Committee Selection with Non-Proportional Weights

Committees are extensively used in the designs of various Proof-of-Stake (PoS) blockchains. A committee is simply a randomly selected subset of the parties/nodes in the system. Ideally, the committee should i) be as small as possible, and ii) properly represent the entire system, in terms of the corruption ratio. Existing committee selection schemes all follow the principle of proportionality, which says that a committee member should neither over-represent nor under-represent the stake it holds.