Ranked Pairs minimizes the $p$-norm as $p \to \infty$

TL;DR

This paper proves that the Ranked Pairs voting method minimizes the maximum (infinite-norm) of the worst head-to-head margins of victory that oppose its candidate ordering, as p approaches infinity.

Contribution

It establishes a theoretical property of Ranked Pairs, showing it minimizes the p-norm of opposing margins in the limit as p approaches infinity.

Findings

Ranked Pairs minimizes the p-norm of opposing margins as p approaches infinity.

The proof provides a new theoretical understanding of Ranked Pairs' optimality.

This result characterizes Ranked Pairs' behavior in terms of margin minimization.

Abstract

We prove that Ranked Pairs orders candidates in such a way as to minimize the $p$-norm, in the limit as $p \to \infty$, of those head-to-head margins of victory which go against its ordering.