---
title: Utility
tags:
  - status/not-started
  - topic/risk
  - type/encyclopedia-entry
---
# Utility

[**Utility**](https://en.wikipedia.org/wiki/Utility)
is a measure of a party's **satisfaction**
with a certain state of the world.

The measure is intended to account for unintuitive quirks
of human perception of value.
A rich man is not as _satisfied_ by receiving one dollar as a poor man would be,
therefore the utility of the dollar is contextual, not objective.

## In This Notebook

I use "utility" perhaps a bit loosely compared to Wikipedia.

If I say that some voluntary activity "has high utility",
I mean that it is worth doing,
even considering the expense
(usually labor or dollars).

In this way "utility" is more of a signal
that I'm speaking objectively,
and that I've thought about

## See Also

[Sorites paradox resolutions in utility theory](https://en.wikipedia.org/wiki/Sorites_paradox#Resolutions_in_utility_theory)

## Normative and Descriptive Utility

**Normative utility** is utility as self-reported,
subject to the biases of the party.

**Descriptive utility** is utility as determined from the party's behavior.

## Formulas

Utility as a function of a gain or loss of some commodity
could be described with a function of the form

$$
a\left(1 - \frac{1}{bx + 1}\right)
$$

for cases where utility is expected to be bounded,
or where utility is expected to increase infinitely
$\sqrt{ax}$ or $\log_{a}(bx+1)$.

For all these functions $f(0)=0$,
meaning (as expected)
a net zero gain of the commodity
represents net zero utility.