Can I just dig in on that? The system you're describing, though, is based on something in relation to median price. It's not based on any objective evaluation. In some cases you could say this is obviously a price that's suspiciously low for whatever reason. You can imagine if that happens.
However, if it's based on median price, and if I'm bidding, I have to worry—and it's within the narrow band that you described—that if I offer the best price, and it happens to be just a little bit lower than what everybody else is offering, I'm going to be penalized for being able to provide the best product at the lowest price.
I have to be increasing my price in order to ensure that I don't fall below. I have no awareness of what prices the other suppliers are putting in. That creates a system, since it's based on median price, in which everybody is going to be bidding higher than they would otherwise, because they're afraid of falling below. If you have five people bidding, and you want to make sure you're not too far below where everybody else is, you're going to bid higher. The basic economics tells us that everybody is then going to be driving up the price.
That's just going to exert significant continuous upward pressure on the price, given how this is designed. It seems so obviously crazy, and it seems like it's an excuse, not a reason. It seems there would be plenty of other ways of solving the problem that you suggest.