It is commonly said there can be three things, A, A+ and B, such that A+ is not better than B and B is not better than A, but A+ is better than A. This is said to be the identifying characteristic of incommensurateness. I doubt it is true.
Instead, I think incommensurateness is a sort of vagueness. I once argued for this conclusion on the basis of an intuitively attractive claim I called ‘the collapsing principle’. Since the collapsing principle has not been universally acclaimed, I now argue on different grounds for the conclusion that incommensurateness is vagueness.
The common view does not give adequate credit to our intuitions about incommensurateness and its normative implications. For example, if A+ is better than B, then A+ is more better than B than A is. If it is permissible to choose A in a choice between A and B, it is more permissible to choose A+ in a choice between A+ and B. Suppose you have A+; something goes wrong if you swap A+ for B and then swap B for A, so you end up with A. And so on. Recognizing that incommensurateness is vagueness gives a better account of these matters. It also better explains the worrisome nature of incommensurateness in practice.