it is a general rule that each doubling tends to bring about the same increase in capability.

This rule smells awfully like a product of positive/confirmation bias to me.

Did you pre-select a wide range of various endeavours and projects and afterwards analysed their rate of progress, thus isolating this common pattern;

or did you notice a similarity between a couple of diminishing-returns phaenomena, and then kept coming up with more examples?

My guess is strongly on the latter.