I cannot find ANY evidence that they have ever been asked.
They have NO sovereignty. All important economic, foreign policy and war decisions have been made by the Crown and the Prime Minister in London.
Maybe they saw benefits before, but now that England has engaged in a vastly unjust war--a war opposed by 80% of the people of England--and is bankrupt like the U.S., they might think differently--particularly with Argentina's booming economy under the Leftist governments of Nestor Kirchner and Cristina Fernandez, in alliance with other economic success stories of the Left in South America.
Argentina is not "sabre rattling" because of "domestic issues." Argentina is prospering and its Leftist government is hugely popular.
"...the residents of the Falklands...have been resoundingly clear on wanting to stay part of the UK"??
The people of the Falklands have never been consulted, as far as I can determine, and conditions change. Will they be consulted now? Tell me how and when.
They are now a colonized base of operations for the British military, allied with the U.S., in what the Pentagon calls "SouthCom"--Southern COMMAND. It is a Pentagon scheme to dominate the "global south" from Asia to Africa and includes the newly reconstituted (by the Bushwhacks) U.S. 4th Fleet in the Caribbean, and expanding military bases in Honduras (rightwing dictatorship, lots of dead leftists), Colombia (rightwing dictatorship and mountains of dead leftists) and other places in Central America, the Caribbean and South America (though the U.S. military is no longer welcome in most parts of South America, except Colombia). The Falklands (the Malvinas) provide a strategic location for British and U.S. plans for corporate resource wars and economic warfare across the "global south." Do Falklanders want to be in the middle of this? Are they different--more warlike--than 80% of the people in England?
I don't know the answer to that question, any more than anyone else does--but it is an important question, along with questions about the role of a "colony" with the "mother country" suffering an induced Great Depression, whereby the rich get richer and the poor get kicked off the island.
Finally, the current issue, with the Falklands/Malvinas, is Argentina's off-shore OIL. THAT is what the British ruling class is out to encroach upon and control. Do all Falklanders want to be dragged into THAT dispute--the current cause of imperial war all over the globe--or is it just the Falklanders who would benefit--the oil elite and the rich--who would welcome another oil conflict?
We have seen such a situation in Venezuela. The tiny oil elite and the rich were hugely benefiting from the oil but the great majority were not--were being, instead, impoverished. Luckily, Venezuela is a sovereign country and a democracy, and Venezuelans were able to elect a government that serves the majority and that courageously took on the transglobal oil industry, on behalf of the Venezuelan people. Could this occur in the Falklands? Absolutely not. They are controlled by the British Crown and the British military, which serve British-based transglobal interests allied with U.S.-based transglobal interests and war profiteers. We think BP have been utter bastards here? What would they do to the Falklands--a British colony?
In any case, it is an open question, in my opinion, what the people of the Falklands would want, if and when they are asked. And, frankly, I will eat my hat if the British ruling class permits a vote on this matter. They never have and they never will (unless, of course, they get Diebold installed*).
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*(Privatized, corporate vote 'counting' with 'TRADE SECRET' code, as here.)