Whether it is about choosing a party to vote for, deciding whether to adopt an innovation, selecting music to listen to, or which social media application to use, people tend to select options that many other people have selected before them. This creates a feedback loop in which popular options tend to become even more popular, potentially leading suboptimal options to become dominant while inhibiting the adoption of better alternatives, a phenomenon known as “lock-in”. Although such rich-get-richer dynamics and the occurrence of lock-in have traditionally been assumed to be ubiquitous in the social world, the experimental evidence is mixed, suggesting that at least in certain settings the macro-consequences of social influence might be much more limited than previously thought.
In this talk I will introduce two distinct mathematical frameworks for studying the long-term dynamics of popularity and the possibility of lock-in when individual choices are affected by other people's choices. The first framework is a generalized Pólya urn, first introduced by Hill, Lane, and Sudderth (1980), and I will show how it can be used to study the possibility of lock-in in binary choice. Using this framework, we find that lock-in is much more likely in the presence of a behavioral phenomenon that we term “the marginal majority effect”, in which people’s choices are disproportionately affected by small popularity differences between two options. We present experimental evidence that such marginal majority effects exist and that they predict the possibility of lock-in.
The second framework I will introduce is new, and it is suitable for studying the dynamics of popularity rankings, such as those often present in search engines, recommendation systems, and social media. We find conditions under which the popularity ranking converges as the number of users grows, and we characterize the possible rankings in the limit. The results can be generalized beyond popularity rankings, to study the long-term behavior of arbitrary ranking systems, when the (stochastic) dynamics are purely ranking-driven.
