Testing a Graph-Theoretic Condition for Aggregating Incomplete Rankings: A Technical Note

TL;DR

This paper demonstrates an efficient graph-theoretic method to test a specific condition for aggregating incomplete rankings and provides an implementation of Okumura's mechanism.

Contribution

It introduces a computationally efficient way to test a ranking aggregation condition and details an implementation of Okumura's mechanism.

Findings

Condition 1 can be tested efficiently with a standard graph algorithm.

Provides an efficient implementation of Okumura's mechanism.

Facilitates practical application of ranking aggregation methods.

Abstract

This note shows how Condition 1 in Okumura (2025) can be tested efficiently using a standard graph-theoretic algorithm. It also describes an efficient implementation of Okumura's mechanism.