  Studies of voluntary vaccination decisions by rational individuals predict
that the population will reach a Nash equilibrium with vaccination coverage
below the societal optimum. Human decision-making involves mechanisms in
addition to rational calculations of self-interest, such as imitation of
successful others. Previous research had shown that imitation alone cannot
achieve better results. Under realistic choices of the parameters it may lead
to equilibrium vaccination coverage even below the Nash equilibrium. However,
these findings rely on the widely accepted use of Fermi functions for modeling
the probabilities of switching to another strategy. We consider here a more
general functional form of the switching probabilities. It is consistent with
functions that give best fits for empirical data in a widely cited
psychological experiment and involves one additional parameter $\alpha$. This
parameter can be loosely interpreted as a degree of open-mindedness. We found
both by means of simulations and analytically that sufficiently high values of
$\alpha$ will drive the equilibrium vaccination coverage arbitrarily close to
the societal optimum.
