Another data point for the definition of Empire being control of foreign policy. H.H. Scullard writes on Rome's run-in with Sparta:

But Flaminius would not go as far as his [Greek] allies desired; as with Phillip [of Macedon], he wished to cripple, but not destroy. Once again it was the Romans and not the allies who dictated terms, which included the surrender by Nabis of Argos and other towns and of his fleet, an indemnity, and the renouncing of the right to make war or alliances.
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And now a jot, following on from one and two : so assuming Pax Unus [unitary peace] and the patterns of how an empire behaves are consistent over time; this suggests that the greatest perceived threat to an empire is not nation-states, rogue-states, terrorism or non-state actors - it is an independent foreign policy.

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The thesis for Chalmers Johnson's book, Nemesis , is that democracy and empire are incompatible. A nation must choose between one or other - as the two cannot co-exist. (more)
Cam Riley: South Sea Republic. Freedom, liberty, equity and an Australian Republic.