The Limits of Popularity-Based Recommendations, and the Role of Social Ties

TL;DR

This paper presents a mathematical model analyzing popularity-based recommender systems that leverage social ties, revealing how they influence market dynamics and user influence, supported by real-world social network experiments.

Contribution

Introduces a general mathematical model for popularity-based social recommender systems and analyzes their impact on market equilibrium and user influence.

Findings

Market always converges to a steady state under general conditions.

Social ties prevent large market distortions despite influential users.

Explicit form of the market's steady state is derived.

Abstract

In this paper we introduce a mathematical model that captures some of the salient features of recommender systems that are based on popularity and that try to exploit social ties among the users. We show that, under very general conditions, the market always converges to a steady state, for which we are able to give an explicit form. Thanks to this we can tell rather precisely how much a market is altered by a recommendation system, and determine the power of users to influence others. Our theoretical results are complemented by experiments with real world social networks showing that social graphs prevent large market distortions in spite of the presence of highly influential users.