Byzantine Preferential Voting

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.

Blockchain and IoT Integration: A Systematic Survey

“…The consensus problem in BC, which is distributed and trustless, can be considered synonymous to Byzantine Generals Problem (BGP) [ 33 ]. The problem is formulated as how the generals can come to a common conclusion in the presence of a small number of traitors and miscommunications.…”

Exact Fault-Tolerant Consensus with Voting Validity

“…In [27], Chauhan et al first considered election in faulty distributed systems and drew preliminary conclusions about social choice and social welfare problems respectively, considering Byzantine faults. Then considering the social welfare problem, Melnyk et al proposed in [28] a deterministic algorithm to solve rankings under Pareto Validity. For the social choice problem, in [23], Fitzi et al proposed the concept of δ-differential consensus that requires the number of occurrences (i.e., plurality) of any other input value cannot exceed the plurality of the output by δ.…”

Robust Sparse Voting

“…For example, the algorithms proposed in [CG13,Tse17] yield the single winner of an election held in the presence of a fraction of Byzantine voters, using the plurality voting rule. Voters' rankings were used in [MWW18] to output an aggregated ranking leveraging the Kemeny rule [KS62], while verifying a correctness condition. Sparse unanimity (Property 1) is closely related to the correctness properties (i.e.…”