Connecting Arrow's Theorem, voting theory, and the traveling salesperson problem

TL;DR

This paper reveals a surprising connection between Arrow's Theorem, voting theory, and the Traveling Salesperson Problem, showing how they share underlying structures and can be simplified using the Borda Count to reflect preferences accurately.

Contribution

It establishes a novel link between voting theory and combinatorial optimization, demonstrating how the Borda Count can unify these seemingly disparate problems.

Findings

Arrow's Theorem and TSP share a common domain.

The Borda Count effectively reflects voter preferences.

Simplification to complementary regions eliminates extraneous terms.

Abstract

Problems with majority voting over pairs as represented by Arrow's Theoremand those of finding the lengths of closed paths as captured by the Traveling Salesperson Problem (TSP) appear to have nothing in common. In fact, they are connected. As shown, pairwise voting and a version of the TSP share the same domain where each system can be simplified by restricting it to complementary regions to eliminate extraneous terms. Central for doing so is the Borda Count, where it is shown that its outcome most accurately refects the voter preferences.