Adherence to public institutions that foster cooperation

The study investigates how public institutions that broadcast reputations influence cooperation sustained by indirect reciprocity, and whether individuals will choose to adhere to such institutions rather than rely on private moral assessments. Prior work shows cooperation can be stable under norms like Stern Judging when reputations are public, but tends to collapse under private, noisy assessments due to disagreements about reputations. The research question is twofold: (1) how do an institution’s design parameters—its size (Q) and strictness threshold (q)—affect equilibrium cooperation across prominent second-order social norms, and (2) under what conditions will adherence to an existing public monitoring institution spread by cultural evolution in populations that initially use private assessments? This is important for understanding when centralized monitoring can resolve reputational disagreements and thereby foster cooperation in realistic settings where observation is noisy and perspectives differ.

The paper builds on the literature of indirect reciprocity and social norms showing that cooperation can be maintained by reputation systems (Nowak & Sigmund; Ohtsuki & Iwasa). Second-order norms, especially Stern Judging, have been found to support high cooperation under public information. However, with private, noisy, or incomplete information, cooperation often collapses (Hilbe et al.). Empathy and perspective-taking can mitigate breakdowns under private assessment (Radzvilavicius et al.), but empathy can be cognitively costly and manipulable. Institutions historically and contemporarily provide public reputation signals (e.g., merchant law, credit bureaus, online feedback), suggesting a role for centralized monitoring. The paper also connects to motivational crowding from economics, where external incentives can crowd out intrinsic motivations, drawing parallels with interactions between empathy and institutions.

The authors model pairwise donation games with payoff matrix [[b−c, −c], [b, 0]]. Strategies: ALLC (always cooperate), ALLD (always defect), and DISC (discriminate: cooperate with recipients of good reputation). Reputations are updated under four second-order social norms: Stern Judging, Simple Standing, Scoring, and Shunning, each specifying how a donor’s action toward a recipient with good or bad reputation affects the donor’s reputation. Errors are included: implementation error e1 (intended cooperation may accidentally defect) and observation error e2 (assessor may flip good/bad). Public institutions are modeled as Q observers forming a consensus with strictness threshold q: a public reputation is good if at least fraction q of institutional observers view an individual as good; q encodes tolerance (low q = tolerant, high q = strict). The study examines two limiting cases: tolerant institutions (q < 1/Q) and strict institutions (q > (Q−1)/Q), as well as general q and Q. First, assuming universal adherence to the institution, replicator dynamics in an infinite population track frequencies of ALLC, ALLD, and DISC. Reputation frequencies are assumed to equilibrate faster than strategy dynamics; closed-form or iterative solutions compute the equilibrium fraction of good reputations by type, accounting for Q and q (including expressions for tolerant and strict institutions). Strategic equilibria and basins of attraction are analyzed across norms and institutional types. Second, the evolution of adherence is studied by introducing two discriminator types: DISC-ADHERE (uses public reputations) and DISC-PRIVATE (uses private assessments with optional empathy E). Replicator dynamics are derived for competition between adherents and non-adherents, tracking cross-perspective reputation agreements and disagreements and distinguishing between an external board (institution members always adherents) and an internal board (institution members drawn from the population). Analytical conditions show that selection for adherence depends on b/c relative to a critical threshold that depends on errors, norm, Q, and q. Monte Carlo simulations complement analysis in finite populations (N = 50), with mutation rate μ = 0.025 for strategy evolution scenarios and pairwise comparison updating with selection strength w = 1. Simulations examine cooperation levels for various Q and q, empathy levels (E = 0, 1), and test invasion/fixation of adherence when rare among DISC-PRIVATE populations, and robustness once adherence is common. Parameter sets include typical values e1 = e2 = 0.02, b = 5, c = 1, and varying Q (e.g., 1, 2, 50) and q across [0,1]. Additional simulations test competition when ALLC and ALLD are present and explore sensitivity to b/c (e.g., > or < 50) and errors.

• Public institutions of moral assessment can facilitate high cooperation across all four norms when appropriately designed. For each norm, there exist combinations of institution size Q and strictness q that produce stationary cooperation rates that meet or exceed those under empathetic private assessment.
• Strict vs tolerant design: strict institutions (high q) best support cooperation under Stern Judging and Simple Standing; tolerant institutions (low q) best support cooperation under Scoring and Shunning. Under Shunning and Scoring, tolerant institutions create large basins of attraction to cooperative equilibria, whereas strict institutions or private assessment may fail to support stable discrimination.
• Institution size matters: maximizing cooperation always requires Q > 1; Q = 2 is typically sufficient to match larger institutions. In contrast, the classic public information assumption (Q = 1) yields high cooperation only under Stern Judging or Simple Standing.
• Basins of attraction: with e1 = e2 = 0.02, b = 5, c = 1, and Q = 2, tolerant institutions produce large cooperative basins under Scoring and Shunning; strict institutions enlarge cooperative basins under Stern Judging and Simple Standing. Increasing b/c increases the size of non-empty cooperative basins, while changing the relative sizes of e1 and e2 has minimal qualitative impact.
• Finite-population simulations (N = 50, μ = 0.025) corroborate analytical predictions: cooperation levels as functions of q and Q follow the same strict/tolerant pattern for each norm; public institutions can outperform even empathetic private assessment.
• Evolution of adherence: adherence to public institutions can spread by social contagion and fix in populations. Fixation probabilities of a single adherent exceed neutral drift (1/N) for many norms and institutional designs, especially: • Stern Judging: adherence to strict institutions is favored, particularly when empathy among private assessors is low; tolerant institutions are disfavored unless b/c is very large. • Simple Standing: adherence is often favored for large Q across a broad range of q in low-empathy populations; in highly empathetic populations, adherence is less likely to evolve. • Scoring: adherence to tolerant institutions with Q > 1 is strongly favored regardless of empathy; Q = 1 is neutral. • Shunning: adherence is near neutral in low-empathy populations, but tolerant institutions are favored in empathetic populations.
• Benefit-to-cost thresholds: selection for adherence depends on b/c relative to a critical value that depends on norm, errors, Q, and q. Qualitative switches occur: • Under tolerant Stern Judging, adherence is disfavored at b/c = 5 but becomes favored when b/c > 50. • Under strict Shunning, adherence is favored when b/c < 50 and disfavored when b/c > 50; under tolerant Shunning, selection for adherence strengthens as b/c increases.
• Robustness: once adherence fixes, it is evolutionarily stable against re-invasion by private assessors. Public monitoring homogenizes reputations, reduces unjustified defections, and increases individual payoffs.
• Design implications: tolerant institutions prevent punitive cascades under Shunning and Scoring by avoiding over-penalization from occasional interactions with bad players; strict institutions under Stern Judging and Simple Standing more effectively deter willful defectors.
• Additional results: In some scenarios (e.g., strict Stern Judging), adherence can invade even when populations are initially dominated by ALLD or ALLC. Institutions with external or internal boards show qualitatively consistent outcomes.

The findings address the problem of cooperation under private, noisy reputational assessments by showing that centralized public monitoring can eliminate reputational disagreements and thereby revive and stabilize cooperation across multiple norms, including those previously seen as poor performers (Scoring, Shunning). The interplay between institutional design and norms is central: strict institutions are preferable where norms primarily punish defection against good recipients (Stern Judging, Simple Standing), while tolerant institutions are crucial where norms risk punitive cascades due to interactions with bad recipients (Scoring, Shunning). The evolution of adherence explains why individuals may rationally abandon private judgments: adherents gain higher payoffs because public reputations reduce unjustified defections, enabling selection to favor adherence and rendering it robust once common. The work also relates to motivational crowding: empathy can reduce the selective advantage of external institutions by already improving cooperation under private assessment, though notable exceptions exist (strict Stern Judging and tolerant Shunning). Sensitivity analyses highlight that increasing b/c strengthens cooperation and can qualitatively shift selection for adherence depending on the norm and institutional strictness. Overall, the results offer a theoretical foundation for the assumption of public monitoring in indirect reciprocity and guide institutional design to maximize cooperation.

The paper contributes a theoretical framework showing that adherence to public institutions of moral assessment can evolve and robustly support cooperation, even under social norms previously considered ineffective. By tuning institution size (Q) and strictness (q), societies can achieve high cooperation: strict institutions for Stern Judging and Simple Standing, and tolerant institutions for Scoring and Shunning, with Q > 1 (often Q = 2) sufficient to approach optimal outcomes. Adherence spreads by social contagion due to higher payoffs from reduced reputational disagreements and remains stable once common. Future research directions include: mechanisms for establishing institutions de novo; addressing institutional corruption and governance; extending from pairwise to n-player public goods settings; coevolution and competition of social norms; cognitive costs and manipulation risk of empathy; and empirical validation through laboratory and field studies of reputation systems.

• The analysis is purely theoretical with no empirical data; models simplify complex human moral judgments.
• Pairwise interactions are assumed; extensions to n-player interactions and public goods are not modeled.
• Reputation updating is assumed to equilibrate faster than strategy change; real-world timescales may differ.
• Empathy is treated as a parameter without explicit cognitive costs or deception dynamics.
• Institutional establishment, governance, and maintenance costs are not modeled endogenously; corruption is only discussed via a simple calculus.
• Results depend on specific strategy sets (ALLC, ALLD, DISC) and second-order norms; richer strategy spaces or evolving norms may yield different dynamics.
• Assumptions about external vs internal boards and fixed institution membership may not capture all institutional architectures.