Election Forecast

Method: Poisson-binomial with a national swing. Every race has its own blended win probability. Treating the races as independent coin flips with different odds, the exact distribution of “how many seats do the Democrats win” is the Poisson-binomial distribution, computed by convolution rather than sampling — so there is no simulation noise. The odds shown are the mass of that distribution at or above the majority line (218 in the House; 51 in the Senate, including the 34 Democratic caucus seats not on the ballot, with 50–50 going to Republicans through the Vice President).

Races do not miss independently, though: when polls and markets are wrong they tend to be wrong in the same direction everywhere. So the calculation is repeated across a grid of national swings — a shift added to every seat on the log-odds scale, drawn from a normal distribution with σ = 0.35 (a coin flip becomes roughly 59/41 at one sigma) — and averaged with normal weights. Without that layer, 470 near-independent contests would add up to false certainty.

How it works. Each of the 10,000 runs plays out all 470 races once. First a national swing is drawn — normal, σ = 0.35 on the log-odds scale, the same as the projection above — and added to every seat. Then each state gets its own smaller swing (σ = 0.15) shared by its House and Senate races, so neighbouring districts miss together. Finally every race is decided by one coin flip at its shifted probability, and the Democratic seats are counted. The bars show how often each seat total occurred; the headline odds are the share of runs on each side of the majority line.

Why the two methods agree so closely. Both start from the same seat odds and the same national swing, which carries most of the uncertainty. Method 1 is exact; this one adds the state layer and about half a point of sampling noise, so the two usually land within a point of each other and often round to the same figure. What the simulation adds is the full seat-count distribution and the joint outcome of both chambers.