  As one of the classic models that describe the belief dynamics over social
networks, a non-Bayesian social learning model assumes that members in the
network possess accurate signal knowledge through the process of Bayesian
inference. In order to make the non-Bayesian social learning model more
applicable to human and animal societies, this paper extended this model by
assuming the existence of private signal structure bias. Each social member in
each time step uses an imperfect signal knowledge to form its Bayesian part
belief and then incorporates its neighbors' beliefs into this Bayesian part
belief to form a new belief report. First, we investigated the intrinsic
learning ability of an isolated agent and deduced the conditions that the
signal structure needs to satisfy for this isolated agent to make an eventually
correct decision. According to these conditions, agents' signal structures were
further divided into three different types, "conservative," "radical," and
"negative." Then, we switched the context from isolated agents to a connected
network; our propositions and simulations show that the conservative agents are
the dominant force for the social network to learn the real state, while the
other two types might prevent the network from successful learning. Although
fragilities do exist in non-Bayesian social learning mechanism, "be more
conservative" and "avoid overconfidence" could be effective strategies for each
agent in the real social networks to collectively improve social learning
processes and results.
