Utility is the tendency of an object to produce happiness or prevent unhappiness for an individual or a community.

How can we assign utilities to represent preferences?

## Interval Scales

- Assign to each outcome $x$ a value $v(x)$ such that $v(x)≥v(y)⟺x≥y$ and $v(x)=v(y)⟺x∼y$
- Transformation is linear
- Called an ordinal transformation

Ordinal Scales must satisfy the following properties:

- Completeness: $x≻y$ or $x∼y$ or $y≻x$
- Asymmetry: if $x≻y$ then it is false that $y≻x$
- Transitivity: if $x≻y$ and $y≻z$ then $x≻z$

## Infinite Utility

An agent values A infinitely relative to B and C if we deny Continuity: $[λA,(1−λ)C]≻B$ for any $λ>0$

The agent is willing to trade B for any gamble that offers a positive chance of A, when the ‘losing outcome’ is C.)