Infrequent social interaction can accelerate the spread of a persuasive idea

We study the spread of a persuasive new idea through a population of continuous-time random walkers in one dimension. The idea spreads via social gatherings involving groups of nearby walkers who act according to a biased "majority rule": After each gathering, the group takes on the new idea if more than a critical fraction 1-ɛ/2<1/2 of them already hold it; otherwise they all reject it. The boundary of a domain where the new idea has taken hold expands as a traveling wave in the density of new idea holders. Our walkers move by Lévy motion, and we compute the wave velocity analytically as a function of the frequency of social gatherings and the exponent of the jump distribution. When this distribution is sufficiently heavy tailed, then, counter to intuition, the idea can propagate faster if social gatherings are held less frequently. When jumps are truncated, a critical gathering frequency can emerge which maximizes propagation velocity. We explore our model by simulation, confirming our analytical results.