Minimal Stable Voting Rules

TL;DR

This paper characterizes minimal stable voting rules and constitutions focusing on power dynamics, revealing that such stable structures are limited and that political parties have evolved to maintain minimal self-stability.

Contribution

It introduces simple notions of minimal stability and shows that the families of such rules and constitutions are small, providing insights into power-based voting systems.

Findings

Families of minimal stable voting rules are small

Political parties evolve to ensure minimal self-stability

Power-focused voting rules can be characterized mathematically

Abstract

In this paper, I characterize minimal stable voting rules and minimal self-stable constitutions (i.e., pairs of voting rules) for societies in which only power matters. To do so, I first let players' preference profiles over voting rules satisfy four natural axioms commonly used in the analysis of power: non-dominance, anonymity, null player and swing player. I then provide simple notions of minimal stability and minimal self-stability, and show that the families of minimal stable voting rules and minimal self-stable constitutions are fairly small. Finally, I conclude that political parties have evolved to ensure the minimal self-stability of otherwise not minimal self-stable constitutions.