How many? vs. How probable?

Class exercise

To reiterate: the evidence shows that people are far less likely to make the conjunction error when probed with the “how many” question than the corresponding “how probable” question. In order to see whether we can reproduce this pattern of results, we hope that you will enlist a couple of people to respond to our short survey.

There are two versions of the survey. Both have the same two questions, but across the two surveys, the order of the two questions is varied. Below are two separate links to the respective versions of the survey. Please send the first link to one person, and send the second to a different person. In this way, half the participants will answer the “how probable” question first and then the “how many”, and the remaining half participants will answer the “how many” question first. By varying the order of the questions across our participants, we should be able to see whether exposure to one sort of question influences responses to the other:

First link

• http://bit.ly/2PjB61g

Second link

• http://bit.ly/2zkNjrM

You can copy a link and paste it into a new tab on a browser or simply send it to a willing participant who can do the same.

Please do not do the survey yourselves because you are no longer naïve – we have told you what results we expect and you also know the correct answers.

The actual questions in the survey are reproduced below and the exact wording has been influenced by the previous research

Question 1

Please consider this brief personal description:

Shelia is 31 years old, single outspoken and very bright. She majored in Philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Using drag and drop, rank the following statements with respect of their probability?

• Shelia is a bank teller
• Shelia is a bank teller and is active in the feminist movement
• Shelia is active in the feminist movement

Question 2

Walter is 34 years old. He is intelligent, but unimaginative, compulsive, and generally lifeless. In school he was strong in mathematics, but weak in social studies and humanities.

Imagine 100 men who fit Walter’s description. Please estimate the frequency of the following events.

• How many of the 100 men play cards as a hobby?

• How many of the 100 men are accountants?

• How many of the 100 men are accountants who play cards for a hobby

What the previous research has shown is that whereas people are seduced into making the conjunction error with the Shelia example, they do not make the same error when thinking about Walter – estimates of the number of card playing accountants are low.

Summaries of the results of the surveys will be made available later in the course.