  Decent social fairness is highly desired both for socio-economic activities
and individuals, as it is one of the cornerstones of our social welfare and
sustainability. How to effectively promote the level of fairness thus becomes a
significant issue to be addressed. Here, by adopting a pinning control
procedure, we find that when a very small fraction of individuals are pinned to
be fair players in the Ultimatum Game, the whole population unexpectedly
evolves into the full fairness level. The basic observations are quite robust
in homogeneous networks, but the converging time as a function of the pinning
number shows different laws for different underlying topologies. For
heterogeneous networks, this leverage effect is even more pronounced that one
hub node is sufficient for the aim, and a periodic on-off control procedure can
be applied to further save the control cost. Intermittent failures are seen
when the pinning control is marginally strong, our statistical analysis
indicates some sort of criticality. Our work suggests that the pinning control
procedure could potentially be a good strategy to promote the social fairness
for some real scenarios when necessary.
