I think you're off a bit though. There is a place for diligence at early VC stage, but it is almost entirely about the people.
That said, they could also just randomly choose without telling anyone and justify actions after the fact. But, as you might guess nobody who does that is going to say they did it that way.
The basic problem is if your going to randomly pick then why should I pay you anything?
PS: One fund did chose to fund every YC company which is close to a random choice.
Alternatively, a common approach when getting a lot of applications is to simply randomly look at half and ignore the other half unless you can't find enough good options.
So, in the real world you would be able to talk up various points. However, I don't think you can convince a politician to use your random methods unless he can sneak a few choices in.
http://www.npr.org/sections/money/2016/05/20/478883658/episo...