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A total of 1,672 eligible voters — vastly outnumbered by the islands' estimated population of one million penguins and 700,000 sheep — will be asked to answer yes or no to a straightforward proposition: "Do you wish the Falkland Islands to retain their current political status as an Overseas Territory of the United Kingdom?"

The alternative would be to begin a transition to Argentine control, perhaps by a period of shared sovereignty, as Argentina has suggested. The vote comes three decades after Argentina tried to settle the issue by force, invading the islands and losing a 10-week war with Britain that cost the lives of 255 British and 649 Argentine soldiers, sailors and airmen, as well as 3 civilians on the islands.

For those inclined to a wager, the referendum is a lead-pipe cinch. The majority of the islands' residents are British citizens, and local pundits expect the vote for retaining the status quo will run a few points short, if that, of 100 percent. About the only uncertainty is whether the fog that sweeps over the Falklands will ground the aircraft that carry the ballots from eight separate islands to Stanley, the capital.

The benchmark is a 2002 referendum in Gibraltar, another British dependency, where the vote for retaining the British link or accepting a new status tying the isthmus on which Gibraltar stands to Spain was 98.5 percent. That, too, was not much of a cliffhanger, since many of those eligible to vote were of British descent.

For Argentina and Britain, the 1982 conflict was a shock — enough to lead, in time, to the collapse of the Argentine military junta that mounted the invasion, and to propel Prime Minister Margaret Thatcher, in deep political trouble at home when the war gave her an opportunity to play the "Iron Lady," to a second election victory in 1983. The hope, sustained for years after the war, was that both countries would put the bitterness behind them and build a relationship on interests like trade that pragmatists on both sides saw as more important than the Falklands.

But in the last few years the old virulence has returned, driven by a surge of Argentine nationalist fervor stirred by President Cristina Fernández de Kirchner, who has adopted a number of measures intended to place economic pressure on the islanders, including banning cruise ships that stop at the islands from Argentine ports.

Both countries have historical claims on the islands, the British one bolstered by their continuous habitation there since the 1830s, the Argentine by the fact that Stanley lies barely 300 miles from the Argentine coast and nearly 8,000 miles from Britain. To the argument of proximity, Argentina has added in recent times the contention that Britain intends, by keeping control of the Falklands, to rob Argentina of the newly discovered deep-sea oil reserves and rich fisheries within the Falklands' territorial waters.

The referendum has been dismissed by Mrs. Kirchner, who has said that islanders are "colonial implants" from Britain whose preferences count for nothing against the fact that the islands, known as Las Malvinas to the Argentines, were "stripped" from Argentina by a British naval flotilla that expelled an Argentine settlement in 1833. That event followed on a convoluted colonial history going back to the 16th century that saw rival claims to the islands, at one point or another, by Britain, France, Portugal and Spain.

The Argentine foreign minister, Héctor Timerman, calling the islanders "settlers," has been equally blunt. "The Falkland Islanders do not exist," he has said.

The aggressive Argentine stand, accompanied at times by belligerent hints from Argentine military and political leaders that they do not exclude another attempt to take the islands by force, has been rejected by the British prime minister, David Cameron.

His aides have said he knows that losing the islands to a new Argentine invasion would be likely to doom his government at the polls. He has led an intensive review of British defenses on the islands, including a 1,200-member military detachment, a new military airfield, the year-round deployment of four Typhoon fighter-bombers, and, some British reports have said, a nuclear-powered attack submarine stationed in the South Atlantic.

But Mr. Cameron's response has been as much political as military. Although the referendum was formally called by the Falklands' popularly elected government, the move came in close consultation with London. Officials at the Foreign Office have said they see a vote by the islanders to remain British as a means to shift the terms of international debate to one of their right to self-determination in place of the colonial struggle depicted by Mrs. Kirchner.

Mr. Cameron describes the Argentine rejection of the referendum as "shouting down the islanders' ability to speak for themselves," and he has vowed to defend them in whatever choice they make for their own future.

In this, he has had the support of all the main political parties in Britain, though some politicians, including a number in his own Conservative Party, have questioned how long Britain, with a $50 billion defense budget that is already severely overstretched, can continue to make such substantial outlays on faraway, thinly populated islands with scant strategic value.

To British frustration, their claim to sovereignty over the islands has failed to win American backing under the Obama administration just as it did under the Reagan administration at the time of the war in 1982. With an eye to the strong support Argentina has won for its claim among Latin American states, the United States has urged London and Buenos Aires to reach a negotiated settlement, a position American officials said was quietly reiterated last month when Secretary of State John Kerry, on his first trip abroad in the post, met Mr. Cameron.

Argentina has other powerful diplomatic cards to play, including the backing of China and Russia, who have joined Argentina in rejecting the right to self-determination by the Falklanders, seeing it as a possible precedent for separatist groups in their own territories.

Agustín Romero, a foreign affairs specialist who sits on a congressional committee on the Falklands in Buenos Aires, said international acceptance of the Falklands vote could open the floodgates to separatist movements around the world.

"What no one wants is a precedent," Mr. Romero said, "which is why none of the world's superpowers will recognize this referendum."