= Solution
Order configurations coordinatewise: $\omega\le\eta$ means $\omega(e)\le\eta(e)$ for every <edge>. Then <stochastic domination> is the condition
$$
\boxed{\mu_1(A)\ge\mu_2(A)\quad\text{for every increasing event }A.}
$$
Equivalently, $\mathbb E_{\mu_1}f\ge\mathbb E_{\mu_2}f$ for every real-valued <order-preserving function> $f$. The equivalence follows on this finite space by writing $f$, up to an additive constant, as a nonnegative linear combination of indicators of its increasing upper level sets. A <coupling of probability distributions> supported on pairs $(X_1,X_2)$ with $X_1\ge X_2$ proves this domination; conversely such an ordered <coupling of probability distributions> exists on a finite partially ordered space.
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