Collective patterns of social diffusion are shaped by individual inertia and trend-seeking

The study investigates how social conventions change via diffusion when a minority-backed alternative replaces a status quo. While classic population models (e.g., Bass) capture macroscopic S-curve dynamics, they do not explain why diffusion occurs. Agent-based models (ABMs) with coordination mechanisms can link individual decisions to population-level outcomes, but often omit two empirically supported behavioral mechanisms: inertia (status quo bias) and trend-seeking (sensitivity to changes in adoption trends). The research question is whether explicitly incorporating inertia and trend-seeking in a game-theoretic ABM can reconcile individual-level behavior with population-level diffusion patterns, such as delayed take-off followed by explosive transitions, commonly observed in real-world convention changes. The purpose is to provide a model consistent with social psychology evidence and experimental data that explains both the delay and explosiveness of diffusion and to identify the roles of explorers, non-explorers, and committed minorities in triggering social change.

Population-level diffusion models (e.g., Bass and variants) succinctly characterize S-shaped adoption and can reproduce explosiveness and delays under certain parametrizations but cannot integrate individual-level mechanisms like inertia and trend-seeking or heterogeneity. ABMs enable exploration of micro-to-macro links and the influence of social networks, heterogeneity, and interventions. Complex contagion literature emphasizes multiple exposures or social reinforcement. Game-theoretic ABMs commonly use coordination games to model conformity and consensus but typically exclude inertia and trend-seeking, despite extensive social psychology evidence on status quo bias and dynamic norms. Prior work highlights the importance of committed minorities for tipping points (e.g., 25% threshold) and heterogeneous adopter categories (early adopters vs. laggards). This paper extends coordination-game ABMs by embedding inertia and trend-seeking, aiming to align with empirical observations and psychological theory.

Experimental design: 180 recruits were enrolled via Prolific; 148 completed the multi-round online game (oTree), divided into 20 groups (8–10 human participants each). Each group also included 2, 3, or 4 pre-programmed committed minority bots to ensure 12 total players. Rounds proceeded until unanimous consensus or 24 rounds. In each round, participants chose between two strategies (status quo vs. alternative; framed as products Eta vs. Tao), and observed only the group-level proportions from the previous round. Incentives: base payment plus a group reward that decayed over time; a participant’s share was proportional to how often their choices matched the final winning strategy. Experimental protocol: Stage I established a status quo with all humans and all but one bot aligning on one strategy; Stage II began the next round when all humans first selected the status quo, and then all committed minority bots consistently chose the alternative until end, stimulating diffusion. Dropout bots replaced missing responses in a round by selecting the current majority. Data collected included per-round choices for all participants and bots. Analyses of experimental data: Individual switching rates were computed for 148 participants, revealing heterogeneity. Regression with fixed effects tested the influence of coordination (fraction adopting in previous round), inertia (individual’s prior choice), and trend-seeking (group trend) on current choice. Additional tests isolated inertia (Wald–Wolfowitz runs test) and trend-seeking (binomial test). Agent-based model (ABM): A game-theoretic coordination model with synchronous, all-to-all interactions and logit (log-linear) learning for strategy updates. Each player v at time t selects strategy x in {0,1} (0 status quo, 1 alternative). The probability of adopting a strategy at t+1 follows a logit rule P[x_v(t+1)=x] = exp{β_v π_v(x)} / (exp{β_v π_v(0)}+exp{β_v π_v(1)}), where β_v ≥ 0 is rationality. Payoffs π_v(x) are a convex combination of: (i) social coordination (benefit increases with the fraction of others choosing x), (ii) inertia (bonus k_v for repeating one’s prior choice), and (iii) trend-seeking (bonus r_v for choosing the strategy whose population share increased in the previous time step). Parameters satisfy b_v + k_v + r_v = 1. Model features all-to-all information and synchronous updates; more complex mechanisms are left for future work. Parametrization: Data cleaning identified 138 participants as non-irregular; trials with too many irregularities were excluded, leaving 119 regular participants across 16 trials for parameter estimation. Participants were classified into explorers vs. non-explorers using a behavioral discriminant that incorporates total switches, switches to minority vs. majority, and switching rate; 74 explorers and 45 non-explorers among the 119 regular participants. Parameters estimated: a common β (rationality), and class-specific b, k, r for explorers and non-explorers (with b inferred from 1−k−r). A Monte Carlo approach recreated each trial’s conditions (including deterministic bots and any stubborn or dropout agents) and simulated 1000 runs per scenario to match empirical distributions of switching rates for explorers and non-explorers via a weighted cost function over means and standard deviations. Best-fit parameters minimized the cost on a discretized grid for β and k, r. Simulation studies: Monte Carlo simulations (typically 200 runs) explored diffusion dynamics across population sizes n and explorer fractions p_e with 25% committed minority (and other fractions in supplementary analyses). Diffusion metrics: take-off time T (time when adoption of the alternative first surpasses a robust threshold and does not fall below it again, operationalized at ~0.4) and transition time ΔT (duration from takeoff to near-complete adoption). Additional experiments varied the fraction of committed minority and explorers to map regimes of diffusion vs. non-diffusion and delays.

- Experimental outcomes: In 18/20 trials, a status quo formed within 1–3 rounds. In 16/20 trials, diffusion to the alternative occurred; in 15 of these, diffusion was explosive, including instances with substantial initial delay before rapid transition. Switching rates were moderate and heterogeneous: 67% of players had y ≤ 0.046 (often switching once or only at consensus), while the remainder switched more frequently and were more prone to try the alternative early. Participants were classified as 85 explorers and 53 non-explorers across all participants (119 regular participants among 16 trials used for parameterization yielded 74 explorers and 45 non-explorers). - Statistical evidence for mechanisms: Fixed-effects regression indicated that an individual’s previous choice (inertia), the fraction of adopters in the previous round (coordination), and the group trend (trend-seeking) significantly predict current choice (F=494.66, p<0.001; R^2=0.46). Estimated effects: choosing a strategy in the previous round increased probability of choosing it again by 36%; if the rest of the group switched strategies in the previous round, the probability of following the trending strategy increased by 31% (all p<0.001). Additional tests supported inertia (Wald–Wolfowitz runs test, p<0.0001) and trend-seeking (binomial test, p=0.005). - Model behavior: Incorporating inertia and trend-seeking reproduces key features: (i) delayed take-off times before diffusion, (ii) explosive transitions after take-off (small ΔT), and (iii) moderate, heterogeneous individual switching. Trend-seeking drives explosiveness irrespective of population size, while inertia controls the delay to take-off. - Role of explorers and population size: With no explorers (p_e=0), take-off time T grows faster than linearly with population size n, potentially preventing diffusion in large populations. With a modest explorer fraction (p_e>0.05), T becomes moderate and essentially independent of n; ΔT remains small across n. - Committed minority thresholds: A committed minority ≥25% guarantees diffusion with small T (e.g., T<150 in simulations) independent of n. Below ~19% committed minority, no diffusion was observed within a very long simulation window (50,000 steps), regardless of explorer fraction. In an intermediate 19–25% regime, explorers critically reduce delays and can unlock diffusion; a sharp phase transition in T occurs as explorer fraction dips below a threshold dependent on committed minority. - Comparison with standard coordination models: Pure coordination models without inertia/trend-seeking cannot simultaneously reproduce delayed take-off, explosive transitions, and realistic individual switching patterns unless imposing unrealistic agent-level assumptions (e.g., extreme explorer shares or altered rationality), which then conflict with empirical individual behavior.

The findings demonstrate that adding inertia (status quo bias) and trend-seeking (sensitivity to changing adoption rates) to a coordination-game ABM resolves mismatches between empirical individual behavior and macroscopic diffusion patterns. Inertia explains extended meta-stable periods where the status quo persists, while trend-seeking ensures rapid, explosive diffusion once take-off begins. The model aligns with experimental observations and broader empirical literature showing delayed tipping followed by rapid change. Explorers act as catalysts: even small fractions dramatically reduce take-off time and decouple it from population size, especially near the committed-minority threshold. The results refine understanding of tipping dynamics by quantifying how explorer prevalence and committed minority sizes interact to produce or prevent social change. Practically, interventions that increase sensitivity to trends or reduce inertia (e.g., highlighting dynamic norms) and that support committed minorities can accelerate convention change without requiring unrealistic population conditions.

This work introduces and empirically grounds a game-theoretic ABM that integrates inertia and trend-seeking alongside coordination to explain social diffusion. The model reproduces key empirical features—delayed take-off and explosive transitions—while yielding individual decision patterns consistent with psychological evidence. It clarifies how explorers and committed minorities jointly determine whether and when diffusion occurs, identifying a robust sufficiency threshold (~25% committed minority) and a critical regime where explorers can unlock change, contrasted with a sub-19% regime where diffusion is practically unobservable. Future research directions include: linking take-off/explosiveness to formal tipping-point theory; incorporating asymmetric payoffs (innovation advantages); exploring cultural differences and parameter variability; embedding network structures and asynchronous/time-varying interactions; and extending to multi-strategy settings. These extensions could broaden applicability to domains like social movements and sustainability adoption, where inertia and trend signals are pervasive.

The model assumes all-to-all communication and synchronous updates, omitting realistic network structures and interaction patterns that can alter diffusion. Inertia and trend-seeking are implemented minimally (short memory of trends; no diminishing effects once majority is reached), and only two strategies with equal payoffs are considered. Experimental constraints include finite rounds (24), online participant pool limited to native English speakers, and the use of bots to induce committed minority behavior. Reported thresholds (e.g., no diffusion below ~19% committed minority within 50,000 steps) depend on model parametrization and simulation windows. Parameter estimation relies on aggregated class-level parameters for explorers and non-explorers and Monte Carlo fitting, which may overlook finer-grained heterogeneity.