How to do cost-effectiveness analysis for elections

A detailed post by Zach Stein-Perlman on the LessWrong forum has captured significant attention by providing a rigorous mathematical framework for calculating the cost-effectiveness of election interventions. The core formula is A*B/C, where A is the 'goodness' if your candidate wins, B is the probability one vote flips the election, and C is the cost per vote. The post focuses intensely on accurately calculating B, arguing that professionals often get this wrong. Stein-Perlman advocates for modeling the election's vote margin as a normal distribution with a mean (μ) and standard deviation (σ), where the probability a single vote is decisive is proportional to the probability density of this distribution at a zero margin, divided by the total number of voters (N).

For practical application, the author provides specific heuristics, suggesting a standard deviation (σ) of around 7% for typical partisan general elections. This yields concrete probabilities: 5.7/N for a toss-up (μ≈0%), 4/N for a moderately favored candidate (μ≈±6%), and 1.3/N for a strongly favored candidate (μ≈±12%). The post crucially distinguishes between 'marginal' interventions (like get-out-the-vote calls affecting a tiny fraction of voters) and 'non-marginal' ones (like nominating a stronger candidate), which require different calculations. It also addresses complexities like Electoral College dynamics and warns that common shortcuts—like assuming an election will be as close as past similar ones—lead to bad inferences, cementing the argument for a proper probabilistic model.