Pairwise similarity method for majority domination problem

TL;DR

This paper introduces heuristic algorithms based on pairwise comparisons to efficiently solve the majority domination problem in two-level voting systems, extending polynomial methods to broader cases.

Contribution

It develops new heuristic algorithms for the majority domination problem tailored to different agent communication graph structures, with accuracy guarantees.

Findings

Algorithms work efficiently for tree, complete, and regular graphs.

Provides criteria for selecting optimal algorithms in post-processing.

Extends polynomial algorithms to more complex voting scenarios.

Abstract

The paper considers the problem of finding the number of dominant voters in two-level voting procedures. At the first stage, voting is conducted among local groups of voters, and at the second stage, the results are aggregated to form a final decision. The goal is to determine the minimum proportion of voters supporting a proposal for it to be accepted. The paper uses the method of pairwise comparisons to analyze the structure of the problem and develop heuristic algorithms with guaranteed accuracy. Special cases are considered, including the agent communication graph as a tree, complete graph, or regular graph with an odd number of vertices. New heuristic algorithms are proposed for each case, along with pairwise comparison functions to estimate the accuracy of the solution. Results extend the use of polynomial algorithms to a broader class of problems, providing criteria for selecting the optimal algorithm during the post-processing stage.