Over-precise numbers manufacture false certainty

What it is

“Confidence 87.42%” looks like a measurement. The number a generative model actually emits is often an uncalibrated softmax maximum that does not have tenths of a percent of meaning. Write digits that have no meaning, and people will read them as if they did. False precision is the look of a number impersonating resolving power.

This is not “should uncertainty be shown,” nor “how fine should a band be.” It is: every digit you write is taken as a promise.

Why it happens

Numerical cognition reads significant figures as evidence quality. Two decimal places are the language of a lab instrument, not “we have a float between 0 and 1.” Risk-communication work has said this for years: the format speaks before the content does. On a badly calibrated model, 87 and 87.42 are usually indistinguishable; the interface uses the latter to imply that 87.42 and 86.91 can be compared.

Worse, the comparison will actually happen. People pick the larger of two unreliable numbers and believe they have made a quantitative decision. False precision turns noise into a sortable pseudo-signal. The decision is then driven by the sort order of the noise, with a feeling of being more scientific than “roughly.”

Studying it

The same latent score, rendered as an integer percent, one decimal, two decimals, and as band words. Measure: when the gap between two numbers is smaller than the model’s calibration error, do people still choose by magnitude; and how accurate do they think the number is. Independent variables: digits, whether a calibration error or the word about is shown. Dependent variables: over-resolution, calibration judgement, stability of choice after a tiny jitter is added to the score.

If choices flip at scale after a jitter smaller than calibration error, people are deciding with the false precision you supplied.

Where it stops holding

A probability that has been carefully calibrated, with error well below the displayed resolution (some forecast points), can carry more digits. That is a measurement, not a softmax. Finance and dosing have statutory decimal rules; those digits are institutional, not model swagger. Even band words reintroduce false resolution if the scale is a fussy seven-step (almost certain / very likely / …). This entry is about precision of appearance. It does not treat whether confidence and accuracy are the same quantity.

Applying it

• Default to band words or coarse tens-of-percent. Digits must not exceed the resolution your calibration can support. If you cannot tell 10 points apart, do not write 87.
• When a number is required, write “about 80%” or an interval “70–90,” so the wide dimension is visible.
• Do not turn uncalibrated logits into a two-decimal bar. Bar length will be read as a precise measurement.
• Check: jitter the displayed value by less than calibration error and see whether people’s choices move. If they move, false precision is driving the decision. Then ask how much surer 87.42 is than 86 — if they tell a fine story, the format is already lying.

Related

• Same group: L1.03.1 Uncertainty must be expressed, not hidden · L1.03.2 The expression must match the granularity of the user’s decision
• Nearby: L1.04 Presenting confidence · L1.08 Confidence displays and their misreadings · L5.05 The moderation principle of transparency
• Search terms: false precision · spurious precision · overprecise probability