I cannot think too much right now (in routing algorithms), but the general principle of the randomness is good and valid, this evens out over time to product stunningly accurate results. Perhaps I can add in a couple of algorithms to throw into this mix, first we have IDA (information Dispersal) and secret sharing. These help with this kind of thinking (both are in SAFE).
IDA (Rabin - Information Dispersal)-> splits up data into N of P (N == number of shares, P == parts required to make up N). Its relatively efficient and the data/P is pretty close to efficient (similar to how RAID works). It is not secret though.
Secret Sharing (Shamir) → Here you have a similar N of P mechanism, but it is secret, that is to say that if you get P - 1 parts then you cannot deduce anything of the original data (unlike IDA where you have a chance). It is not space efficient as each P is approx equal to the whole data size.
Perhaps your ideas can be honed a little if somehow groups were to come together, but had to recreate a crypto key for instance that proved they were real, or perhaps each person who does stay gets another P (part). In IDA for instance you can add more shares at any time. Then the owner can give another share to all who stay as proof of staying or voting etc.
Just random thoughts to throw in some more possibilities for your ideas, hope you don’t mind.