Prior belief

Prior mean vote share: 50.0% Prior std. dev: 10.0 pts

Add a poll

Sample size (n): 800 Observed share: 52.0%

Random poll generator

Simulated true share: 52.0%

Posterior

Polls combined0

Posterior mean50.0%

Posterior std. dev10.00 pts

95% credible interval—

Smallest single poll var.—

Posterior narrower than any poll?—

Each poll's sampling variance is p̂(1−p̂)/n, converted to precision (1/variance). The posterior combines the prior's precision with every poll's precision — larger, more decisive polls (n large, or p̂ far from 50%) carry more precision and move/narrow the posterior more. Depth in the 3D view = poll order (closest = most recent); height = posterior density, normalised per step so the narrowing width is the visual signal.

Drag to rotate the ridge · X = vote share % · Depth = poll order (nearest = most recent)

Posterior mean (solid) and 95% credible interval (shaded) after each poll