"A very fast, simple solution that is 2% correct is an unacceptable balance."
That begs the question (in the original sense) of "unacceptable". If I banged out that 2% solution in an hour, and it lacked other costs that outweighed the benefits, it may still be something we ship! It is unlikely that we'd stop there, just because the numbers as you've given are unlikely to favor it because something else substantial would have to overcome the small amount of the problem we've solved, but to be firmly confident it's "unacceptable" you'd have to define "acceptable" a lot more carefully.
I understand the deep temptation to turn to discussions of the virtues of letting bugs through or something, but the costs/benefits framework completely handles that already. If you ship a buggy piece of "incorrect" shit, well, you've incurred a ton of costs with no benefits. That's wrong, by whatever standards you are measuring costs and benefits by. There isn't a "what if your 98% solution actually has a massive bug in it because you were unconcerned about 'correctness'?" argument to be made, because if it does have a massive bug, it's not a 98% solution.
That begs the question (in the original sense) of "unacceptable". If I banged out that 2% solution in an hour, and it lacked other costs that outweighed the benefits, it may still be something we ship! It is unlikely that we'd stop there, just because the numbers as you've given are unlikely to favor it because something else substantial would have to overcome the small amount of the problem we've solved, but to be firmly confident it's "unacceptable" you'd have to define "acceptable" a lot more carefully.
I understand the deep temptation to turn to discussions of the virtues of letting bugs through or something, but the costs/benefits framework completely handles that already. If you ship a buggy piece of "incorrect" shit, well, you've incurred a ton of costs with no benefits. That's wrong, by whatever standards you are measuring costs and benefits by. There isn't a "what if your 98% solution actually has a massive bug in it because you were unconcerned about 'correctness'?" argument to be made, because if it does have a massive bug, it's not a 98% solution.