The Mathematics of Superstars: Two Theories of Cultural Consumption

• In Event: 425 - Regular Session. Mathematical Sociology

Abstract

The popularity of cultural objects such as music recordings, baby names, or novels is characterized by a large number of relatively unpopular “flops” as well as a few superstars that are several orders of magnitude more popular than the average. Despite these large ex post differences in popularity, ex ante it is very difficult to predict which objects will become hits, and which will flop. Scholars have proposed two major theories about the mechanisms leading to these outcomes. The first is based on cumulative advantage (CA), or rich-get-richer processes, wherein the success of cultural objects breeds future success. The other is based on convex returns (CR) and suggests that small differences in the talent of artists, or qualities of cultural objects, lead to large differences in popularity. I study mathematical models of both CA and CR processes, and derive their distributional implications. I first validate these models on experimental data from Salganik’s Music Lab project. I then apply the models to the distribution of US baby girls names, showing that CR is a better fit to those data. I end with a discussion on the models’ implications for theories of cultural consumption.
*This paper has won "best graduate student" paper awards from the ASA sections on Culture, Mathematical, and Rationality & Society

Author

• Charles F. Seguin, University of North Carolina-Chapel Hill