The first thing the USA should do is (re)join the
("British") Commonwealth of Nations, even as a Republic.
What does this get us? Participation in the Commonwealth Games, occasional Commonwealth Heads of Government Conferences, closer relations and trade with much of the Third World--fellow-former colonies of England (mostly) throughout the Americas, Africa, Asia, and the all-important Pacific Basin.
Most of these countries have English as an official language, and many perpetuate the "Anglo-American Legal System." And after all, we were the first colony to cut ties with "Mother England," so we blazed the trail all the rest have followed, so to speak. Yet now we are arguably the UK's strongest ally and trading partner. Just tune to PBS to see what I mean!
In a sense America founded the Commonwealth, by becoming independent of Britain while maintaining linguistic, cultural, and economic ties, and in the last hundred years, political and military ones as well. (140 years if you include the Confederate States of America!)
We already share "the longest unguarded border in the world" with a Commonwealth power, Canada, our #1 trading partner. This, after Canada confederated for protection against invasion from us!
The Commonwealth is in a sense an association of (mostly) English-speaking countries. Sure, the Queen is honorary--hereditary--head of it...but many say that may change in the near future. In any case, most of its members are Third World...and America can always use better relations with the Third World.
We also stand to benefit from interaction among lawyers and judges using versions of the same legal tradition as ourselves. It's not uncommon for Commonwealth-member Supreme Courts to learn from each other's precedents. And they're not all flaming Socialists out there, either! But American courts often forget that there's additional help available as they seek to rule within the Anglo-American legal/constitutional system. As they face a legal quagmire, maybe some insight from Australia or New Zealand or Canada could shed some light on the situation.
There are many Republics in the Commonwealth today, including India, the largest or second-largest country in the world. England has no influence over internal or external Indian affairs whatsoever. They're merely international friends.
Nevermind that the USA would become the new 800-pound gorilla of the Commonwealth...!
Finally (for now), we in the USA haven't been quite sure how to think of England since 1776. Friend? Foe? Tentative ally? Best buddy? 'Agree to disagree'? Competitor? Yet Britain and Canada are our best friends in the world! And Britain isn't as enthusiastic about the European Union as our other NATO Allies are. We don't give anything up by joining their Commonwealth but, as it were, gain a whole world!
Tiernan O Faolain 10/10/2002