# The performance guarantee of randomized perfect voting trees

## TL;DR

This paper investigates the limitations of randomized voting trees in providing performance guarantees, showing that uniformly random trees cannot achieve guarantees linear in the number of individuals, and explores connections to Volterra quadratic stochastic operators.

## Contribution

It demonstrates the limitations of uniformly random voting trees and explores their connection to Volterra quadratic stochastic operators.

## Key findings

- Uniformly random voting trees cannot guarantee linear performance.
- Connections established between voting trees and Volterra quadratic stochastic operators.
- Provides insights into the theoretical bounds of randomized voting structures.

## Abstract

In this note we study randomized voting trees, previously introduced by Fisher, Procaccia and Samorodnitsky. They speculate that a non-trivial performance guarantee may be achievable using randomized, balanced trees whose height is carefully chosen. We explore some connections to the so-called Volterra quadratic stochastic operators, and show that uniformly random voting trees cannot provide a performance guarantee that is linear in the number of individuals.