  Strategy changes are an essential part of evolutionary games. Here we
introduce a simple rule that, depending on the value of a single parameter $w$,
influences the selection of players that are considered as potential sources of
the new strategy. For positive $w$ players with high payoffs will be considered
more likely, while for negative $w$ the opposite holds. Setting $w$ equal to
zero returns the frequently adopted random selection of the opponent. We find
that increasing the probability of adopting the strategy from the fittest
player within reach, i.e. setting $w$ positive, promotes the evolution of
cooperation. The robustness of this observation is tested against different
levels of uncertainty in the strategy adoption process and for different
interaction network. Since the evolution to widespread defection is tightly
associated with cooperators having a lower fitness than defectors, the fact
that positive values of $w$ facilitate cooperation is quite surprising. We show
that the results can be explained by means of a negative feedback effect that
increases the vulnerability of defectors although initially increasing their
survivability. Moreover, we demonstrate that the introduction of $w$
effectively alters the interaction network and thus also the impact of
uncertainty by strategy adoptions on the evolution of cooperation.
