Fig 5. The consensus distribution and consensus time in the CVM.

Numeric results confirm that these properties of the CVM depend only on m (defined in Eq 2), the initial strength of the red opinion. (In the plot, we have deliberately added jitter in the horizontal direction to make individual data points visible. Otherwise the overlap would obscure that there are multiple points on top of each other.) Each symbol shows the mean of 1000 simulations. All simulations use e = 1/4 and i = 1/16. N, c, and the initial conditions vary. (N is symbolized by the size, c by the shape, and the initial condition by the color; see legend.) (A) Proportion of simulations in which the red opinion wins (F) as a function of the initial strength of red [m(t = 0)]. The diagonal line indicates F = m. The overlapping symbols exemplify that simulations with different initial conditions produce the same F if the initial m is the same, despite different abundances of hypocrites. (B) The mean consensus time $T_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}^{\left(\mathrm{C}\mathrm{V}\mathrm{M}\right)}$ as a function of m. The gray curves are theoretical predictions from Eq 9, which is derived under the assumption that N is large [53]. The simulations confirm that Eq 9 is a good approximation even for moderately large N. For different N and c, the values of $T_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}^{\left(\mathrm{C}\mathrm{V}\mathrm{M}\right)}$ fall on different curves. However, for given N and c, $T_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}^{\left(\mathrm{C}\mathrm{V}\mathrm{M}\right)}$ depends only on m, but not on any further details of the initial conditions.