Westminster's plurality system rewards whoever finishes first. A French-style runoff asks a different question: who can beat everyone else head to head? Set the first-round vote below, and the second round resolves by ideological proximity — each eliminated candidate's voters move toward whichever finalist sits closest to them, or stay home if neither does.
Low values mean voters only transfer to candidates very close to them. High values mean they spread more willingly across the spectrum.
How readily voters stay home when neither finalist appeals to them. At 0 everyone turns out and picks a side; at 1 disaffection is maximal.
Each candidate carries the left–right score from the centre of gravity analysis — Green −7, Labour −2, Lib Dem −1, Conservative +5.5, Reform +8.5, Restore Britain +9.5, and so on. Those positions do all the work in the second round.
For every eliminated candidate, the model measures the distance from their position to each finalist and converts it into an attraction weight that decays exponentially with distance. Two things follow. Voters split between the finalists in proportion to those weights, so a Lib Dem facing Labour and Reform breaks heavily one way. And a share of them abstain, rising as the nearer of the two finalists gets further away — a Green voter offered a choice between two right-wing candidates has nobody within reach, and many simply don't vote. That abstention is the mechanism that decides most real runoffs.
The turnout sliders work on the first round instead. They scale each candidate's raw support before renormalisation, so you can model an energised base or an apathetic one without changing anyone's underlying popularity. This matters more than it sounds: on current polling Labour and Reform reach the runoff with barely a point between second and third place, and a modest turnout swing on the right is enough to put the Conservatives into the final instead — producing a runoff with no left-wing candidate at all, and an abstention rate to match.
Two caveats. Real presidential candidates are people, not parties, and personal appeal routinely overrides party position — this model has no way to represent a popular moderate or a toxic nominee. And a UK presidential race would almost certainly reshape the party system before its first ballot, since the parties themselves are artefacts of first past the post. Treat this as a way of interrogating the shape of British opinion, not as a forecast of an election that isn't going to happen.