Networks of commitments: from social ties to normative expectations

Technical Summary: Networks of Commitments: From Social Ties to Normative Expectations

Problem Statement
The paper addresses the challenge of scaling collective action, particularly in the context of global issues like climate change, which represent collective action problems involving conflicts between self-interest and public goods. While existing research highlights the multi-level nature of these problems, there is insufficient exploration of the specific behavioral mechanisms through which individuals update their beliefs regarding collective action. Specifically, the authors note a gap in understanding how successful scaling occurs, or why it often fails, when moving from local experimentation to broader societal adoption. The core problem is explaining how local joint commitments interact with network-level normative expectations to determine whether belief changes scale up or remain confined to subgroups.

Methodology
The authors develop a co-evolutionary agent-based model (ABM) integrated with social network analysis (SNA) to simulate the interaction between joint commitment and normative expectations. The model operates on a population of $n=1000$ agents within a dynamic, binary, unweighted network where links represent social ties formed through joint commitment.

The mechanism is structured as a two-phase feedback loop:

1. Phase 1: Joint Commitment and Tie Formation. Agents possess an initial "individual readiness" ($p_j$) to engage in collective action, drawn from various distributions (Uniform, Gaussian, or Gamma). In each time step, agents interact. A joint commitment (and the resulting social tie) is formed between two agents if the product of their individual readiness ($p_j \cdot p_k$) exceeds a threshold ($s$). This threshold $s$ represents the accessibility and salience of information regarding the collective goal. Lower $s$ implies higher salience, making tie formation easier.
2. Phase 2: Normative Expectations and Belief Updating. Agents update their readiness based on "normative expectations," defined as second-order beliefs about what others deem appropriate. Agents compare their local clustering coefficient ($c_j$), representing the density of ties within their immediate group, against the global clustering coefficient ($c$), representing the density of ties across the entire network.
   • The difference $d_j = c - c_j$ serves as a gradient.
   • Agents update their readiness ($p_j$) according to the rule: $p_j(t+1) = p_j(t) \cdot e^{\omega_j \cdot d_j(t)}$.
   • The parameter $\omega_j$ represents an agent's sensitivity to normative expectations. If $\omega_j > 0$, the agent follows the global tendency; if $\omega_j < 0$, they follow the local tendency; if $\omega_j = 0$, they are unaffected.

The simulation runs until convergence, testing 12 scenarios formed by crossing three initial readiness distributions (ipc) with four distributions of sensitivity to normative expectations (sne), across varying levels of information salience ($s$).

Key Contributions

• Theoretical Integration: The paper integrates Margaret Gilbert's theory of joint commitment (focusing on mutual obligations arising from direct interaction) with Cristina Bicchieri's theory of social expectations (focusing on second-order beliefs about what others think ought to be done). This creates a unified framework where commitment formation and norm-based inference co-evolve.
• Endogenous Network Dynamics: Unlike models with fixed topologies, this framework treats network structure as endogenous. Links are created or destroyed based on the agents' evolving readiness and the salience of information.
• Mechanism for Scaling: The model formalizes how the discrepancy between local engagement and global diffusion drives belief updating. It posits that scaling depends on the alignment between local joint commitments and the perceived broader normative environment.

Simulation Results
The simulations reveal non-linear, path-dependent dynamics resulting in three primary aggregate outcomes: polarization, convergence, and fragmentation.

• Impact of Information Salience ($s$): High salience (low $s$) facilitates the formation of ties and allows for significant belief updating. Low salience (high $s$) hinders link formation, causing the system to remain close to its initial state.
• Initial Conditions and Sensitivity:
  • Polarization: Emerges strongly when information salience is high and agents are heterogeneous in their sensitivity to local vs. global signals (e.g., the sne-ΓR case where agents are locally anchored). This can lead to a bimodal distribution where agents either fully commit or fully disengage.
  • Convergence: Occurs when agents are sensitive to global signals (sne-ΓL) or when initial readiness is low but information salience is high, driving agents toward a shared level of commitment.
  • Fragmentation: Observed in scenarios with moderate salience and specific sensitivity distributions, where the network fails to coalesce into stable clusters.
• Aggregate Social Contribution (ASC): The total contribution to collective action does not always increase with interaction. In some scenarios (particularly high salience with local anchoring), polarization can lead to an ASC lower than the initial state. Conversely, high salience can compensate for polarization to maintain contribution, while low salience makes converging behavior more effective for social performance.
• Individual Trajectories: At the micro-level, agents exhibit volatile, idiosyncratic paths, including oscillations around the threshold, sudden shifts, and divergence from initial conditions, highlighting the chaotic nature of the system.

Significance and Claims
The paper claims to offer a "stylized, theory-driven account" of how joint commitments and normative expectations co-evolve within network structures. It does not claim to provide a general account of all collective action or to model strategic payoffs and institutional enforcement.

The primary significance lies in demonstrating that joint commitment is a necessary but not sufficient condition for large-scale coordination. The model shows that the success of scaling depends critically on:

1. The alignment between local engagement and perceived global support.
2. The salience of information regarding collective goals.
3. The heterogeneity of agents' sensitivity to normative expectations.

The authors conclude that effective responses to collective action problems require fostering local joint commitments while simultaneously ensuring these commitments are perceived as normatively appropriate at the broader network level. They suggest that targeted campaigns amplifying early commitments could strengthen the feedback loop between commitment and expectation, potentially resolving collective action problems. The study acknowledges its limitations, noting that the model is not empirically calibrated and that future work should focus on empirical validation through survey experiments and network-based interventions.