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Invariant Causal Routing for Governing Social Norms in Online Market Economies

Xiangning Yu, Qirui Mi, Xiao Xue, Haoxuan Li, Yiwei Shi, Xiaowei Liu, Mengyue Yang

TL;DR

In heterogeneous agent simulations calibrated with real data, ICR yields more stable norms, smaller generalization gaps, and more concise rules than correlation or coverage baselines, demonstrating that causal invariance offers a principled and interpretable foundation for governance.

Abstract

Social norms are stable behavioral patterns that emerge endogenously within economic systems through repeated interactions among agents. In online market economies, such norms -- like fair exposure, sustained participation, and balanced reinvestment -- are critical for long-term stability. We aim to understand the causal mechanisms driving these emergent norms and to design principled interventions that can steer them toward desired outcomes. This is challenging because norms arise from countless micro-level interactions that aggregate into macro-level regularities, making causal attribution and policy transferability difficult. To address this, we propose \textbf{Invariant Causal Routing (ICR)}, a causal governance framework that identifies policy-norm relations stable across heterogeneous environments. ICR integrates counterfactual reasoning with invariant causal discovery to separate genuine causal effects from spurious correlations and to construct interpretable, auditable policy rules that remain effective under distribution shift. In heterogeneous agent simulations calibrated with real data, ICR yields more stable norms, smaller generalization gaps, and more concise rules than correlation or coverage baselines, demonstrating that causal invariance offers a principled and interpretable foundation for governance.

Invariant Causal Routing for Governing Social Norms in Online Market Economies

TL;DR

In heterogeneous agent simulations calibrated with real data, ICR yields more stable norms, smaller generalization gaps, and more concise rules than correlation or coverage baselines, demonstrating that causal invariance offers a principled and interpretable foundation for governance.

Abstract

Social norms are stable behavioral patterns that emerge endogenously within economic systems through repeated interactions among agents. In online market economies, such norms -- like fair exposure, sustained participation, and balanced reinvestment -- are critical for long-term stability. We aim to understand the causal mechanisms driving these emergent norms and to design principled interventions that can steer them toward desired outcomes. This is challenging because norms arise from countless micro-level interactions that aggregate into macro-level regularities, making causal attribution and policy transferability difficult. To address this, we propose \textbf{Invariant Causal Routing (ICR)}, a causal governance framework that identifies policy-norm relations stable across heterogeneous environments. ICR integrates counterfactual reasoning with invariant causal discovery to separate genuine causal effects from spurious correlations and to construct interpretable, auditable policy rules that remain effective under distribution shift. In heterogeneous agent simulations calibrated with real data, ICR yields more stable norms, smaller generalization gaps, and more concise rules than correlation or coverage baselines, demonstrating that causal invariance offers a principled and interpretable foundation for governance.
Paper Structure (75 sections, 9 theorems, 31 equations, 4 figures, 6 tables, 1 algorithm)

This paper contains 75 sections, 9 theorems, 31 equations, 4 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Social Norms.
  4. From Correlational to Causal Policy Governance.
  5. OOD Prediction and PNS
  6. Preliminaries and Problem Formulation
  7. Social Norms in Online Market
  8. Distance convention.
  9. Existence of feasible limits.
  10. System Setup and Dynamics
  11. Problem Definition
  12. Method: Three-Stage Causal Governance
  13. Stage I: Causal Identification via PNS
  14. PNS Identification
  15. Estimation.
  16. ...and 60 more sections

Key Result

proposition 1

If $\Sigma(P^{(\theta)}, \phi) \cap \mathcal{S}_\varepsilon \neq \varnothing$, the social norm is feasible, meaning there exists a stationary regime whose averages satisfy the band. Conversely, if $\Sigma(P^{(\theta)}, \phi) \cap \mathcal{S}_\varepsilon = \varnothing$, then there exists a constant $ That is, stable attainment is impossible if all invariant averages lie outside the band.

Figures (4)

  • Figure 1: Social norms in onlineeconomies.
  • Figure 2: Three-stage framework for discovering causal strategies in social norm formation. Stage I tests causal effects by identifying implicit contracts $(\theta, g \mid \psi)$ where policy $\theta$ enables group $g$ to reach the norm under context $\psi$. Stage II learns a compact rule router $S^\star$ selecting effective strategies for robust norm attainment. Stage III explains success by attributing norms to key factors where user responses differ from the baseline $\theta_0$.
  • Figure 3: Last-50-year trajectories of $\phi_1$ (ST) and $\phi_2$ (RI) with norm bands (per objective $\times$ group). Shaded regions of the same color indicate the band within which individuals of the corresponding group are expected to remain under the associated social norm. When all trajectories lie within their respective same-colored shaded regions, the social norm is fully attained.
  • Figure 4: Key factors attribution for invariant causal routes.

Theorems & Definitions (14)

  • definition 1: Social Norm Band
  • definition 2: Social norm attainment
  • proposition 1: Norm Feasibility Criterion
  • definition 3: Potential Outcome and PNS
  • definition 4: Implicit Contract
  • lemma 1: Tightness of Cesàro averages
  • lemma 2: Invariance of weak limits
  • theorem 1: Krylov--Bogolyubov Theorem
  • lemma 3: Tightness of occupation measures
  • lemma 4: Cesàro average of martingale differences
  • ...and 4 more