  In social systems subject to indirect reciprocity, a positive reputation is
key for increasing one's likelihood of future positive interactions. The flow
of gossip can amplify the impact of a person's actions on their reputation
depending on how widely it spreads across the social network, which leads to a
percolation problem. To quantify this notion, we calculate the expected number
of individuals, the "audience", who find out about a particular interaction.
For a potential donor, a larger audience constitutes higher reputational
stakes, and thus a higher incentive, to perform "good" actions in line with
current social norms. For a receiver, a larger audience therefore increases the
trust that the partner will be cooperative. This idea can be used for an
algorithm that generates social networks, which we call trust based attachment
(TBA). TBA produces graphs that share crucial quantitative properties with
real-world networks, such as high clustering, small-world behavior, and power
law degree distributions. We also show that TBA can be approximated by simple
friend-of-friend routines based on triadic closure, which are known to be
highly effective at generating realistic social network structures. Therefore,
our work provides a new justification for triadic closure in social contexts
based on notions of trust, gossip, and social information spread. These factors
are thus identified as potential significant influences on how humans form
social ties.
