  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 $\frac{1-\varepsilon}{2} < \frac{1}{2}$ 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 L\'{e}vy 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.
