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Sampling a model several times and taking a majority vote raises accuracy — but you pay for every sample, so the bill scales with N while the accuracy gain flattens fast. This prices the true cost per correct answer of voting, shows the accuracy each N buys, warns you when voting makes things worse, and tells you whether N samples of a cheap model beats one call to a better one.
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voted accuracy (N)
—1 sample / correct
—N samples / correct
—cheaper per correct
Accuracy and cost at each N
The voted accuracy climbs fast then flattens; the cost per correct answer is N samples divided by that accuracy. The cheapest-per-correct row is highlighted — it is almost always a low N. Your chosen N is marked.
N samples
Voted accuracy
Cost/query
$/correct
Monthly
Voting buys accuracy, almost never savings
Self-consistency is one of the cheapest accuracy tricks in the book and one of the easiest to misread on a spreadsheet. The mechanism is honest: ask the model the same question a handful of times at a real temperature, take the answer that shows up most, and you lean on the fact that a decent model is right more consistently than it is wrong in any single way. The accuracy really does go up. What goes up faster is the bill, because there is no discount for the second, third or fifth sample — each one is a full-price call. And the accuracy curve is unkind: it leaps from one sample to three, gives you noticeably less from three to five, and by the seventh you are paying full freight for a rounding error of improvement. Divide the N-times cost by the voted accuracy and the cost per correct answer usually climbs, not falls — which is why voting is an accuracy tool, not a savings tool. There is also a trap on the low end: if your single-sample accuracy is under 50%, majority voting does not rescue you, it drags you down, because the majority is now voting for the wrong answer. The one number this calculator cannot show you is what a mistake costs; that is the number that decides whether the extra samples are worth it. Price a single call first with the token cost calculator, weigh a cheap-but-wrong model against a pricier-but-right one with the cost-per-correct-answer calculator, and if you are chaining calls into an agent where failures cascade, size the full run with the AI agent cost calculator.
It takes the cost of one sample, the single-sample accuracy as a success rate, and N. The cost of a voted query is simply N times the sample cost. The voted accuracy is the binomial probability that more than half of N independent samples are correct — the majority-vote result — which rises toward 100% when single-sample accuracy is above 50% and falls toward 0% when it is below. The cost per correct answer is the voted query cost divided by the voted accuracy, and monthly spend is that per-correct cost times queries per day times 30.4. The alternative model is priced the same way: its cost per call divided by its accuracy. This assumes the samples are independent and that wrong answers are diverse rather than colluding on one wrong value; when a model is confidently wrong the same way every time, real-world voting helps less than this binomial model suggests.
Frequently asked questions
What is self-consistency and why does it cost more?
You sample the model several times at a non-zero temperature and take the answer that recurs most — the majority vote. It works because the correct answer tends to recur while wrong ones scatter. It costs N times a single call because you pay for every sample, and the accuracy gain flattens after the first few, so late samples buy very little. That mismatch — linear cost, flattening benefit — is what this calculator prices.
How much does majority voting actually improve accuracy?
It depends on single-sample accuracy and flips at 50%. Above half, voting drives accuracy toward 100% — 70% single-sample might reach ~78% at three votes and ~84% at five. Below half, voting makes it worse, pushing toward zero, because the majority reinforces the wrong answer. This calculator uses a binomial majority and flags the sub-50% case where voting is harmful.
Is self-consistency cheaper than just using a better model?
Usually not. Voting buys accuracy at N times the cost, so its cost per correct answer typically rises even as raw accuracy improves — five samples of a cheap model can cost more per usable result than one call to a pricier, more accurate one. It wins mainly when a better single model is far more expensive or unavailable. This calculator puts N samples against a single alternative call so you can see which is cheaper per correct.
When is paying for self-consistency worth it?
When a wrong answer costs far more than a few extra samples. Gating an automated action, extracting a value for a financial decision, or grading at scale can justify 3–5× spend to move accuracy up ten points — cheap insurance against costly mistakes. On high-volume, low-stakes work where a human quickly corrects errors, it rarely pays. Weigh the extra spend against what a mistake actually costs — the one number not on the calculator.