# Friendship Paradox Biases Perceptions in Directed Networks

## TL;DR

This paper investigates how the friendship paradox in directed networks causes perceptions of popularity to differ from actual global popularity, affecting social behavior and enabling more efficient polling methods.

## Contribution

It identifies structural conditions causing perception bias in directed networks and introduces a polling algorithm leveraging this paradox for efficient global prevalence estimation.

## Key findings

- Perception bias arises from the friendship paradox in directed networks.
- The proposed polling algorithm improves estimation efficiency using network structure.
- Empirical validation on Twitter data confirms the theoretical insights.

## Abstract

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.