Cloture Votes:n/4-resilient Distributed Consensus in t + 1 rounds

The Distributed Consensus problem involves n processors each of which holds an initial binary value. At most t processors may be faulty and ignore any protocol (even behaving maliciously), yet it is required that the nonfaulty processors eventually agree on a value that was initially held by one of them. We measure the quality of a consensus protocol using the following parameters; total number of processors n, number of rounds of message exchange r, and maximal message size m. The known lower bounds are respectively 3 t + 1, t + 1, and 1. While no known protocol is optimal in all these three aspects simultaneously, Cloture Votes-the protocol presented in this paper-takes further steps in this direction, by making consensus possible with n = 4 t + 1, r = t + 1, and polynomial message size. Cloture is a parliamentary procedure (also known as "parliamentary guillotine") which makes it possible to curtail unnecessary long debates. In our protocol the unanimous will of the correct processors (akin to parliamentarian supermajority) may curtail the debate. This is facilitated by having the processors open in each round a new process (debate), which either ends quickly, with the conclusion "continue" or "terminate with the default value," or lasts through many rounds. Importantly, in the latter case the messages being sent are short.