Axiom:Axioms of Uncertainty/Axiom 1

Axiom

Let $Z$ be a random variable.

Let $Z$ take the values $a_i$ with probability $p_i$, where $i \in \set {1, 2, \ldots, n}$.

Let $H_n: Z^n \to \R$ be a mapping which is to be defined as the uncertainty of $Z$.

$H_n$ fulfils the following axiom:

$\map {H_n} {p_1, p_2, \ldots, p_n}$ is a maximum when $p_1 = p_2 = \dotsb = p_n = \dfrac 1 n$

Sources

• 1988: Dominic Welsh: Codes and Cryptography ... (previous) ... (next): $\S 1$: Entropy = uncertainty = information: $1.1$ Uncertainty