vault backup: 2026-05-30 21:37:23

utility.md

@@ -11,7 +11,8 @@ tags:
 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.
+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.
 
@@ -38,3 +39,21 @@ and that I've thought about
 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.