Equivalence of Connected and Peak-Pit Maximal Condorcet Domains

TL;DR

This paper proves that three different classes of maximal Condorcet domains—peak-pit, connected, and directly connected—are mathematically equivalent through a combinatorial proof, clarifying their relationship.

Contribution

It establishes the equivalence of peak-pit, connected, and directly connected maximal Condorcet domains using combinatorial methods, resolving a key theoretical question.

Findings

Proves the equivalence of three classes of Condorcet domains

Provides a combinatorial proof for the equivalence

Clarifies the structure of maximal Condorcet domains

Abstract

This paper provides a combinatorial proof to show that, in the study of maximal Condorcet domains, the class of peak-pit Condorcet domains, the class of connected Condorcet domains, and the class of directly connected Condorcet domains are all equivalent.