L ABOUR AND the Conservatives have dominated British politics for a century. Combined, they have won over 60% of votes in every general election since 1922. But lately polls have suggested the duopoly is over. Four parties are polling at around 20%, as Labour and the Tories jostle with the Liberal Democrats and the new Brexit Party (see chart). A fifth lot, the Greens, are on nearly 10%.

What sort of Parliament might emerge if an election were held? The next one is not due until 2022, but an incoming prime minister stuck with a deadlocked Commons will face pressure to go to the country. Under a proportional system, seats would be split four ways. But Britain’s first-past-the-post system awards seats only to the winner in each constituency, punishing parties that come a consistent second or third, however narrow the margin. So the next election could resemble a lottery.

Forecasting the result means projecting national polls onto constituencies, adjusting for the profile of the people who live in them. This is tricky enough in a two-party race, in which votes lost by the Tories might be assumed to accrue mainly to Labour, and vice versa. In a four-way contest it is far harder.