I don't know enough early American history to really pursue this myself, but I know that Edmund Burke argued very strongly in Britain for peace with the American colonies, prior to the war commencing. What if he was successful in swinging the opinion of the House of Commons and Britain reduced taxes and/or granted full independence?
I'd assume there'd be some kind of Parliament, such as the other former British colonies such as Canada, Australia and New Zealand (plus Canadian provincial Parliaments, Australian state Parliaments, etc). I guess also that Canada would have been incorporated into the US at some point, too.
Anyway, that's just a thought I'm putting out there. Perhaps someone with a greater knowledge of US history might like to turn this thought into a timeline?
Oh, also looked up on Wikipedia Burke's speeches on the US:
On 22 March 1775 Burke gave a speech (published in May 1775) on conciliation with America:
The Tory administration of Lord North (1770-1782) tried to defeat the colonists' rebellion by military force. British and American forces clashed in 1775 and in 1776 came the American Declaration of Independence. Burke was appalled by celebrations in Britain of the defeat of the Americans at New York and Pennsylvania. He claimed the English national character was being changed by this authoritarianism. To Burke Britain was fighting "the American English" ("our English Brethren in the Colonies"), with a German-descended King employing "the hireling sword of German boors and vassals" to destroy the colonists' English liberties.
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