Long Ties Accelerate Noisy Threshold-based Contagions

77 Pages Posted: 22 Oct 2018 Last revised: 21 Aug 2023

See all articles by Dean Eckles

Dean Eckles

MIT Sloan School of Management

Elchanan Mossel

Massachusetts Institute of Technology (MIT)

M. Amin Rahimian

University of Pitttsburgh; Massachusetts Institute of Technology (MIT)

Subhabrata Sen

Massachusetts Institute of Technology (MIT)

Date Written: May 22, 2019

Abstract

Network structure can affect when and how widely new ideas, products, and behaviors are adopted. In widely-used models of biological contagion, interventions that randomly rewire edges (on average making them "longer") accelerate spread. However, there are other models relevant to social contagion, such as those motivated by myopic best-response in games with strategic complements, in which an individual's behavior is described by a threshold number (theta) of adopting neighbors above which adoption occurs (i.e., complex contagions). Recent work has argued that highly clustered, rather than random, networks facilitate spread of these complex contagions. Here we show that minor modifications to this model reverse this result, thereby harmonizing qualitative facts about how network structure affects contagion. To model the trade-off between long and short ties, we analyze the rate of spread over networks that are the union of circular lattices and random graphs on n nodes. Allowing for noise in adoption decisions (i.e., adoptions below threshold) to occur with order n^(-1/theta) probability along at least some "short" cycle edges is enough to ensure that random rewiring accelerates the spread of a noisy threshold-theta contagion. This conclusion also holds under partial but frequent enough rewiring and when adoption decisions are reversible but infrequently so, as well as in high-dimensional lattice structures that facilitate faster-expanding contagions. Simulations illustrate the robustness of these results to several variations on this noisy best-response behavior. Hypothetical interventions that randomly rewire existing edges or add random edges (versus adding "short"', triad-closing edges) in hundreds of empirical social networks reduce time to spread. This revised conclusion suggests that those wanting to increase spread should induce formation of long ties, rather than triad-closing ties. More generally, this highlights the importance of noise in game-theoretic analyses of behavior.

Keywords: social networks, game dynamics, social contagion

JEL Classification: D85, D83, C73

Suggested Citation

Eckles, Dean and Mossel, Elchanan and Rahimian, M. Amin and Sen, Subhabrata, Long Ties Accelerate Noisy Threshold-based Contagions (May 22, 2019). Available at SSRN: https://ssrn.com/abstract=3262749 or http://dx.doi.org/10.2139/ssrn.3262749

Dean Eckles

MIT Sloan School of Management ( email )

Elchanan Mossel

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

M. Amin Rahimian (Contact Author)

University of Pitttsburgh ( email )

135 N Bellefield Ave
Pittsburgh, PA 15260
United States

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Subhabrata Sen

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

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