Why 99% does not feel like 100%
Expected utility theory has a tidy prediction about probability. A one-percentage- point reduction in risk is a one-percentage-point reduction in risk, and it should be worth the same whether it takes you from 60% to 59% or from 1% to 0%.
People do not behave that way, and they are consistent about not behaving that way. The move from 1% to 0% is valued far above the move from 60% to 59%. Certainty itself carries a premium. Kahneman and Tversky called it the certainty effect, and it is one of the most reliably reproduced findings in decision research.
Why it matters in health
Almost every health decision is a probability statement. A treatment reduces recurrence risk. A screening test has a false-negative rate. A vaccine is effective at some percentage. If the value people place on a risk reduction is non-linear in the probability, then three things follow.
Willingness to pay is not proportional to risk reduction. A treatment that eliminates a small risk can command a price well out of proportion to the expected harm it prevents. That is not irrationality to be corrected. It is a preference, and cost-effectiveness analysis that assumes linearity will misprice it.
Communication format changes decisions. “Reduces your risk from 2% to 1%” and “halves your risk” describe the same fact and produce different choices. Neither framing is neutral, so there is no option to avoid framing; there is only the choice of which framing to use, made deliberately or by accident.
Partial protection is undersold. A vaccine described as 95% effective is frequently heard as it might not work, and the residual 5% does more work in the listener’s mind than the 95%. Public health messaging that leads with an effectiveness percentage is leaning on a number that people process in a predictably skewed way.
What to do about it
Not much can be done about the underlying preference, and it is not obvious that anything should be. The practical response is to stop assuming linearity where the evidence says there is none: use elicitation methods that can detect the non-linearity, model it rather than average it away, and test message framings empirically instead of choosing them by intuition.
There is a recorded webinar covering this in more detail: watch it.