Pseudocertainty Effect: Why a Conditional Sure Thing Feels Certain

The two versions of the problem above are the same gamble. In the two-stage game, Option C pays 30 dollars only if the first stage is survived, which happens one time in four, so it is a 25 percent chance of 30 dollars. Option D is a 25 percent chance of reaching the second stage multiplied by an 80 percent chance of winning there, which is a 20 percent chance of 45 dollars. Those are exactly Options E and F. A decision maker who weighed final outcomes and their odds would choose the same way in both versions. Most people do not, and the direction of the switch is predictable: the version with a stage in which 30 dollars is certain pulls choices toward the 30 dollars.

The reason is that certainty carries extra weight. Prospect theory, which Kahneman and Tversky set out in 1979, describes a decision weight that rises steeply as a probability approaches one, so that a sure outcome is valued out of proportion to a merely probable one. That is the certainty effect, and it explains why most people prefer a sure 30 dollars to an 80 percent chance of 45 even though the gamble has the higher expected value. The pseudocertainty effect is what happens when the certainty is an illusion: the 30 dollars in the two-stage game is contingent on a stage that usually ends the game, but because the choice is presented as if the second stage had already been reached, the option still gets the weight of a sure thing.

Underneath is a habit of simplifying. The first stage is shared by both options, so people set it aside and decide between what remains, a sure 30 dollars and a gamble. Kahneman and Tversky called this the isolation effect in 1979: when a problem can be broken into a common part and a distinctive part, people decide on the distinctive part and ignore the rest, and different ways of carving up the same problem lead to different choices. The two-stage format carves the problem so that one option looks safe. The single-stage format gives both options their honest odds, and the preference moves toward the larger prize.

The same mechanism works on losses and on protection. The 1981 paper reports an unpublished study by Slovic, Fischhoff and Lichtenstein in which a vaccine that halves the chance of a disease was less attractive when described as effective in half of cases than when described as giving full protection against one of two equally likely strains that produce the same illness. The protection is identical; what changes is that the second description contains a certainty, and that certainty, though it applies to only part of the risk, makes the vaccine feel more worth having.

Amos Tversky and Daniel Kahneman published "The framing of decisions and the psychology of choice" in Science in January 1981. The paper is best known for the Asian disease problem, but it also contains a set of three money problems designed to separate the certainty effect from the pseudocertainty effect. Each problem went to a different group of respondents, and each group was told that one respondent in ten, picked at random, would play for real money, with chance events settled by drawing a ball from a bag in the respondents' presence and winners paid on the spot.

Problem 5, answered by 77 people, was a plain choice between a sure win of 30 dollars and an 80 percent chance to win 45 dollars: 78 percent took the sure 30. Problem 6, answered by 85 people, was the two-stage game reproduced above, with a 75 percent chance of being knocked out before the choice mattered: 74 percent chose the sure 30 dollars of the second stage. Problem 7, answered by 81 people, stated the same two prospects as single-stage odds, a 25 percent chance of 30 dollars against a 20 percent chance of 45 dollars: here only 42 percent chose the 30 dollars, and 58 percent preferred the larger prize.

The authors drew two conclusions from the pattern. The contrast between Problems 5 and 7 is the certainty effect, first described by Maurice Allais in 1953: reducing the probability of an outcome by the same factor has more impact when the outcome started out certain than when it was merely probable. The contrast between Problems 6 and 7, which are identical in outcomes and probabilities, is what they named the pseudocertainty effect. The 30 dollars in Problem 6 is relatively more attractive than in Problem 7, as if it had the advantage of certainty, when in fact the gain depends on reaching the second stage.

The problem had an earlier life. In the 1979 prospect theory paper the same two-stage game was posed with prizes of 3,000 and 4,000 Israeli pounds: 78 percent of 141 respondents chose the conditionally sure 3,000, while in the single-stage version of the same gamble a majority had preferred the 20 percent chance of 4,000. The 1979 paper used the result to introduce the isolation effect; the 1981 paper gave the phenomenon its own name.

The effect appears whenever a risky process has a step that can be described as guaranteed. The rows are illustrations, not findings from the cited studies.

The effect lives in how the stages of a decision are laid out, so the counter is to lay them out yourself before choosing.

• Collapse the stages. For each option, multiply the probability of every step that has to go right, and write the final odds next to the final prize. In the demo this turns a sure 30 dollars into a 25 percent chance of 30 dollars, which is the number that should be compared.
• Ask what has to happen first. Whenever something is described as guaranteed, certain or risk-free, ask whether the guarantee is conditional on an earlier step, and how likely that step is.
• Rewrite protection in terms of the whole risk. A measure that removes one of several risks completely should be valued by the share of total risk it removes, not by the word complete.
• Compare options in the same format. If one option is described in stages and another as a single probability, convert both to the same form before deciding.
• Be wary of the sure thing in a pitch. A guaranteed step inside an uncertain plan is often placed there because it changes how the plan feels, not what it is worth.

The pseudocertainty effect is one of several ways certainty and its appearance distort a choice. Its neighbors differ in whether the certainty is real and in what gets weighed.

• It is not the framing effect, which comes from the same 1981 paper and turns on whether an outcome is described as a gain or a loss. Framing moves the reference point; pseudocertainty leaves the gain and loss alone and changes whether an outcome looks certain.
• It is not zero-risk bias, the preference for eliminating one risk entirely over reducing a larger risk by more. The two are close relatives: zero-risk bias is the real certainty effect applied to risk reduction, while pseudocertainty is the same preference triggered by a certainty that only holds conditionally.
• It is not neglect of probability, where the odds of an outcome barely register at all, often because the outcome is emotionally charged. In the two-stage game people are sensitive to probability; the error is in which probability they attend to.