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Oh, OK then!
Yes, but "we want to use calculus to solve this" isn't a very natural constraint on the set of orderings. :) It's a "we want to make the math easier" constraint, not a "we have reason to believe that any rational agent should act this way" constraint.
Not that it's necessarily inappropriate in the example you give -- it probably makes sense there. Just a bit surprising that UDT would restrict itself in such a way.
2*40 degrees = 80 degrees
2*40 degrees = 80 degrees
Except 2*40 degrees isn't 80 degrees; the operation "2*40 degrees" is simply meaningless in the first place. (I mean, unless that's a temperature difference of 40 degrees.)
(I mean, OK, you can strictly speaking double a temperature, but in order to do so you need to know what absolute zero is.)
An advantage of using Fahrenheit -- the zero is clearly arbitrary! :)
Again, individual utility numbers are not meaningful.
I'm not sure which "situations and arguments" you're saying this still allows. It doesn't allow the divergent sum that started all this.
That's true. People don't seem to mess those up as often as "utils". I wonder why?
Hypothesis: For energy and voltage, it's becaue these are mostly only used by people who know what they're talking about in the first place. For time, it's because we usually measure time as "12:00", etc.; the only people saying "the time is 5 seconds" are people who know what they're doing.
...except that explanation doesn't quite work, because it doesn't explain years. But then, with years we usually use a bare number... hm, this is sounding pretty contrived.
Better hypothesis: Time is familiar enough that people know not to do that, utility isn't.
...actually, now that I think about it some more, I agree that there is something to your line of thinking; I'm just not certain it leads to the conclusion you suggest.
The problem is that we don't have any way of talking about this that intuitively prompts how it actually works, and "degrees utility" is problematic because it suggests it accounts for all the problems. OK. However, the thing is, so does "utils". I mean, it's possible that people see that and know to tread carefully; I don't have any data here. I just feel like I've seen people try to add 1 util and 1 util often enough that I suspect that that isn't the case, and that most people do read "utils" as indicating that it is correct to treat it as an amount of stuff.
But perhaps reverting to an even worse solution would suggest to tread carefully -- namely, bare numbers. Again, this is pure speculation, I have no data; but I get the feeling that bare numbers will raise people's hackles more than "utils". Bare numbers suggest "something's been left out here; tread carefully"; using a unit suggests "yes, this is a sensible way to measure it."
So, if I'm correct about that, "utils" actually seems like the worst suggestion of the three -- compared to "degrees utility", it's more misleading, but doesn't come with an additional warning sign; compared to a bare number, it lacks the obvious warning sign, and isn't that much more misleading. (Because adding and scaling will be the most tempting meaningless things to do anyway; multiplication seems a bit more exotic...)
Again: "Utils" has all the same problems, and more. For a single agent, the comparison is meaningful.
If you prefer sticking to stick with the existing terminology despite it suggesting even worse meaningless comparisons, OK, but don't act like you are pointing out anything that isn't obvious, or that is specific to my suggestion.
Yes, to be absolutely clear, I'm talking about the sort of utility functions you get from the VNM theorem or Savage's Theorem.
It's not really clear to me what the use is for a utility function if all you have is ordering; why not just use an ordering? Seems that using a utility function then would just be needlessly restricting what sort of orderings you can have. Well, depending on what requirements you want that ordering to satisfy... after all if you have all of Savage's axioms then you do get a utility function! But that requires ordering actions, not just outcomes...
Indeed. It's an improvement over "utils", though, which has the same problem and also suggests linearity. I'm not sure what to do to fix this problem, but I'm also not sure it's that important (it seems pretty clear that we have to measure it somehow, after all).
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