Discussion
Why is a utility function determined only up to a linear transformation?
Answer: B
Adding a constant or multiplying by a positive number leaves every comparison of expected utilities unchanged, so the scale carries no meaning beyond the ordering and the relative sizes of differences. Arbitrary transformations would change decisions, and normalisation is a convention. Knowing which transformations leave a quantity's meaning intact tells you exactly how much information it carries, which is a useful check on any numerical measure.
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