  A $biased\ graph$ is a pair $(G,\mathcal{B})$, where $G$ is a graph and
$\mathcal{B}$ is a collection of `balanced' circuits of $G$ such that no
$\Theta$-subgraph of $G$ contains precisely two balanced circuits. We prove a
Ramsey-type theorem, showing that if $(G,\mathcal{B})$ is a biased graph which
$G$ is a very large complete graph, then $G$ contains a large complete subgraph
$H$ such that the set of balanced cycles within $H$ has one of three specific,
highly symmetric structures, all of which can be described naturally via
group-labellings.
