The way it would likely work is that a cryptographically secure open source random algorithm is made known long in advance which takes, say, a full hour to run on top of the line computers. In the hour before it is run, anyone can send in a number of their choosing, which are all added up (or rather their concatenation is cryptographically hashed) to make the seed. Then anyone can check that their number was indeed included and run the algorithm themselves to verify. It really only takes a single honest person to send in a 20-digit number to make it basically impossible to manipulate. Maybe I'm missing something.
One way to resolve the issue is to use a distributed randomness generator like DRand which is threshold decryption based and hence can offer some robustness as well.
Why take random samples if you tell your citizens that everyone has a vote? How do you proof it was random, and what do you do if by random chance you got a really on sided group? Sorry we have now a fascist state but it was random so it's fair.
