That's O.K. Back during the Battle of Lepanto, my ancestors were the Big Dog (the Spanish Empire) and today I'm still part of the Big Dog (the USA). ;-)
I must agree, however. "Big 3" is not a good name.
I am opposed to empires in general and particulary an American empire. I prefer that we observe the Constitution and listen to the wisdom expressed in Washington's Farewell Address.
I apologize if I gave the wrong impression. The US, UK, and Spain certainly will NOT call themselves the "Big 3". LOL That is completely my term, or shorthand for the countries to be represented there. They indeed are the "Big 3" of this coalition.
Oh, but it's a great backhand across the face of the worm, Chiraq... not to mention Russia, China, and Deutschland.
I don't know about "big"--but certainly, in today's world, "best" might apply. Then again, I'm biased.