Bayesian Election Probability & Polling Variance Simulator

Posterior Mean

39.8%

Expected Viability Share

Posterior SD

0.024

Uncertainty Standard Dev

Win Probability

88.4%

Chance Candidate Gains Viability

Median EVs

284

Electoral Votes (50th Pct)

P-Value vs Null

0.012

Null: Viability < 30%

1. Bayesian Updating Distribution Curves (Prior vs Likelihood vs Posterior)

Prior

Poll Likelihood

Posterior

2. Monte Carlo Electoral College Simulation (5,000 Iterations)

< 270 EVs (Loss)

≥ 270 EVs (Win)

Political Presets

Interactive Parameter Scrubbers

Historical Prior Mean (μ₀) 35.0%

Candidate initial baseline viability standard.

Prior Standard Dev (σ₀) 8.0%

Uncertainty surrounding historical candidate baseline.

Fresh Poll Support Mean (μ_x) 42.0%

Observed support share in latest polling aggregation.

Poll Sample Size (N) 1,000

Directly determines polling variance & margin of error.

Battleground State Correlation (ρ) 0.65

Systemic polling error shared across swing states.

Monte Carlo Simulations 5,000

95% Credible Interval & Margin of Error

Poll Margin of Error: ±3.1%

95% Posterior Interval: [35.1%, 44.5%]

Prior vs Poll Weight: 3.7% / 96.3%

Canonical Statistical State & Bayesian Updating Derivation

Conjugate Normal Formulas

            1/σ²post = 1/σ²prior + 1/σ²poll

            μpost = σ²post (μprior/σ²prior + μpoll/σ²poll)

Representative Fixture Verification

Prior: N(0.35, 0.08²)
Poll: N(0.42, 0.0156²) with N=1,000
Computed Posterior Mean: 0.398

Monte Carlo Electoral Model

Base Safe EVs: 210
Battleground EVs: 93 (PA, MI, WI, GA, NC, AZ, NV)
Win Odds (≥270 EVs): 88.4%

Trace the saved watermark counting rules and fixture limits

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Read the explanation

The saved election scenario treats the poll as binomial and sets its standard error to square root of p times one minus p over sample size. At an illustrative share one half, four hundred observations give standard error point zero two five, and sixteen hundred give point zero one two five. Both bars measure standard error at sixteen thousand pixels per share unit. Four times the sample halves this assigned error; it does not account for polling bias, survey design or changing political conditions. It combines normal prior and poll distributions by inverse-variance precision. With illustrative equal standard deviations, prior share point three and poll share point five receive equal weight, giving posterior point four. Both bars display the input means at one thousand pixels per share unit. Reducing one standard deviation increases its precision quadratically. The source scenario is pedagogical, not a current election forecast or evidence that its assumptions are calibrated. Its electoral simulation adds a shared normal error with standard deviation posterior sigma times square root rho, and independent state error with sigma times square root one minus rho. At illustrative sigma point zero two and rho point two five, shared error is point zero one, while independent error is about point zero one seven three two. Both bars measure standard deviation at thirty thousand pixels per share unit. Synthetic safe votes and swing-state baselines drive the result; Monte Carlo outcomes do not certify a real forecast.