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OrphanWilde comments on How do humans assign utilities to world states? - Less Wrong
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Humans don't. "Utility" is part of the map, not part of the territory. We make choices, but utility theory is only a modeling language used to describe choice-making processes.
One are of research you may want to investigate is "Revealed Preference", a concept developed primarily by Paul Samuelson.
"Revealed Preference" has issues, because of things like circular preferences - although it's a mistake to conclude that circular preferences are proof that humans are irrational. Rather, it demonstrates that utility theory in general is just a model, and an incomplete one.
The fundamental issue is that utility, as a model, attempts to compress a topography of many dimensions - human preferences - into a topography of exactly one - a utility value for each potential choice. Impossible Objects - "contradictions", such as circular preferences - are to be expected in the abbreviated topography.
Well, there is one case in which naive utility theory makes perfect sense: when the utility function is just measuring the value of some real-number random variable inside the epistemic model (ie: when reading a number off your map tells you the utility of the territory). Since utility theory was invented to deal with economics, in which such a random variable exists and is called "money", nobody ever bothered to ask what happened when you didn't have such a convenient real-valued, assumed-monotonic random variable.
True. Although I think most utility theorists would be somewhat horrified if you suggested that money was the only thing worth measuring, when measuring utility.
Well of course, because they conceived of utility theory as giving value to money. They also invented a utility theory that only really applies to measuring money. It was a kind of doublethink in which, if real human preferences don't fit a model constructed to deal with money, then economists conclude that humans are Irrational (in a capital-letter ideological sense) rather than trying to come up with a model of evaluative reasoning that actually explains the data gained from real people.
Why is self-reference expected when reducing the dimensions? Is it because these dimensions might influence each other in a circular way?
Circles are valid two-dimensional objects. What mapping do you use to represent a circle in one dimension?