Certainty Effect

What it is

The certainty effect is the top end of the decision-weight curve in prospect theory. In Kahneman's account in Thinking, Fast and Slow, a decision weight equals the probability only at 0 and at 100 per cent, and it departs sharply from probability near those two points. At the top, outcomes that are almost certain are given less weight than their probability justifies. A 99 per cent chance is treated as clearly short of a sure thing, and the final step to certainty is treated as a change in kind.

The demonstration that started the line of work was Maurice Allais's. In Kahneman's retelling Allais put two choice problems to some of the leading decision theorists in the world and then revealed that their preferences across the two violated expected utility theory, which was the theory they worked with. Kahneman writes that Allais had intended the announcement to be a bombshell. In the first problem the choice was a 61 per cent chance of $520,000 against a 63 per cent chance of $500,000. In the second it was a 98 per cent chance of $520,000 against a certain $500,000.

The same two points of probability separate the options in both problems. Kahneman's reading is that the two points are not equal in force: the difference between 100 and 98 per cent is far more impressive than the same difference between 63 and 61. Kahneman records that his and Tversky's initial goal was a satisfactory psychological account of Allais's paradox, and the account they built, prospect theory, replaced the probability in the expected value calculation with a decision weight.

We can put numbers on the contrast. The weighting function in Tversky and Kahneman's 1992 paper, run at the median gain parameter of 0.61, gives a weight of 47.9 to a 61 per cent chance and 49.1 to a 63 per cent chance, a difference of 1.1 points. It gives 87.1 to a 98 per cent chance and 100 to certainty, a difference of 12.9 points. The same two points of probability are worth about eleven times as much at the top of the scale as in the middle. These figures are our own calculation from the published formula and the median parameter. They are not a measurement of any person, and the function reproduces ten of the eleven rows of the table that Kahneman prints.

Kahneman also writes that the certainty effect appears to be the stronger of the two ends of the curve. The anxiety of the second situation, he says, appears more salient than the hope in the first.

In effect

In research: the 1992 estimates

Tversky and Kahneman's 1992 paper, which called the revised theory cumulative prospect theory, reports median parameters of 0.61 for gains and 0.69 for losses. They came from a new experiment with 25 graduate students from Berkeley and Stanford choosing among monetary prospects, such as a 25 per cent chance to win $150 and a 75 per cent chance to win $50. At the top of the curve the calculation gives a weight of 79.3 to a 95 per cent chance and 91.2 to a 99 per cent chance. Going from 95 per cent to certainty adds 20.7 weight points for five points of probability. The paper's abstract says its review of experimental evidence and its new experiment support a fourfold pattern of risk attitudes, with risk aversion for high-probability gains and risk seeking for high-probability losses.

In everyday life: settling a lawsuit

Kahneman reports that the legal scholar Chris Guthrie applied the fourfold pattern to civil lawsuits. A plaintiff with a 95 per cent chance of winning outright, offered a settlement at 90 per cent of the claim, sits in the cell where the certainty effect makes a sure sum attractive, so the plaintiff is inclined to accept less than the claim is worth on average. The defendant facing a likely loss is in the opposite cell and is inclined to gamble on trial rather than lock in the loss. Kahneman says that the prediction from the pattern, that the risk-seeking defendant holds the stronger hand, was confirmed in experiments with law students and practising judges and in analyses of actual negotiations. The book gives no paper for that confirmation.

In consumer choice: paying to remove a risk

Kahneman describes a survey by a team of economists in the 1980s of parents of small children, who were asked what they would pay for a safer insecticide spray. A bottle cost $10. Each 10,000 bottles carried 15 inhalation poisonings and 15 child poisonings, and the safer version cut each to 5. Parents would pay an extra $2.38 for the two-thirds reduction and an extra $8.09 to eliminate the risk completely, which Kahneman calls more than three times as much. By our arithmetic, removing the last 15 cases rather than 10 of them is 1.5 times the reduction, and the price premium was about 3.4 times. The book names none of the economists and gives no sample size, so the figures are Kahneman's report of the study, not figures we have checked at source.

What it does not say

It does not say that preferring a sure thing is a mistake. The effect describes how weight behaves near certainty. Whether a given choice is wise depends on the stakes and the person, and the pattern does not by itself say whether a particular settlement is good or bad.

It does not hold at the extremes without qualification. Kahneman writes that probabilities below 1 per cent and above 99 per cent are a special case, that no unique decision weight can be assigned to very rare events, and that such events are sometimes ignored entirely. The row for 99 per cent in the table sits at the edge of that qualification.

It is not a universal constant. The 87.1 and 100 are calculated from a median parameter fitted to 25 graduate students choosing among monetary gambles, and the original table is printed in the book with no paper beside it. Individuals differ and the numbers illustrate a shape.

It says nothing yet about what experience does to the top of the curve. The description-experience literature has been tested mainly on rare events at the bottom of the scale, and this site has not traced what it implies for near-certain ones. The evidence status here is robust on the strength of the 1992 review of experimental evidence and the fourfold pattern, and we have not audited the replication record beyond that.

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