the eight types obtained from pairing one of the four strategies (ALLC, ALLD, DISC1/2,2 and DISC2/2,2) with one of the two social norms. The initial proportion of the two social norms is set to 50%. The four different bars in cell represent different probabilities of strategy imitation (w) versus social norm imitation (1−w). Each bar summarizes steady states reached by numerical integration from 975 uniformly distributed different initial strategy frequencies. Hues represent strategies; the brightness of each hue (lighter or darker) indicates the social norm. The rate of cooperation at the equilibria where the population consists entirely of discriminator strategies exceeds 97.5% in all cases. For all panels, the benefit-to-cost ratio is b/c = 5, with error rates of assessment and execution α = 0.02 and ε = 0.02, respectively.
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Supplementary Methods sections 1 and 2 (including Supplementary Table 1), and Figs. 1 and 2.
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Michel-Mata, S., Kawakatsu, M., Sartini, J. et al. The evolution of private reputations in information-abundant landscapes. Nature (2024). https://doi.org/10.1038/s41586-024-07977-x
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DOI: https://doi.org/10.1038/s41586-024-07977-x
