Our new model captures the lottery of Britain’s electoral system

Two extraordinary things happened in Downham Market at the general election last year. One is that Liz Truss lost the seat of South West Norfolk, the first former prime minister to be ousted since 1935. In the woods nearby, the words “Liz Truss Memorial” have been graffitied on a bin containing dog waste.

The more significant is that her successor, Labour’s Terry Jermy, won with a mere 27% of the vote—the lowest of any MP elected that year. Mr Jermy owes his victory to first-past-the-post (FPTP) voting, under which each person casts one ballot and the candidate with the highest tally in every one of Britain’s 650 constituencies wins. Against eight competitors, Mr Jermy won by a fraction. It’s doubtful, he admits, that he has a real mandate.

Downham Market is the most extreme example of a new reality that is starting to sink into voters’ perceptions of how British politics now works. When lots of parties have similar levels of support, small shifts in their share of votes can lead to huge shifts in their share of seats. The trouble is that it is hard to know where this insight leads—beyond the vague intuition that it makes politics volatile and confusing.

This week The Economist brings some clarity to this baffling new order. Our new model shows, constituency by constituency, how FPTP interacts with vote shares to produce election results. Using scenarios prompted by the latest polling, we set out a forecast of the parties’ representation if an election were held today. As the election draws closer and the polls continue to shift, we will be able to use this model to illustrate how their share of seats is seesawing from victory to coalition-building to defeat—or even obliteration.

We call it slot-machine politics. It is confusing and hard to predict, but it is not random and it leaves Britain on the threshold of many dramatically divergent futures. To illustrate this, we’ve picked several scenarios.

One is a Reform landslide. Some recent polls have put the vote share of Nigel Farage’s right-wing populists as high as 32%. If so, Reform could win more than 400 seats, just as Labour managed to do in 2024. Other polls are more prudent, leading to a second scenario: a hung parliament. If Reform won 27% of the vote, that difference in polling of only five percentage points could result in a staggering 116 fewer seats for Mr Farage.

The model’s simulations include a grim scenario for Kemi Badenoch, the Tory leader: a Conservative wipeout. After nigh-on two centuries as a major party—the most electorally successful in the world—a further slippage in the polls of eight points could reduce Britain’s centre-right to a handful of MPs. There could also be a small-party surge. Under the new leadership of Zack Polanski, the Green Party has taken many left-wing voters from Labour in recent polls. If the Greens do well, four parties—Labour, Conservatives, the Greens, and the Liberal Democrats under Sir Ed Davey—could be scrapping for second place behind Reform.

Yet Labour, led by Sir Keir Starmer, can still hope to hit the jackpot. A Labour recovery is plausible. If the party outperforms its polls by seven percentage points, the most likely scenario according to our model is Labour being the largest party in a hung parliament, relying on other centre-left parties to form a government. If the party manages to overtake Reform, another Labour majority will be possible.

Our model works by estimating how an election might unfold in each constituency based on the latest polling. This means we will be able to keep returning to it in future. Drawing on 80 years of data, including 9,000 opinion polls and 20 general elections, we simulated 10,001 elections. The fragmentation of the electorate means that, despite drawing on a single underlying data set, the range of potential results is remarkably wide (see chart 1). When elections are won on tiny margins, like the one in Downham Market, they become as unpredictable as a night in Las Vegas.

British voters, like others in Europe, are abandoning the centre parties for challengers, such as Reform and the Greens. But Britain is the only democracy in Europe to use FPTP, which works best with two dominant parties. When this collides with multiparty competition, the electoral slot machine spins into operation.

For example, were an election held today, Reform would probably be the largest party with, our simulations find, a 90% chance of securing anywhere between 112 and 373 seats. That wild range spans the difference between being the largest opposition party (like the Conservatives today) and a governing one with a big majority (like Labour now). The simulations suggest Labour would probably be the second-largest party, with a 90% chance of winning between 36 and 295 seats.

Geography adds another twist to this game of chance. FPTP rewards parties that distribute their vote to maximise their gains. Our modelling suggests that if Reform wins 27% of the vote nationally, it could receive anywhere between 208 and 305 MPs, depending on the geographical allocation of those votes. In 2024 the Liberal Democrats won 12% of the vote in Britain and an impressive 72 MPs, thanks to ruthless targeting. Reform got 14% of the vote, but just five MPs.

At the next election, Labour could cling to power with just 26% of the national vote, despite being unpopular. So long as it lost the popular vote to Reform by less than two percentage points, it would even have a one-in-three chance of winning the most seats. Advocates of FPTP have long claimed it is good at ejecting unpopular governments; when the electorate fragments that stops being true.

The consequence will be a widening gulf between how Britons vote and the parliaments they get. FPTP tends to produce two big parties in Parliament while suppressing smaller rivals. Since 1900 the “effective number” of parties in Parliament (a measure of the number of parties which win a substantial share of the vote) has ranged between two and three, according to Jack Bailey of the University of Manchester (see chart 2). Yet the effective number of parties by votes cast has jumped, to 4.8 at the last election. It would be 5.1 on today’s polling. Britons are increasingly voting for an array of parties as if they were modern Europeans while getting the two-party parliaments of Victorian England.

As the electorate fragments, the share of the vote needed to win an election in each constituency falls—in the way Mr Jermy found in South West Norfolk. Since 1945, 19 MPs have won elections with less than 30% of the vote; ten of them were elected in 2024. Our model suggests the average winning vote share for an election held tomorrow would be 38%, compared with 55% in 2019. In our 10,001 simulated elections, Cardiff West is the constituency with the lowest average winning share, of 27%. There is a one-in-ten chance that the seat would be won with a mere 23%.

Defenders of FPTP argue that the ends justify the means. Even if it is unfair, the dominance of two parties avoids the haggling over coalitions that can plague some European countries. Stable governments get things done, they say.

Those arguments are becoming weaker. In an age of fragmentation, FPTP compounds the volatility of the electorate, making election results even more capricious. A shift of just two percentage points could be the difference between Mr Farage entering Downing Street with a majority or falling far short of power.

The unfairness of FPTP could undermine the legitimacy of the governments it produces. In 2024 Labour won 63% of the seats in Parliament with 34% of the vote, the most skewed result in history. As its support has slid to 19%, the government has fallen into paralysis and infighting. A system intended to produce strong governments now produces weak ones. Robert Ford of the University of Manchester calls FPTP “a destabilisation mechanism. It is a volatility amplifier.” That instability is unlikely to go away, as the demographic forces that have been driving the fragmentation of voting behaviour are not abating.

Last year MPs voted by a narrow majority for electoral reform, but the government will not give the bill the parliamentary time needed to become law. Yet support for a new system has surged, including among Labour members and the party’s backers in the trade unions (see chart 3).

British politicians have a choice. They may attempt to reform the electoral system now. Or they can wait until voters, like gamblers on a losing streak, direct their frustration at the Westminster machine. ■