60 lines
1.5 KiB
Markdown
60 lines
1.5 KiB
Markdown
---
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title: Utility
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tags:
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- status/not-started
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- topic/risk
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- type/encyclopedia-entry
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---
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# Utility
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[**Utility**](https://en.wikipedia.org/wiki/Utility)
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is a measure of a party's **satisfaction**
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with a certain state of the world.
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The measure is intended to account for unintuitive quirks
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of human perception of value.
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A rich man is not as _satisfied_ by receiving one dollar as a poor man would be,
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therefore the utility of the dollar is contextual, not objective.
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## In This Notebook
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I use "utility" perhaps a bit loosely compared to Wikipedia.
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If I say that some voluntary activity "has high utility",
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I mean that it is worth doing,
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even considering the expense
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(usually labor or dollars).
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In this way "utility" is more of a signal
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that I'm speaking objectively,
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and that I've thought about
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## See Also
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[Sorites paradox resolutions in utility theory](https://en.wikipedia.org/wiki/Sorites_paradox#Resolutions_in_utility_theory)
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## Normative and Descriptive Utility
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**Normative utility** is utility as self-reported,
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subject to the biases of the party.
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**Descriptive utility** is utility as determined from the party's behavior.
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## Formulas
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Utility as a function of a gain or loss of some commodity
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could be described with a function of the form
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$$
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a\left(1 - \frac{1}{bx + 1}\right)
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$$
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for cases where utility is expected to be bounded,
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or where utility is expected to increase infinitely
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$\sqrt{ax}$ or $\log_{a}(bx+1)$.
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For all these functions $f(0)=0$,
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meaning (as expected)
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a net zero gain of the commodity
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represents net zero utility.
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