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Experimental evidence for tipping points in social convention

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Science  08 Jun 2018:
Vol. 360, Issue 6393, pp. 1116-1119
DOI: 10.1126/science.aas8827
  • Fig. 1 Predicted tipping points in social stability.

    (A) Theoretical modeling of the proportion of outcomes in which the alternative behavior is adopted by 100% of the population. In this system, the number of agents (N) = 1000, the number of interactions (T) = 1000, the number of past interactions used in agent decisions (M) = 12. (B) The size of the predicted critical mass point is shown as a function of individuals’ average memory length, M, where (N = 1000, T = 1000). The dashed lines indicate the range enclosed by our experimental trials, showing the largest unsuccessful minority (21%) and the smallest successful minority (25%). Although the expected size of the critical mass point increases with M, this relationship is concave, allowing the predicted tipping point to remain well below 50% as M gets large (>100). (Inset) Effect of increasing population size on the precision of the size of the committed minority (C) prediction (M = 12, T = 1000). For N < 1000, small variations in the predicted tipping point emerge due to stochastic variations in individual behavior. Shaded region indicates C sizes where success was observed frequently but without certainty. Above this region, for larger C sizes, the probability of success reaches 1; for C sizes below this region, the likelihood of success goes to 0.

  • Fig. 2 Time series showing adoption of the alternative convention by noncommitted subjects (i.e., experimental subjects).

    Gray lines indicate the popularity of the established convention; black lines show the adoption of the alternative convention. Success was achieved when more than 50% of the noncommitted population adopted the new social convention. Trials in the left column show failed mobilization, whereas trials in the right column show successful mobilization. A transition in the collective dynamics happens when C reaches ~25% of the population. Each round is measured as N/2 pairwise interactions, such that each player has one interaction per round on average.

  • Fig. 3 Final success levels from all trials (gray points indicate trials with C < 25%; black points indicate trials with C ≥ 25%.

    Also shown is the theoretically predicted critical mass point (solid line) with 95% confidence intervals (N = 24, T = 45, M = 12; gray area indicates 95% confidence intervals from 1000 replications). The dotted line indicates C = 25%. The theoretical model of critical mass provides a good approximation of the empirical findings. For short time periods (T < 100 interactions), the critical mass prediction is not exact (ranging from 20% < C < 30% of the population); however, over longer time periods (T > 1000) the transition dynamics become more precise (solid line, 25).

Supplementary Materials

  • Experimental evidence for tipping points in social convention

    Damon Centola, Joshua Becker, Devon Brackbill, and Andrea Baronchelli

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