  Increased interest in scalable and high-throughput blockchains has led to an
explosion in the number of committee selection methods in the literature.
Committee selection mechanisms allow consensus protocols to safely select a
committee, or a small subset of validators that is permitted to vote and verify
a block of transactions, in a distributed ledger. There are many such
mechanisms, each with substantially different methodologies and guarantees on
communication complexity, resource usage, and fairness. In this paper, we
illustrate that, despite these implementation-level differences, there are
strong statistical similarities between committee selection mechanisms. We
concretely show this by proving that the committee selection of the Avalanche
consensus protocol can be used to choose committees in the Stellar Consensus
Protocol that satisfy the necessary and sufficient conditions for Byzantine
agreement. We also verify these claims using simulations and numerically
observe sharp phase transitions as a function of protocol parameters. Our
results suggest the existence of a "statistical taxonomy" of committee
selection mechanisms in distributed consensus algorithms.
