Hung parliament expected

At stake in Thursday's election is the UK's continued EU membership, threatened by the Tories promise of an in-out referendum; also, the very existence of the union, with Scotland likely to demand an exit from the UK if Britain leaves the EU; and the role and existence of the welfare state and the National Health Service (NHS), if the Tories or their coalition partners, the Lib Dems, return on another austerity ticket.

But for just the second time in the post-war era, the British public looks set to reject the legislative proposals made by all of the main parties. What takes their place is undecided, uncertain and essentially unknowable.

Every poll suggests no single party will gain the required majority to command the House of Commons. As in 2010, a coalition deal will likely have to be struck, but just five years after that election, the outlook today is much more complex and volatile, thanks to the quirks of the UK's electoral system, shifting political allegiances and Britain's lack of a written constitution.

George Osborne, the Chancellor, told journalists this week that if the incumbent, David Cameron, does not win a majority, his Downing Street neighbor won't be budging until a deal of some kind is done. "The government remains the government until there is another government," he said.

In Britain's first-past-the-post voting system, a party must control over 50 percent of the 650 seats in the House of Commons to be sure of passing laws. In principle, that is 326 seats, but in reality, as the five Irish republican MPs of Sinn Fein reject Westminster's rule in Northern Ireland and do not attend, that figure drops to 323.

Robert Hazell of University College London's Constitution Unit, the UK's leading research body on constitutional change, has said the days following the election could be confused and chaotic if, as looks likely, the share of seats won is sufficiently close that both Labour and Conservatives claim to be able to form a government.

In 2010, it took just five days to form a coalition. This time, Hazell says, negotiations could possibly take weeks as more parties will be involved and backbench party members will demand consultation.

The numbers game

Blunt math and sharp politics will decide who runs Britain for the next five years far more emphatically than any voter marking an X on a ballot paper on Thursday.

Although the Tories may end up winning most seats, an anti-Tory bloc of 323 seats is more easily attainable than any pro-Tory majority.

Yougov polls on Tuesday put both center-left Labour and center-right Conservatives at 33 percent. This would translate to 276 seats for Labour, and 272 for the Tories, who have ruled under Prime Minister David Cameron in an uneasy coalition with Nick Clegg's Liberal Democrats since 2010.

Both main parties will, therefore, lack the numbers required to rule alone and will be forced to scramble to forge alliances enabling them to form a government capable of commanding the confidence of the House of Commons.

The problem for the Conservatives, who have failed to win a majority since 1992, is that it is simply outnumbered by its opponents.

Compounding matters, the Tories' coalition partners have seen their support dwindle since 2010: the Lib Dems are now polling at just 10 percent, which would win them 24 seats - down from 57 seats in the last election. The Lib Dems lost credibility and support almost instantly in 2010, when leader Nick Clegg voted with the Tories to treble university tuition fees having pledged that he would resist any increase.

Meanwhile, the Scottish National Party looks set to obliterate Labour in its traditional Scottish heartland, winning 50 seats, giving them the balance of power in Westminster, since the SNP refuses to align itself with the Conservatives.

The collapse of Labour's vote north of the border and its transfer to the SNP adds further complexity to any coalition talks, as Labour has also emphatically - if perhaps unconvincingly - ruled out any deal with the nationalists, who have gained strength since a narrow defeat in a 2014 referendum on independence. Labour's stance is explained by the pre-election desire to maintain a united front and to offer unequivocal support to its Scottish candidates.

The right-wing UKIP vote stands at 12 percent nationally, though it is unlikely to win more than a handful of seats as its vote is diffuse and support has drained away following crotchety appearances by leader Nigel Farage during televised debates.

Nick Clegg has said the Liberal Democrats will talk first to the party with the greatest number of seats, claiming that any minority-led government would "lack legitimacy."

That, says Hazell, is a rule purely of Clegg's own imagining. "It's a principle he invented. It's not a constitutional rule. We have no rule, unlike, say, Germany, about who is the first mover. There is nothing to prevent all parties negotiating at the same time. There is nothing to prevent Cameron raising his flag and Miliband raising his, and saying to minor parties: 'Come and talk to us.'"

The popular press in Britain and the Tory party itself has spent much of the last few weeks of the campaign claiming that a minority government that ruled with the support of other minor parties would be somehow illegitimate. Hazell says that idea is "complete nonsense, constitutionally and historically."

As Thursday's vote unfolds, it is impossible to know what will happen, and how the parties will align themselves, and who will occupy Number 10 Downing Street in a few weeks' time.

But what seems certain, beyond any question, is that this new uncertainty in British politics looks likely, as Hazell says, to become "the new norm."