Persistent Homology Meets Behavioral Economics: Topological Analysis of Rationality and Anomaly in Human Decision Networks

Inspired by the interdisciplinary applications in Heo & Jung (2024) and the underexplored power of PH in social sciences, this idea seeks to bring persistent homology into behavioral economics. Imagine representing networks of human choices (from survey data or market transactions) as evolving graphs, then using PH to detect "topological anomalies"—loops or holes that correspond to cycles of irrational behavior, market bubbles, or systemic biases. Unlike Pietrosanu (2016), who applied PH to linguistic networks, this project would focus on economic and psychological data, potentially linking topological features to well-known paradoxes such as preference reversals or information cascades. The novelty is in providing a quantifiable, geometric language for phenomena that have previously been described only qualitatively. If successful, this could introduce a new class of behavioral indicators for economists and policymakers.

References:

1. Persistent homology of featured time series data and its applications. Eunwoo Heo, Jae-Hun Jung (2024). AIMS Mathematics.
2. The analysis of topological structure in data using persistent homology: applications to lexical word association networks. M. Pietrosanu (2016).