= Solution
<Exchangeability> means that the joint <prior distribution> is invariant under breed relabelling:
$$
p(\theta_1,\ldots,\theta_I)
=p(\theta_{\pi(1)},\ldots,\theta_{\pi(I)})
$$
for every permutation $\pi$. The labels carry no prior information about maximum size. This is reasonable for comparable breeds before observing their measurements when no covariates or biological knowledge distinguish them.
<Exchangeability> does not imply <independence>. In a <hierarchical Bayesian model>, the parameters can be independent conditional on a shared <hyperparameter> but dependent after it is integrated out. Known systematic biological differences would call for a model of those differences, with exchangeability only for the remaining unexplained variation.
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