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thomblake comments on You cannot be mistaken about (not) wanting to wirehead - Less Wrong
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If you take a utility function and multiply all the utilities by 0.01, is it the same utility function? In one sense it is, but by your measure it will always win a "most pessimistic" contest.
Update: thinking about this further, if the only allowable operations on utilities are comparison and weighted sum, then you can multiply by any positive constant or add and subtract any constant and preserve isomorphism. Is there a name for this mathematical object?
A utility function is just a representation of preference ordering. Presumably those properties would hold for anything that is merely an ordering making use of numbers.
You also need the conditions of the utility theorem to hold. A preference ordering only gives you conditions 1 and 2 of the theorem as stated in the link.
Good point. I was effectively entirely leaving out the "mathematical" in "mathematical representation of preference ordering". As I stated it, you couldn't expect to aggregate utiles.
You can't aggregate utils; you can only take their weighted sums. You can aggregate changes in utils though.