# How to do cost-effectiveness analysis for elections

*Some professionals get this wrong.*

You should use three parameters:

A. Goodness if your preferred candidate wins rather than loses

B. Probability that one vote for your candidate would flip the election

C. Cost per vote

Then cost-effectiveness is A*B/C.

I'm only really going to discuss B in this post. For B, you should come up with a probability distribution for the vote margin. In general you should use a normal distribution, with parameters depending on the election. Let μ be the mean and σ the standard deviation of vote margin as a fraction of the total (for example, an election you win 60-40 has margin +20%). Then the density of the normal distribution at zero is e^(-1/2 * (μ/σ)^2) / (σ*√(2π)). And so B is that divided by the number of voters, N. You can also use this [Google Sheet formula](https://docs.google.com/spreadsheets/d/1oPjs0SIW1ADjVVpAlt8m3N6I-w5MaxSKKf15y7eT2YM/copy).

If you have a good understanding of US (or wherever) politics, the particular election. and math, you can choose μ and σ well. And N is easy.

![](https://res.cloudinary.com/lesswrong-2-0/image/upload/v1774417719/lexical_client_uploads/vjtigfi9enjdhbtqmhpy.png)*Probability distribution of vote margin. Your candidate wins if x>0. The probability that one vote for your candidate will flip the election is proportional to the height of the curve at x=0 and inversely proportional to N. (In this image, μ is +4% and σ is 5%.)*

You can stop reading now; the rest is minor.

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Normal distribution resources: [calculator](https://onlinestatbook.com/2/calculators/normal_dist.html) and [graph](https://www.desmos.com/calculator/jxzs8fz9qr).

You can use *1% vote margin* rather than *1 vote*; you just have to do so for both B and C.

For B, here's a simple heuristic for partisan general elections: assume σ is 7%. Then if the election is a tossup (μ ≈ 0%, P(win) ≈ 50%), B is 5.7/N. If one candidate is favored (μ ≈ ±6%, P(win) ≈ 20% or 80%), B is 4/N. If one candidate is strongly favored (μ ≈ ±12%, P(win) ≈ 5% or 95%), B is 1.3/N. But really σ depends on the election; it can be between about 3.5% (e.g. two weeks before a presidential election) and 10% (far out from an off-cycle state-level election with a high-variance candidate), depending.

For B, one common flawed approach is to assume *this election will be about as close as similar elections in the past*. That generally leads to bad inferences. Past election results can inform your normal distribution, but you basically have to make a distribution. (I'm not justifying this view here, but I feel confident.)

C is often tricky; it depends on the intervention (and the election). Note that online sources and chatbots are often wrong about cost per vote.

If you're determining C by averaging over a distribution, you have to take the *harmonic* mean rather than the arithmetic mean. Or: you have to think in terms of votes per cost, not cost per vote.

Some kinds of elections are more complicated. If your goal is a majority in the House, what matters in winning *in worlds where the House is close*, so you should multiply probability that the House is close, goodness *in worlds where the House is close*, and probability that one vote for your candidate would flip the election *in worlds where the House is close* (for any consistent operationalization of *the House is close*). If your goal is flipping the presidency, you need to think about the Electoral College; one good approach is to multiply *probability of flipping a state* by *probability that state is the tipping point*. For elections with more than two strong candidates, vote margin isn't normally distributed so you need a different approach for B.

Most interventions are *marginal*: the number of voters they affect is a tiny fraction of the total. Other interventions are not; for example, nominating a stronger candidate can increase vote margin by several percentage points. This matters because for marginal interventions you can just consider *the probability that each vote for your candidate flips the election*, but for non-marginal interventions that probability changes as you add votes. Instead you have to consider the probability that your candidate wins before and after the intervention (generally by inferring this from probability distributions for vote margin, before and after), then take the difference.

The fact that votes can tie doesn't matter. One way to think about this is to think in units of 1000 votes rather than 1 vote. Another way is to suppose ties will be broken in one direction or the other.

In the last 15 years, election work has become more effectiveness-focused. We're now most of the way through the moneyball transition. Election efforts now use data-based targeting, use RCTs, and try to minimize "cost per net vote." But many professionals still only care about numbers in certain contexts. For one, it's unusual to use numbers to prioritize between different elections, even though elections differ dramatically in (1) importance and (2) probability that one vote will flip them.

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*This post is part of* [*my sequence inspired by my prioritization research and donation advising work*](https://www.lesswrong.com/s/kvBmY5GaB3qdCRQ29)*.*