A behavioral reinvestigation of the effect of long ties on social contagions

TL;DR

This study tackles the conflicting evidence on how long ties affect diffusion by empirically grounding social influence in measured individual decision rules under payoff uncertainty. The authors elicit complete choice functions for individuals via lottery-based tasks and a strategy-method adaptation, then embed these functions into agent-based diffusion simulations on synthetic networks with varying levels of long ties. They find that payoff uncertainty increases both susceptibility to social influence and the social reinforcement required for adoption, with substantial heterogeneity driven by risk preferences and subjective interpretations of uncertainty; at the collective level, long ties generally promote diffusion but their advantage weakens as uncertainty grows and may vanish under full uncertainty, though heterogeneity often sustains diffusion. Crucially, the results show that the effect of long ties is not determined by a simple vs. complex contagion dichotomy but by the distribution of individual choice functions in the population, linking microfoundations to macro diffusion in a way that reconciles prior theoretical debates. The work provides a framework for integrating behavioral data with diffusion models, with practical implications for designing interventions in technology uptake, public health, and organizational diffusion strategies.

Abstract

Faced with uncertainty in decision making, individuals often turn to their social networks to inform their decisions. In consequence, these networks become central to how new products and behaviors spread. A key structural feature of networks is the presence of long ties, which connect individuals who share few mutual contacts. Under what conditions do long ties facilitate or hinder diffusion? The literature provides conflicting results, largely due to differing assumptions about individual decision-making. We reinvestigate the role of long ties by experimentally measuring adoption decisions under social influence for products with uncertain payoffs and embedding these decisions in network simulations. At the individual level, we find that higher payoff uncertainty increases the average reliance on social influence. However, personal traits such as risk preferences and attitudes toward uncertainty lead to substantial heterogeneity in how individuals respond to social influence. At the collective level, the observed individual heterogeneity ensures that long ties consistently promote diffusion, but their positive effect weakens as uncertainty increases. Our results reveal that the effect of long ties is not determined by whether the aggregate process is a simple or complex contagion, but by the extent of heterogeneity in how individuals respond to social influence.

Figures (15)

• Figure 1: Connecting behavioral experiments and computational simulations (A) In the experiment, subjects decided whether to adopt risky products with uncertain payoffs. Subjects provided a separate adoption decision for each possible peer-adoption level (0–4 adopting peers, presented in a pre-specified order). This procedure yields each subject’s complete choice function. (B) The measured choice functions serve as decision rules for nodes in network simulations. Subjects are randomly assigned to nodes, and diffusion begins by selecting a pair of connected nodes (seeds) and setting their state to adopted. At each time step, nodes with at least one adopted neighbor simultaneously update their state by evaluating their experimentally measured choice function at the current peer-adoption level. Panel B illustrates a focal node evaluating the choice function elicited in Panel A. In this example, the subject assigned to the focal node is connected to four neighbors, two adopters (the seeds) and two non-adopters. Following the measured choice function the focal node will adopt the product.
• Figure 2: Individual-level results (A) Fraction of individuals susceptible to social influence in the different uncertainty conditions ($N=399$). Error bars are the $95\%$ confidence intervals. (B) Average social reinforcement required to adopt in the different uncertainty conditions (computed from adopting individuals in the different uncertainty conditions, $N_{\text{no}} = 365,\; N_{\text{low}} = 351,\; N_{\text{high}} = 329,\; N_{\text{full}} = 253$). Error bars are the $95\%$ confidence intervals. (C) Fraction of individuals exhibiting simple and complex adoptions pattens in their choice functions for the different uncertainty condition (computed from adopting individuals, $N_{\text{no}} = 365,\; N_{\text{low}} = 351,\; N_{\text{high}} = 329,\; N_{\text{full}} = 253$. Error bars are the $95\%$ confidence intervals. (D) Distribution of thresholds (choice functions patterns) for each uncertainty condition. Threshold values indicate the fraction of adopting peers required for adoption, $>1$ indicates no adoption, NM indicates non-monotonic threshold ($N=399$).
• Figure 3: Collective-level results (A) We manipulate long ties by rewiring pairs of edges starting from a ring lattice while keeping the degree of the network fixed maslov2002specificity. Each rewiring introduces long ties, moving the network from a ring lattice to a random graph. (B) Average final fraction of adopters in the different uncertainty conditions in function of the number of rewiring. Results from the ABM simulations with: network size $N = 399$, degree $k = 4$. The initial seeds are random pair of connected nodes. Each point in the graph is the average of $R = 500$ diffusion realization in which subjects are randomly placed on the network. Error bars are the $95\%$ confidence intervals.
• Figure 4: Product configurations. Products were represented as urn lotteries. Each lottery is denoted by $(n_b, n_o, n_g; X)$ in an urn of $N = 40$ balls: $n_b$ blue balls (giving a payoff of $X$), $n_o$ orange balls (giving payoff of $0$), and $n_g$ gray balls (hidden color). The seven products varied along two dimensions: uncertainty, given by the proportion of hidden (gray) balls ($0\%$, $25\%$, $50\%$, $100\%$), and risk, defined as the probability of a winning $X$ based on the visible balls (low risk: $90\%$; high risk: $50\%$).
• Figure S1: Adoption task measuring choice functions. Subjects pre-specified whether they would adopt for each possible number of adopting peers (contingent plan for $k\in\{0,\dots,4\}$). This adapts the strategy method to incorporate social influence selten1967strategiemethode and measure choice functions. The screenshot illustrates the low risk, high uncertainty product configuration.