  Motivated by online reputation systems, we investigate social learning in a
network where agents interact on a time dependent graph to estimate an
underlying state of nature. Agents record their own private observations, then
update their private beliefs about the state of nature using Bayes' rule. Based
on their belief, each agent then chooses an action (rating) from a finite set
and transmits this action over the social network. An important consequence of
such social learning over a network is the ruinous multiple re-use of
information known as data incest (or mis-information propagation). In this
paper, the data incest management problem in social learning context is
formulated on a directed acyclic graph. We give necessary and sufficient
conditions on the graph topology of social interactions to eliminate data
incest. A data incest removal algorithm is proposed such that the public belief
of social learning (and hence the actions of agents) is not affected by data
incest propagation. This results in an online reputation system with a higher
trust rating. Numerical examples are provided to illustrate the performance of
the proposed optimal data incest removal algorithm.
