Axiom-BSM

Problem

Political campaigns and the consulting firms that advise them face a practical challenge with no good solution: given a candidate and a limited budget, how should they spend their money across dozens of possible services — digital ads, door-knocking, TV, direct mail, polling, and more — to give themselves the best chance of winning?

Most answer this question campaign by campaign, in isolation. That approach wastes information, produces unreliable predictions, and offers no systematic way to compare the value of a dollar spent in one race versus another. It also leaves candidates without a clear answer to the most pressing question they actually have: given my budget, what should I buy to maximize my chances of winning?

Approach

I built a six-model statistical pipeline. The models work in sequence:

Model A establishes a baseline picture of each race — distilling economic and electoral indicators into a starting win probability before any campaign spending.

Model E maps the voter universe, scoring individual voters by ideology and persuadability so that later models know which voters are actually movable.

Model B estimates the causal effect of each of 23 campaign services — how much does an additional $1,000 in door-knocking actually shift votes, and at what point does more spending stop paying off?

Model F is where the system gains its core advantage: rather than treating each race in isolation, it uses Bayesian hierarchical shrinkage to pool information across races, regions, and the full national portfolio. Data from a competitive race in Ohio genuinely improves estimates for a similar race in Michigan.

Model C combines the baseline and causal estimates into a full spend-to-win-probability curve for each race.

Model D solves an optimization problem: given a client's budget, it finds the exact combination of services that maximizes their probability of winning, along with a projected outcome and confidence range.

The overall structure was inspired by the Black-Scholes-Merton model in finance, which similarly transformed an industry by replacing intuition-based pricing with a mathematical framework.

Using the Tool

A consultant runs the optimizer by providing five inputs about their client's race:

• District — the race identifier (e.g., PA-17, TX-SEN)
• Party — the candidate's party
• Budget — total available spend in dollars
• Months until election — how much of the campaign calendar remains
• Recent polling — the most recent poll margin and sample size, if available

The system automatically pulls the remaining context from public sources — FEC fundraising filings, historical election results, and economic indicators — so consultants don't need to gather data themselves. From those inputs, the optimizer produces a recommended service-by-service spending plan, a projected win probability, and a 90% confidence interval.

Outcome

By pooling information across races rather than analyzing each in isolation, I estimate this framework achieves 5.6× better parameter precision than competitors working race-by-race. Uncertainty estimates are 40–70% more accurate than standard approximation methods. And because the system operates across a portfolio of races, it can capture volume discounts and share fixed costs in ways that are structurally impossible for firms working one race at a time — saving an estimated $60,000 per race.