[xn]

Then you know that it's going to take at least, say two weeks, one week for the first implementation and a week to finish it if it works.

On the high end, could it take more than 2 years? 1 year? 6 months? Stop when you are 80% confident that it won't take longer than some period.

So your estimate might be between two weeks and six months. Is that an acceptable estimate for the "buyer"? If not, is it worth expending effort to narrow the estimate?

[n4r9]

Yes, this is basically what happens. Except sometimes there's no realistic way to narrow the estimate. In research-focused teams you don't "scrap" a project that you can't break down. Instead you need to have a way to manage wide estimate windows.