I found the explanation at the point where you introduce b confusing.
Here’s a revised version of the text there that would have been less confusing to me (assuming I haven’t made any errors):
Complexity of simplest deceptive objective: l+b where l is the number of bits needed to select the part of the objective space which is just long term objectives and b is the additional number of bits required to select the most simple long run objective. In other words b is the minimum number of bits required to pick out a particular objective among all of the deceptive objects (aka the simplest one).
We’re assuming that a<l+b, but that l<a. That is, the measure of any long run objective is higher than the measure on the (simplest) aligned objective.
Casting into infinite bitstring land, we see that the set of aligned objectives includes those with anything after the first a bits, whereas the set of deceptive objectives includes anything after the first l bits (as all of these are long run objectives, though the differ). Even though you don’t get a full program until you’re l+b bits deep, the complexity here is just l, because all the bits after the first l bits aren’t pinned down. So if we’re assuming that l<a, then deception wins.
I found the explanation at the point where you introduce b confusing.
Here’s a revised version of the text there that would have been less confusing to me (assuming I haven’t made any errors):
Yep, I endorse that text as being equivalent to what I wrote; sorry if my language was a bit confusing.