Like Perth said... we don't know how to define it.
But we do know that Aurvandil does not make the cut. Asylon probably isn't republican enough either, though their much closer. Madina is probably too wacky.
Pragmatically, having one republic in the federation means we need all republics. We need stability of lords and mid-level positions to promote the kind of regional cooperation, especially for food, that the Moot is built on. Simultaneously, we need to have stability of the upper tiers of power... but we don't want a hegemon. We don't want to have one ruler last forever while others cycle through, allowing one state to accumulate huge amounts of political power.
Democracies are too unstable, autocracies too likely to produce political hegemons. So republics, constitutional monarchies (Hireshmont refers to D'Hara as a "republican monarchy" in order to convince himself that they aren't violating the Treaty), limited democracies, liberal theocracies.... any of these might work.
Aurvandi autocracy would not work. Madinan decentralization would not work. Why? Because Aurvandi autocracy clearly leads to hegemonic behavior, while Madinan decentralization is infuriating to work with across realm boundaries.
