Let $\mathcal{R} : = \text{Random}(\mathbb{R})$ be the D5721: Class of random basic real numbers.
The stochastic ordering relation is the D4: Binary relation
\begin{equation}
{\preceq} : =
\left\{ (X, Y) \in \mathcal{R} \times \mathcal{R} \mid \forall \, t \in \mathbb{R} : \mathbb{P}(X \leq t) \geq \mathbb{P}(Y \leq t) \right\}
\end{equation}