Axioms of Utility in Deterministic Environments

The vNM utility theory rests on a set of axioms, which are easy to interpret as elements of rationality. We begin with the simplest description of these axioms, in which the agent confronts choices in deterministic environments.

Elements

1. 2.1.aCompleteness

   The ability to determine a preference between two options $A$ and $B$. E.g., prefer $A$ over $B$, $B$ over $A$, or indifference.

2. 2.1.bTransitivity

   The ability to be consistent in preferences over options. E.g., if $A$ is preferred over $B$, and $B$ over $C$, then $A$ should be preferred over $C$.

3. 2.1.cIndependence

   The ability to remain consistent in preferences between pairs of options regardless of the presence of other alternatives. E.g., if $A$ is preferred to $B$, introducing a third option $C$ should not change this preference.