# Pseudo-Precision as Rhetoric A number stated to four significant figures makes an implicit claim: that it is known to four significant figures. When the underlying estimate is a rough approximation, the extra digits are not information. They are a persuasion device, and an effective one. ## The forms **Spurious decimals.** "Immigrants commit 47.3% more offenses" implies a measurement precise to a tenth of a percent, drawn from data with sampling error, definitional ambiguity about who counts as an immigrant, and reporting variation across jurisdictions that swamps the stated precision several times over. **Point estimates without intervals.** A projection reported as a single number when the honest output is a range. The [[Congressional Budget Office]] publishes uncertainty discussion; coverage reports the point estimate. See [[CBO Baselines and Scoring Windows]]. **Precision imported through arithmetic.** Multiply a rough per-unit figure by a rough count and the calculator returns many digits. Reporting them all manufactures precision from two approximations — an error a first-year physics student is drilled out of and that appears constantly in policy argument. **Unwarranted specificity in headcounts.** Crowd sizes, casualty figures, and program-fraud estimates reported to the individual when the method cannot resolve to thousands. ## Why it persuades **Specificity reads as evidence of investigation.** "About 40%" sounds like an impression. "41.7%" sounds like a finding, and the listener infers a study behind it — inferring, correctly, that precise numbers usually come from careful work, and being exploited via that reasonable inference. **It preempts challenge.** Disputing "about 40%" is easy. Disputing "41.7%" seems to require your own number, which shifts the burden and makes the skeptic look unprepared rather than appropriately cautious. **It exploits the numeric-authority asymmetry.** Most audiences do not track significant figures. A digit costs nothing to add and buys credibility. ## The inverse move Vagueness is deployed with equal purpose in the other direction. **"Many," "countless," "a growing number," "some say"** — unquantified magnitude claims that cannot be checked and that the audience fills in generously. The two techniques are typically used by the same speaker in the same argument, and the pattern is diagnostic: **precise numbers for the claim being asserted, vague quantifiers for anything that would qualify it.** "There were 3,847 fraudulent ballots, and many more that went undetected." The first half invites verification it will not survive; the second half is unfalsifiable and does the actual work. ## The honest practice Report figures to the precision the method supports. State intervals. Distinguish measured quantities from estimated and modeled ones. Round when rounding is warranted, and say why. Communicating uncertainty is genuinely hard — see [[Reading Probabilistic Forecasts]] — and there is a real tension, because vague-sounding honesty loses to confident-sounding falsehood in a public argument. **That asymmetry is structural and not solvable by better manners.** The most useful defensive habit is not learning to argue better but learning to read the digits as a claim in themselves, and to ask what method could possibly have resolved to that precision. ## Related [[Curve-Fitting and Cherry-Picked Windows]] · [[Statistical Impossibility Arguments]] · [[Reading Probabilistic Forecasts]] · Margin of Error · [[Risk vs Uncertainty]] · [[Framing]] · [[Manufacturing Doubt]] · [[Mathematics and Power Hub]]