Abstract
Complex innovations– ideas, practices, and technologies that hold uncertain benefits for potential adopters—often vary in their ability to diffuse in different communities over time. To explain why, I develop a model of innovation adoption in which agents engage in naïve (DeGroot) learning about the value of an innovation within their social networks. Using simulations on Bernoulli random graphs, I examine how adoption varies with network properties and with the distribution of initial opinions and adoption thresholds. The results show that: (i) low-density and high-asymmetry networks produce polarization in influence to adopt an innovation over time, (ii) increasing network density and asymmetry promote adoption under a variety of opinion and threshold distributions, and (iii) the optimal levels of density and asymmetry in networks depend on the distribution of thresholds: networks with high density (>0.25) and high asymmetry (>0.50) are optimal for maximizing diffusion when adoption thresholds are right-skewed (i.e., barriers to adoption are low), but networks with low density (<0.01) and low asymmetry (<0.25) are optimal when thresholds are left-skewed. I draw on data from a diffusion field experiment to predict adoption over time and compare the results to observed outcomes.
Highlights
Central to the study of how innovations diffuse in society is an understanding of the processes by which individuals learn from and influence each other over time [1,2,3]
Many prior studies have examined the relationship between network structure and opinion formation [6,7,8,9], few have modeled how collectively formed opinions affect the spread of complex innovations—new technologies, practices, and ideas that hold uncertain benefits for potential adopters—within social networks
In relation to prior studies of opinion formation in networks, the results suggest that two parameters regulate the benefits of network structure for diffusion: network asymmetry and network density
Summary
Central to the study of how innovations diffuse in society is an understanding of the processes by which individuals learn from and influence each other over time [1,2,3]. I conduct network simulations by varying: (i) the structure of social influence (as characterized by network density and asymmetry), (ii) individual thresholds for adoption, and (iii) the distribution of initial opinions about the underlying value of the complex innovation. The simulations reveal parameter values under which identical innovations will vary in their diffusion rates within a community, depending on the structure of the network topology through which people form collective opinions, the shape of the distribution of initial opinions ( its functional form and skew), and the distribution of thresholds for adoption. Let S be stochastic mathematically equivalent to the transition probability matrix for a Markov chain with n states and stationary transition probabilities [27] Given this initial structure of social influence, let us define the initial distribution of individual opinions and threshold values at the start of the process. To illustrate how this model can be applied in both cases, I examine diffusion dynamics on Bernoulli random graphs with varying network density and network asymmetry, and varying distributional assumptions for the vector of initial opinions p and individual thresholds v
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