At least when you fail to not eat cake, you notice.
It's true that people don't always notice but at least some of the time biases do end up smashing against reality (like the two examples I gave here).
albeit with great difficulty, but bias can't simply be willed away.
I think Luke has given us reason to think they can be, although my point was that even if we know how to avoid biases, will we? Are we like fat people avoiding cake?
There's a big difference between being able to train biases away and being able to will them away.
When you try to cut something out of your diet, you have a conflict between your urge to eat it and your desire to avoid it, which comes down to a battle of willpower unless you engineer your life to make the resolution easier. A fat person confronted with cake they have resolved not to eat knows that they will regret eating it, and with sufficient willpower, can resist.
When dealing with cognitive bias, on the other hand, the hard part is usually noticing you'...
An example of real world problems from cognitive biases:
Forensic science - Ignorance is bliss
Hat-tip to Bruce Schneier.