By William M. Downs

On Thursday, an anticipated 30 million voters will head to polling stations to cast ballots in what is easily the most important — and uncertain — election to occur this year beyond America’s shores.

Thursday’s parliamentary contest in the United Kingdom pits the incumbent Labour Party of Prime Minister Gordon Brown against challengers from David Cameron’s Conservative Party and Nick Clegg’s upstart Liberal-Democrats.

Much more is at stake than 650 seats in the House of Commons; indeed, the next government in London will confront not only domestic economic malaise but also a “special relationship” with the United States that has shown renewed signs of strain.

Labour swept to power in 1997 on the oratory and energy of a youthful Tony Blair. When Blair resigned the premiership a decade later, then-Chancellor of the Exchequer Gordon Brown parlayed his experience at the helm of Britain’s economic and financial ministry into his party’s leadership and a new address at 10 Downing Street.

Thirteen years of Labour rule have, however, taken their toll. Blair left office dogged by claims that Britain subserviently and ineptly followed the United States into an unjustified invasion of Iraq in 2003.

As successor, Brown has struggled to right the ship amidst a global financial crisis and an intractable mission in Afghanistan. Brown’s announcement on April 6 of an election to be held in early May was followed immediately by opinion polls showing the opposition Conservatives with a commanding lead.

Unbelievably brief by American standards, the one-month campaign that ends this week has been marked by shifting fortunes and the country’s first-ever televised prime ministerial debates.

Cameron’s right-of-center Conservatives squandered their once comfortable advantage, and Clegg’s left-of-center Lib-Dems surged enough to now appear as legitimate contenders. Labour must consider the possibility of a third-place finish, which would be its worst in a century.

The introduction of American-style televised debates — a development lamented by some as the triumph of personality over policy — catapulted the boyish-looking 43-year-old Clegg into the spotlight with a telegenic performance that earned him the label of “the British Obama.”

Clegg’s Liberal-Democrats even tout a remarkably familiar slogan: “Change that works for you.” The veteran Brown, fighting for his political life, has shot back by likening Clegg to a “TV game show host.”

One of three scenarios will likely play out on Thursday. If the opinion polls prove correct, the Conservatives will eke out a victory. A Tory majority would mean a Britain more skeptical of further European integration and determined to “champion a distinctive British foreign policy.”

A second scenario is that the Conservatives win the plurality of the votes but fail to capture the 326 seats necessary for a parliamentary majority. A majorityless “hung parliament” would vault the Liberal-Democrats into the role of kingmaker. Markets and allies (including the United States) would at least temporarily react with skepticism to the uncertainty of coalition government and the prospect of new elections on the near horizon.

A third, but increasingly distant, possibility is that voters get skittish about a hung parliament and return the underdog Labour Party yet again to power.

Relations with the United States have been featured among the campaign issues. Britons are still stinging from a series of perceived snubs received during Gordon Brown’s visit to Washington in March 2009. The absence of a full-scale press conference and the failure to provide a state dinner to acknowledge the first visit by a European head of government following President Barack Obama’s inauguration captured headlines for weeks. Obama’s gift to Brown of 25 DVDs of American movie classics (contrasted with Brown’s lavish offerings) did not sit well.

Diplomatic faux pas aside, there have been substantive rows about the British government’s decision (over U.S. objections) to release the Libyan convicted of the 1988 bombing of Pan Am 103 over Lockerbie, Scotland. Washington’s refusal in February to endorse British claims of sovereignty over the Falkland Islands in its latest dispute with Argentina has sparked real ire. Extrication from Iraq and Afghanistan, as well as strategies for dealing with threats such as that in Iran, remain sources of tension.

American foreign policy has relied for decades on a supportive United Kingdom. While other European partners (e.g., the French) could be predictably prickly, past U.S. presidents have routinely counted on their British counterparts to translate “shared interests and values” into common policies. Obama does not appear to share his predecessors’ sentimentality for the special relationship with the U.K., and appearing to cozy up to the United States is today a liability for British politicians.

Whatever the result of Thursday’s vote, the special transatlantic relationship will not be in imminent danger. It is, however, suffering from benign neglect and slow erosion. Leaders on both sides should seize the opportunity after Thursday to reverse that course.

William M. Downs is chairman of the Department of Political Science at Georgia State University.