  How popular a topic or an opinion appears to be in a network can be very
different from its actual popularity. For example, in an online network of a
social media platform, the number of people who mention a topic in their
posts---i.e., its global popularity---can be dramatically different from how
people see it in their social feeds---i.e., its perceived popularity---where
the feeds aggregate their friends' posts. We trace the origin of this
discrepancy to the friendship paradox in directed networks, which states that
people are less popular than their friends (or followers) are, on average. We
identify conditions on network structure that give rise to this perception
bias, and validate the findings empirically using data from Twitter. Within
messages posted by Twitter users in our sample, we identify topics that appear
more frequently within the users' social feeds, than they do globally, i.e.,
among all posts. In addition, we present a polling algorithm that leverages the
friendship paradox to obtain a statistically efficient estimate of a topic's
global prevalence from biased perceptions of individuals. We characterize the
bias of the polling estimate, provide an upper bound for its variance, and
validate the algorithm's efficiency through synthetic polling experiments on
our Twitter data. Our paper elucidates the non-intuitive ways in which the
structure of directed networks can distort social perceptions and resulting
behaviors.
