  A vast body of experiments share the view that social norms are major factors
for the emergence of fairness in a population of individuals playing the
dictator game (DG). Recently, to explore which social norms are conducive to
sustaining cooperation has obtained considerable concern. However, thus far few
studies have investigated how social norms influence the evolution of fairness
by means of indirect reciprocity. In this study, we propose an indirect
reciprocal model of the DG and consider that an individual can be assigned as
the dictator due to its good reputation. We investigate the `leading eight'
norms and all second-order social norms by a two-timescale theoretical
analysis. We show that when role assignment is based on reputation, four of the
`leading eight' norms, including stern judging and simple standing, lead to a
high level of fairness, which increases with the selection intensity. Our work
also reveals that not only the correct treatment of making a fair split with
good recipients but also distinguishing unjustified unfair split from justified
unfair split matters in elevating the level of fairness.
