  Based on a recent model of paradigm shifts by Bornholdt et al., we studied
mean-field opinion dynamics in an infinite population where an infinite number
of ideas compete simultaneously with their values publicly known. We found that
a highly innovative society is not characterized by heavy concentration in
highly valued ideas: Rather, ideas are more broadly distributed in a more
innovative society with faster progress, provided that the rate of adoption is
constant, which suggests a positive correlation between innovation and
technological disparity. Furthermore, the distribution is generally skewed in
such a way that the fraction of innovators is substantially smaller than has
been believed in conventional innovation-diffusion theory based on normality.
Thus, the typical adoption pattern is predicted to be asymmetric with slow
saturation in the ideal situation, which is compared with empirical data sets.
