Who will win the 2027 French presidential election?

A transparent Bayesian poll-aggregation forecast — first-round vote intention and the runoff.

Who's running?

Choose the field — the left and centre are multi-select, the RN fields one nominee (Le Pen or Bardella), and Les Républicains may sit it out. Only candidates polled recently enough to estimate are shown; the always-included set and minor candidates are fixed. The forecast recomputes live from the model's posterior draws.

Who wins the presidency?

Each dot is one simulated election, placed in the row of the candidate who won it — so the width of each cloud is that candidate's chance of winning. Hover a dot to see that simulation's first-round result and the runoff it produced. ()

First-round vote intention over time

Lines are the model's estimate; shaded bands are the 80% credible interval, widening toward election day. Dots are individual polls (renormalised within the line-up).

1,000 simulated elections

Each dot is one simulated first-round result. The two candidates with the highest scores advance to the runoff, so candidates clustered near the top are fighting for the second qualifying spot.

Most likely runoff match-ups

The runoffs that occur most often across simulations. Each dot is one simulated runoff, placed by the RN candidate's second-round share and coloured by the winner; the dashed line is the 50% threshold. Hover a dot for that runoff's result.

The forecast is a Bayesian poll-aggregation model in the tradition of FiveThirtyEight and the Economist's 2020 model (Gelman, Morris & Heidemanns), which in turn build on the dynamic state-space election forecasting of Linzer (2013). We adapt that lineage to France's two-round, many-candidate system. It has two stages — a first-round vote-share model and a runoff model — and every prior is calibrated on the 2012–2022 cycles, so the uncertainty is empirically grounded rather than assumed. Everything is fit in Stan (first round: 4 chains, R̂ ≈ 1.00), and this page recomputes the forecast for any chosen line-up directly from the posterior draws.

1 · First round: latent vote intention as a random walk

For candidates c = 1…C over weeks w = 1…W (with W the election week), a latent support β_c,w on an unbounded (log-odds–like) scale follows a Gaussian random walk:

Latent / log-odds scale Vote shares live between 0 and 1, which is awkward to model directly. We instead track an unconstrained number for each candidate — a log-odds-like “support” (latent = not observed, inferred) — and turn the whole vector back into shares with the softmax below. On this scale movements are additive and take tidy Normal priors.

β_c,w = β_c,w−1 + σ ε_c,w, ε_c,w ∼ Normal(0, 1), β_c,1 ∼ Normal(0, 1.5²).

Random walk A random walk lets each candidate's support wander week to week by small Normal steps, with no built-in trend: today's level is yesterday's plus noise. It encodes “opinion moves gradually, and we're more uncertain about weeks with no polls” — which is why the bands pinch at polls and widen in the gaps. Treating opinion as a latent time series like this is the core device of Linzer (2013) and the Economist model.

The weekly step σ = 0.045 is fixed rather than estimated. This is a deliberate regularisation: the 2027 field is volatile, and letting σ float lets it soak up scenario-to-scenario disagreement as if it were real movement. (This departs from the usual “let the data speak” instinct — cf. Gelman's weakly-informative-prior advice — trading a little in-sample fidelity for a smoother, less overconfident line; the genuine forecast-horizon spread is recovered from history in §3.) The overall level is unidentified by the softmax below, so we anchor it with a soft sum-to-zero each week, ∑_c β_c,w ∼ Normal(0, 0.1²).

2 · How a poll sees the latent state (subset softmax)

French polls test different line-ups: one release may or may not include a given candidate. A poll i fielded in week w_i by pollster p_i reports shares only over the candidate subset S_i present in that hypothesis. We model it as the softmax over exactly that subset of the latent state plus a pollster house effect δ_p,c:

Softmax The softmax turns a vector of unbounded latent numbers into positive shares that sum to 1 — the many-candidate generalisation of the logistic function. Restricting it to just the candidates in a given poll is what makes a “Le Pen vs…” poll and a “Bardella vs…” poll both usable: each reports the conditional shares among the candidates actually offered to respondents.

η_i,c = β_{c,w_i} + δ_{p_i,c}, θ_i,c = exp(η_i,c) ⁄ ∑_{c′∈S_i} exp(η_i,c′), c ∈ S_i.

(y_i,c)_{c∈S_i} ∼ Multinomial(ñ_i, θ_i).

This renormalisation is exactly what a restricted-line-up poll measures (conditional shares), so polls with different fields all inform the same β. House effects use a hierarchical scale δ_p,c ∼ Normal(0, σ_house²) and are soft-centred, ∑_p δ_p,c ≈ 0, so β tracks the average pollster.

House effect Pollsters have persistent “house” leans — one firm consistently a point or two higher for a given candidate, from its methods and weighting. We give each pollster×candidate a bias δ and force them to average to zero, so the latent β reflects the average pollster rather than any single house. (Pollster house effects and ratings are central to FiveThirtyEight's aggregation.)

Effective sample size. Reported shares are counts on a deflated sample,

ñ_i = n_i ⁄ (d_eff · m_i),

Design effect & effective sample size A real poll varies more than a simple random sample of the same size (quotas, weighting, mode). The design effect d_eff ≈ 2.2 measures how much more; dividing the headline n by it gives the effective sample the model should actually trust. We also divide by m_i, the number of line-ups tested in one fieldwork, so five hypotheses from a single sample aren't double-counted as five independent polls. (FiveThirtyEight similarly scales each poll's effective sample size by pollster quality.)

3 · Calibration from history, and the forecast

Using final-stretch polls vs. actual results in 2012/2017/2022, we regress squared poll error on horizon h (days to the election). A random walk implies variance growing linearly in time:

Var( poll error at horizon h ) ≈ a² + c h.

The intercept gives the irreducible election-day poll error a ≈ 0.038 (about 3.8 points); the slope gives the daily drift √c ≈ 0.0020 (0.2 pt/day). To forecast, we take the latent state at the last poll week w^∗ and add (i) random-walk drift to election day and (ii) the systematic election-day miss — the piece that does not shrink with more polls:

Forecast-horizon spread How wrong are polls as a function of how far out they are? Two things widen the forecast toward election day: opinion is still drifting (the random-walk term, growing like √time), and even final polls miss by a bit in a correlated, national way (the a term, which never shrinks no matter how many polls you average). Measuring both from past cycles is how the model knows to be wide now and tighter in April. (The Economist model adds an explicit election-day polling-error term for exactly this reason, and forecasters such as Nate Silver likewise widen their intervals when polls are sparse or inconsistent, so the model isn't overconfident.)

β̃_c = β_c,w^∗ + s_rw √(W−w^∗) ζ_c + s_err υ_c, ζ_c, υ_c ∼ Normal(0,1).

The share for a chosen line-up 𝒜 is the softmax over just those candidates, π_c = softmax_𝒜(β̃)_c. The drift/error sds are the historical quantities mapped from the share scale to the latent scale by κ = 1⁄[π(1−π)] ≈ 5.9 (evaluated at a typical π ≈ 0.22), i.e. s_rw = √c · √7 · κ and s_err = a · κ.

4 · Runoff: a Bradley–Terry model

Each candidate has a latent runoff strength s_c. A head-to-head poll of A vs. B gives A's expected share as

Bradley–Terry model A classic paired-comparison model (Bradley & Terry, 1952): give every candidate one “strength”, and the chance A beats B depends on the difference in strengths. It pools sparse head-to-heads and predicts unpolled pairings by transitivity — if A beats C handily and B only narrowly, we can estimate A vs. B.

Overdispersion / beta-binomial Overdispersion means more spread than a plain binomial would predict. Modelling the count k_A with a beta-binomial (concentration φ) lets runoff polls disagree a little more than coin-flip sampling implies — a standard, gentle fix for survey counts.

p = logit⁻¹(s_A − s_B), k_A ∼ BetaBinomial(ñ, pφ, (1−p)φ),

with s_c ∼ Normal(0, 1.5²) (soft sum-to-zero) and over-dispersion φ ∼ Gamma(2, 0.05). Bradley–Terry pools sparse matchup polls and predicts any pairing through shared opponents. For a runoff between the first-round top two X, Y, the winner probability adds a horizon inflation σ₂ = √(s_err² + s_rw,day² H):

P(X wins) = logit⁻¹(s_X − s_Y + σ₂ ξ), ξ ∼ Normal(0,1).

Does Bardella tell us about Le Pen? Because each candidate has a single runoff strength, a poll of Philippe vs. Bardella sharpens s_Philippe, which in turn tightens the predicted Philippe vs. Le Pen result — information flows through the shared opponent (Bradley–Terry transitivity). In the first round, by contrast, Le Pen and Bardella are separate latent series with no party-level pooling; they become comparable only because they face the same opponents, so Bardella's numbers barely move Le Pen's first-round share directly.

5 · What the dots are

One simulated election = one posterior draw of {β̃, s} plus fresh drift/error/runoff noise: draw the first-round shares π, take the top two, sample the runoff winner (Bernoulli at P(X wins)). Repeating over the thinned posterior gives the posterior predictive distribution you see — the trajectory bands are per-week quantiles of π, and each dot in the “who wins” and “1,000 simulations” panels is one such draw.

Posterior predictive distribution After fitting, we don't report one number; we draw many plausible worlds consistent with the data and priors — the posterior predictive distribution. Each dot is one such world (one simulated election); the spread of the dots is the forecast's uncertainty.

6 · Assumptions & limitations

Shares among expressed votes. Turnout and undecideds are not modelled; reported shares are renormalised over modelled candidates, i.e. undecideds are assumed to split like decideds.
The line-up is a scenario, chosen by you, not inferred.
Softmax independence (IIA). Two candidates never polled together are placed on a common scale only through shared opponents; for true substitutes (e.g. the two RN nominees) the softmax would overstate their combined support, which is why they are mutually exclusive in the picker.
Runoff uses posterior-mean strengths plus horizon inflation, not the full strength posterior — a modest understatement of runoff uncertainty.
Polls-only. No economic or approval “fundamentals”.

Calibrated quantities

quantity	symbol	value
election-day poll error (sd)	a	3.8 pts
opinion drift (random walk)	√c	0.20 pt/day
pollster house-effect sd	σ_house	0.9 pt
design effect	d_eff	2.2
weekly RW step (fixed, smoothing)	σ	0.045 (latent)
share→latent conversion	κ	≈ 5.9

Full source (R + Stan + this page) accompanies the model; calibration is produced by R/03_calibrate.R, the fits by 04–05, and the shipped draws by R/08_export_draws.R.