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calef comments on No independence of irrelevant alternatives (picture proof) - Less Wrong
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Comments (24)
Why does IIA allow you to rescale the two utility axes using different scaling functions?
I think this is a feature of utility functions rather than the IIA assumption; they are unique up to a scaling and offset (positive affine transformation). See this wikipedia article for more. The intuition is that, adding an offset to the whole function, or rescaling it does change the relative comparisons of different points on that function and thus doesn't change the choices for an agent with that utility function.
Assumption that there is no canonical scales for the utility functions.