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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.
Traditional techniques for handling Byzantine failures are expensive: digital signatures are too costly, while using $3f{+}1$ replicas is uneconomical ($f$ denotes the maximum number of Byzantine processes). We seek algorithms that reduce the number
The growth of data, the need for scalability and the complexity of models used in modern machine learning calls for distributed implementations. Yet, as of today, distributed machine learning frameworks have largely ignored the possibility of arbitra
We present new protocols for Byzantine state machine replication and Byzantine agreement in the synchronous and authenticated setting. The celebrated PBFT state machine replication protocol tolerates $f$ Byzantine faults in an asynchronous setting us
Consider a distributed system with $n$ processors out of which $f$ can be Byzantine faulty. In the approximate agreement task, each processor $i$ receives an input value $x_i$ and has to decide on an output value $y_i$ such that - the output values
The Byzantine agreement problem requires a set of $n$ processes to agree on a value sent by a transmitter, despite a subset of $b$ processes behaving in an arbitrary, i.e. Byzantine, manner and sending corrupted messages to all processes in the syste