The Pitman-Yor process and an empirical study of choice behavior

TL;DR

This paper models choice behavior using a voting system influenced by recent votes, deriving the Pitman sampling formula as an equilibrium, and applies it to analyze user posting behavior on online bulletin boards.

Contribution

It introduces a voting model with finite memory that explains choice dynamics and derives the Pitman sampling formula as its equilibrium distribution.

Findings

The model accurately describes posting behavior on bulletin boards.

Choice dynamics depend on the last r posts and their distribution.

The Pitman sampling formula emerges as the equilibrium distribution.

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.