Certainty and Pseudo-Certainty

In making certain decisions (like the one in Question 1), we have to determine the probabilities of different outcomes. Consider the experience of coming up for a decision for Question 1, or the experience of doing probability problems in maths class in high school – was it easy or difficult? Perhaps you experienced something like this…

Humans are typically poor at estimations that involve probabilities, presumably because of the heavy load on cognitive resources. Because of this, we tend to prefer simplistic determinations of probability. One reflection of this is our preference for certainty. It is easy to understand and deal with 100% probability. This is illustrated by Questions 6a and 6b.

Questions 6a and 6b

Which choice would you make in each of the two following situations?

Question 6a

Choice 1: Winning $1000 with a probability of 1.00 (i.e., a certain win).

Choice 2: Winning $1000 with a probability of .89, $5000 with a probability of .10, and $0 (i.e., nothing) with a probability of .01.

Question 6b

Choice 1: Winning $1000 with a probability of .11, and $0 with a probability of .89.

Choice 2: Winning $5000 with a probability of .10, and $0 with a probability of .90.

Question

How did you respond to these questions? How do you think most people responded? How might Question 6a and 6b differ in the answers they receive? Let’s have a look at the data:

For Question 6a, people typically prefer Choice 1. The reason for this is that, all else being equal, people will prefer a certain gain to an uncertain gain. The difference in the certainty of the outcomes is salient. Choice 1 provides a certain win whereas Choice 2 provides an uncertain win. The preference for certainty biases one toward Choice 1 and away from Choice 2 (which has a higher expected utility) – a choice inconsistent with Expected Utility Theory.

For Question 6b, people general select Choice 2. When there is no certain choice and the options are equally difficult to evaluate, people make the effort to compare the uncertain outcomes. In other words, the difference in certainty between the two choices is less salient (because neither offers certainty). Without preference for certainty to bias them, people generally select Choice 2 (which has the higher expected utility) – a choice consistent with Expected Utility Theory.

In certain cases, participants show a preference for Choice 2 when answering Question 6a, but it is worth noting that the preference for Choice 2 is weaker in Question 6a compared to Question 6b. In other words, the difference in the proportion of participants choosing Choice 1 versus Choice 2 is smaller for Question 6a compared to Question 6b. This still reflects the above idea that preference for certainty biases responses towards Choice 1 to some extent, even if Choice 1 does not end up being selected more than Choice 2 overall.

Question 7

Version A

Consider the following two-stage game. In the first stage, there is a 75% chance to end the game without winning anything, and a 25% chance to move on to the second stage. If you reach the second stage, you have a further choice. This choice, however, must be decided upon before the game starts, that is, before the outcome of the first stage is known. Which do you choose?

Choice 1: a 100% chance to win $3000.

Choice 2: an 80% chance to win $4000.

Version B

Which of the following two options would you choose?

Choice 1: a 25% chance to win $3000.

Choice 2: a 20% chance to win $4000.

Question

What was your response in this case? Do you think you would have made the same response for the other version of the question? Let’s compare with the data:

This question demonstrates an extension of the certainty effect to a “pseudo-certainty” effect. Version A involves a two-step calculation/decision whereas Version B only requires a single step. For Version A, preferences tend to be Choice 1 because it has the appearance of certainty. However, if the first step is taken into account, the steps are identical in terms of expected utility to the options in Version B! Despite this, responses to Version B typically reflect a stronger preference towards Choice 2. Therefore, even when there isn’t true certainty in Version A, bias can arise from the appearance of certainty.