In this study, I present a theoretical social learning model to investigate how confirmation bias affects opinions when agents exchange information over a social network. Hence, besides exchanging opinions with friends, agents observe a public sequence of potentially ambiguous signals and interpret it according to a rule that includes confirmation bias. First, this study shows that regardless of level of ambiguity both for people or networked society, only two types of opinions can be formed, and both are biased. However, one opinion type is less biased than the other depending on the state of the world. The size of both biases depends on the ambiguity level and relative magnitude of the state and confirmation biases. Hence, long-run learning is not attained even when people impartially interpret ambiguity. Finally, analytically confirming the probability of emergence of the less-biased consensus when people are connected and have different priors is difficult. Hence, I used simulations to analyze its determinants and found three main results: i) some network topologies are more conducive to consensus efficiency, ii) some degree of partisanship enhances consensus efficiency even under confirmation bias and iii) open-mindedness (i.e. when partisans agree to exchange opinions with opposing partisans) might inhibit efficiency in some cases.