Given the prohibitive costs associated with Vaults, most were built at government expense for the experiments. People were probably selected randomly in order to have a good sampling for proper science. But I wouldn't be surprised if they used non-random sampling in an effort to try to improve their results. They don't seem the type to do the tests properly, anyway.
I dont think vault construction was really as expensive as depicted. In current US dollars they would cost equivalent of about $50-60 billion (all dollars stated are from this point adjusted for inflation (approximate) ).
Some comparisons (to real world military/govt bunkers):
Project Greek Island at Greenbriar hotel, finished in the 60s, cost $105 million and could house 1000 people for 40 days and had 112k sq feet.
Mount Weather, finished in the 50s, cost $1 billion and had 600k sq feet .. .
A standard vault level has 20k square feet. From what I can find in drawings, maps and diagrams a typical vault has 8-12 levels. So its about twice the size of the Greenbriar bunker at 200-300k square feet. By that estimation a vault likely truly cost less than a billion each.
My guess is that Vault-Tec purposefully over-inflated the cost for Vault construction to cover the costs associated with secret enclave research and development into other projects like their space program, the oil rig, and military projects.