Possibility Effect

What it is

The possibility effect is the bottom end of the decision-weight curve in prospect theory. In Kahneman's account in Thinking, Fast and Slow, the effect causes highly unlikely outcomes to be weighted disproportionately more than they deserve, and the step from 0 to 5 per cent transforms the situation by creating a possibility that did not exist earlier. At the low end, he writes, unlikely events are considerably overweighted. It is the mirror of the certainty effect, which operates at the top of the curve.

The weights are the 1992 estimates by Tversky and Kahneman. The published formula, run at the median gain parameter of 0.61, gives a weight of 5.5 to a 1 per cent chance, 8.1 to a 2 per cent chance, 13.2 to a 5 per cent chance and 18.6 to a 10 per cent chance. The step from 0 to 5 per cent adds 13.2 weight points, and the step from 5 to 10 per cent adds 5.4. Almost all of the inflation arrives in the first few points. We calculated these figures from the formula and the median parameter, and they reproduce the table Kahneman prints in his book.

The middle of the curve is flattened to match. From 5 to 95 per cent the weights run from 13.2 to 79.3, which Kahneman calls about two-thirds as much as rationally expected, and he writes that people are almost completely insensitive to variations of risk among small probabilities. Together the two ends produce the fourfold pattern: risk seeking for low-probability gains, which is the lottery ticket, and risk aversion for low-probability losses, which is insurance.

The 1992 paper puts the qualification in the same breath as the finding. People overweight low probabilities, and "very small probabilities can be either greatly overweighted or neglected altogether." Kahneman repeats the point after his table: below 1 per cent no unique decision weight can be assigned to rare events, and some are ignored entirely. In the chapter on rare events he adds that the original theory said highly unlikely events are either ignored or overweighted but did not specify the conditions under which one or the other will occur, and he gives attention as the missing condition.

In effect

In research: emotion and the shape of the curve

In 2001 Yuval Rottenstreich and Christopher Hsee proposed that the S-shape of the weighting curve reflects emotion as well as the psychophysics of chance. Outcomes of equal money value differ in how much emotion they evoke, they argued, and the weighting curve is more S-shaped for emotionally rich outcomes, so people are more sensitive to moving away from impossibility and certainty and less sensitive in the middle. In their test a prize low in emotion was preferred to a prize high in emotion when each was certain, and the preference reversed at low probability. Kahneman reports a later Princeton test in which a rich, vivid picture of an outcome reduced the role of probability whether or not the outcome was emotional. The book names no author and no paper for it.

In everyday life: the bus and the red light

Kahneman gives his own experience as an illustration. Between December 2001 and September 2004 there were 23 bus bombings in Israel, with 236 fatalities, among about 1.3 million daily bus riders, and he reports that he disliked stopping next to a bus at a red light, against a base rate that was very small. In his account an extremely vivid image of death, reinforced by media attention and frequent conversation, becomes highly accessible, and the weight it carries outruns the arithmetic. The figures are the book's, and he gives them as his own period of observation, not as a controlled study.

In commerce: chances instead of discounts

Probabilistic promotions offer a chance of a large saving in place of a sure small one. A 2025 paper in the Journal of Consumer Research by Celia Gaertig and Joseph Simmons, five studies with 8,969 participants, notes that past research suggests such promotions often beat sure discounts of equal value and that two explanations had become standard. One was diminishing sensitivity. The other was that people overweight small chances, which is the possibility effect. The authors report that their findings are inconsistent with both standard accounts, and that the appeal of the uncertain offer depended on how large the sure discount looked. The result shows that the effect is not the whole of what a promotion does.

What it does not say

It does not say that people always overweight small probabilities. Hertwig, Barron, Weber and Erev (2004) gave 100 students six problems with rare events at probabilities of 0.2, 0.1 or 0.025. People who read the odds chose differently from people who learned them by sampling, by an average of 36 percentage points, and the direction was underweighting after experience in every problem. A 2006 reanalysis of those data attributed most of the gap to sampling error, because small samples tend to miss low-probability outcomes, and a 2013 study reports that underweighting persists even without sampling error. See Description-Experience Gap.

It does not give a single number for a rare event. Kahneman writes that no unique weight can be assigned below 1 per cent, so the 5.5 for a 1 per cent chance sits at the edge of the range where the curve is dependable. It was estimated from choices involving gains, from 25 graduate students choosing among monetary prospects, and it is a median parameter, not a trait.

It does not say that format is irrelevant. A 2002 study of 226 experienced clinical psychologists found that frequency formatting and a vivid depiction of a violent outcome both produced more conservative decisions, but only among clinicians working in forensic facilities. Presentation shifts the weight under some conditions.

The evidence status is mixed. The weighting at the low end is documented in choices from description, and it is unstable, qualified by its own author and reversed in some experiments with sampling.

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