Byzantine Preferential Voting

TL;DR

This paper extends Byzantine agreement to preference rankings, proposing algorithms for consensus on rankings under Pareto-Validity and analyzing the Kemeny median's approximation limits in the presence of Byzantine nodes.

Contribution

It introduces a deterministic algorithm for Byzantine agreement on preference rankings with Pareto-Validity and establishes optimal approximation bounds for the Kemeny median under Byzantine faults.

Findings

Proposed a deterministic algorithm for ranking consensus with Pareto-Validity.

Derived a lower bound on the approximation ratio for the Kemeny median.

Provided an algorithm matching the lower bound, tolerating a constant fraction of Byzantine nodes.

Abstract

In the Byzantine agreement problem, n nodes with possibly different input values aim to reach agreement on a common value in the presence of t < n/3 Byzantine nodes which represent arbitrary failures in the system. This paper introduces a generalization of Byzantine agreement, where the input values of the nodes are preference rankings of three or more candidates. We show that consensus on preferences, which is an important question in social choice theory, complements already known results from Byzantine agreement. In addition preferential voting raises new questions about how to approximate consensus vectors. We propose a deterministic algorithm to solve Byzantine agreement on rankings under a generalized validity condition, which we call Pareto-Validity. These results are then extended by considering a special voting rule which chooses the Kemeny median as the consensus vector. For this rule, we derive a lower bound on the approximation ratio of the Kemeny median that can be guaranteed by any deterministic algorithm. We then provide an algorithm matching this lower bound. To our knowledge, this is the first non-trivial multi-dimensional approach which can tolerate a constant fraction of Byzantine nodes.