Seldom has a single debate had such an impact on a political campaign. A week ago, jaded observers were wondering whether David Cameron’s Conservatives could hold on to the lead over Gordon Brown’s Labour Party that they had enjoyed for more than two years, and the Liberal Democrats seemed doomed to their traditional also-ran status. In the wake of Liberal Democratic leader Nick Clegg’s strong performance in the first of three face-to-face encounters, though, the Liberal Democrats have surged into contention, vaulting ahead of Labour in several surveys and ahead of the Conservatives in at least one.

Underlying this development are deep reservations about the two major parties. While Gordon Brown gets grudging credit for a kind of stolid persistence, the fact remains that he was chancellor of the exchequer for a decade before succeeding Tony Blair as prime minister, so he can hardly evade responsibility for Britain’s acute fiscal crisis. As for the Tories, the electorate wonders whether David Cameron’s effort to reinvent his party as greener and more compassionate goes more than skin-deep. The Liberal Democrats’ gains reflect a desire—especially among younger voters—for something new and different … even if the third party’s platform offers an inadequate response to the structural problems Britain faces.

Whatever its cause, the Liberal Democrats’ surge does not mean that they have a serious chance of emerging with the most seats—let alone a majority—in the next parliament. Largely because of the way their votes are distributed among the electoral districts, the Liberal Democrats are almost certain to receive a much smaller percentage of seats than their share of the popular vote—which helps explain why they favor dramatic changes in the voting system. All other things equal, they could receive 30 percent of the popular vote and end up with fewer than 100 seats—less than 15 percent of the 650 seat total.

The oddities of this election do not end there. Labour’s votes are distributed far more efficiently than are those of the Conservatives. In 2005, Labour’s 35.2 percent of the vote brought them 356 seats, versus 198 seats for the Conservatives (32.4 percent) and only 62 for the Liberal Democrats (22.1 percent). Based on an algorithm found at ukpollingreport.co.uk, I was able to calculate that while Labour could retain a narrow majority this year with about only 34.5 percent of the popular vote, the Conservatives would need about 39.5 to win an outright majority, and the Liberal Democrats would need an implausible 41.3 percent. Otherwise put, Conservatives need to increase their share of the popular vote by about 7 percent points over last time to take over—not out of the question, but well above their showing in recent surveys.

What does all this mean? Well, there’s a good chance that the 2010 election will result in a “hung” parliament, in which neither Labour nor the Conservatives enjoys an outright majority. This would leave the Liberal Democrats as the kingmaker, and their price for entering a coalition government would include a major modification of the first-past-the-post system that has disadvantaged them for decades. This would change the dynamic of U.K. politics in ways that are hard to calculate but sure to be consequential.