The Pitman–Yor Process and an Empirical Study of Choice Behavior

Abstract

This study discusses choice behavior using a voting model in which voters can obtain information from a finite number of previous $r$ voters. Voters vote for a candidate with a probability proportional to the previous vote ratio, which is visible to the voters. We obtain the Pitman sampling formula as the equilibrium distribution of $r$ votes. We present the model as a process of posting on a bulletin board system, 2ch.net, where users can choose one of many threads to create a post. We explore how this choice depends on the last $r$ posts and the distribution of these last $r$ posts across threads. We conclude that the posting process is described by our voting model with analog herders for a small $r$, which might correspond to the time horizon of users' responses.