Thanks @saguillo2000!
In this proposal, we assume validators will get selected to be part of the IL committee randomly and independently of their stake.
It would use RANDAO (see Upgrading Ethereum | 2.9.2 Randomness) as a source of randomness, which is already used to select proposers and assign validators to committees. It is known to be bias-able to some extent, but it’s been studied extensively and would be easy to detect.