Universal size effects for populations in group-outcome decision-making problems

TL;DR

This paper uncovers universal size effects in group decision-making processes like elections, revealing hierarchical structures and proposing a model that explains participation patterns based on perceived social links.

Contribution

It identifies universal scaling laws in electoral participation and introduces a phenomenological model linking abstention to perceived social connectivity.

Findings

Universal size scaling observed in local elections and representation numbers

Hierarchical structure with subgroups scaling as N^{1/3}

Model reproduces empirical participation data quantitatively

Abstract

Elections constitute a paradigm of decision-making problems that have puzzled experts of different disciplines for decades. We study two decision-making problems, where groups make decisions that impact only themselves as a group. In both studied cases, participation in local elections and the number of democratic representatives at different scales (from local to national), we observe a universal scaling with the constituency size. These results may be interpreted as constituencies having a hierarchical structure, where each group of $N$ agents, at each level of the hierarchy, is divided in about $N^{\delta}$ subgroups with $\delta \approx 1/3$. Following this interpretation, we propose a phenomenological model of vote participation where abstention is related to the perceived link of an agent to the rest of the constituency and which reproduces quantitatively the observed data.