Fait Accompli Committee Selection: Improving the size-security tradeoff of stake-based committees

We study the problem of committee selection in the context of proof-of-stake consensus mechanisms or distributed ledgers. These settings determine a family of participating parties-each of which has been assigned a non-negative “stake”-and are subject to an adversary that may corrupt a subset of the parties. The challenge is to select a committee of participants that accurately reflects the proportion of corrupt and honest parties, as measured by stake, in the full population. The trade-off between committee size and the probability of selecting a committee that over-represents the corrupt parties is a fundamental factor in both security and efficiency of proof-of-stake consensus, as well as committee-run layer-two protocols. We propose and analyze several new committee selection schemes that improve upon existing techniques by adopting low-variance assignment of certain committee members that hold significant stake. These schemes provide notable improvements to the size-security trade-off arising from the stake distributions of many deployed ledgers.