[adrian_b]

I think that it is for the president where this would be most beneficial.

For senators and representatives there still is a little randomness, but when I look at many presidents that have been elected in recent years in various countries, it is more than obvious that any randomly chosen individual would have been almost certainly a less bad human and more suitable for the presidential position.

After a president is chosen by lottery, there should be a rejection procedure, to eliminate any really inappropriate candidate, but then a new candidate should be chosen by lottery to replace the rejected one, until no reasons for rejection can be found.