I wrote this essay with Mika MacInnis.
Here are three reasoning tasks for your consideration: The first task is to figure out the probability that Joe loves movie number 1 if you know that he loves 8 of the 10 movies he has seen recently. This is simple. The probability is .8.
The second task is to figure out the probability that at least two of three movie-goers, Joe, Olaf, and Eric, whose preferences are independent of one another, love movie number 1 if each of them loves this movie with a probability of .8. This is more complicated. The probability that all three will love movie number 1 is ..8 × .8 × .8, or .512. To this, you add the probability that two of the three-and that could be Joe and Olaf, Joe and Eric, or Olaf and Eric-love the movie. This is a surmountable task. Knowledge of factorials and a spreadsheet program come in handy to provide the solution of .384 (i.e., (3! ÷ 2!1!) × .8 × .8 × .2). The total probability of having at least two endorsements of the movie is .896.
The third task is to figure out the probability with which an individual (Joe, Olaf, or Eric) loves the movie so that the probability that at least two of them love it is .8. This is the second problem in reverse, and it is much harder. The binomial formula and the spreadsheet will produce no answer. From eyeballing alone, and from remembering the second problem, you know that the probability in question is lower than .8, but how much lower? To get an exact answer, you have to call a mathematician. We did, by the way, and know the result. At this time, however, we only reveal that it involves derivatives and headaches. Still, it can be done.
The psychological point of the story is that the reasoning tasks we encounter vary in their difficulty. Like duh! Yet, in the psychological literature, ordinary humans are often faulted for failing to reason rationally, and their failures are blamed on the limited capacity of their minds. There are also many trade books that tell you how stupid people are, which many readers take to mean "other people," which by itself is an interesting case of self-enhancement. We do not want to advertise any of these books because we disagree with the message. As evidence for our point that psychological science has produced many "discoveries" related to the inanity of humanity, we recommend a check of the "list of cognitive biases" at Wikipedia.com.
There is a more enlightened view, credited to Herbert Simon (see photo), who received the Nobel Prize in economics in 1978. Simon suggested that rationality does not arise from the human mind alone, but from the match between the mind's evolved mental capacities and the problems encountered in the person's daily ecology. He captured this idea with the "incisive" scissors metaphor, where the mind and the environment are the two blades. According to Simon, you are being rational if you solve a reasoning problem that you can reasonably be expected to solve. Hence, any test of rationality is simultaneously a test of the subject who solves, or fails to solve, the problem, and of the tester who selected it.
Take course exams as a real-world scenario. Exams focus on the recall of rehearsed material. This is unfortunate, for exams can also open a window into rational reasoning. In a recent course on child development, we played with this idea. Consider the following question (you may want to take this opportunity to assess your knowledge of the history of developmental psychology):
"We have studied many theorists this semester. They can be broadly categorized into theorists who study cognitive development, social development, and learning. Take each of the theorists and put them into the category they belong.
Pavlov Piaget Harlow Ainsworth
Kohlberg Vygotsky Drews Skinner
Bandura Freud Baumrind Bowlby"
Were you able to categorize all 12? Did you notice that Drews is a decoy? There was no famous developmental psychologist named Drews (as far as we know). What is a student to do? We know that it is difficult to remember with certainty that something did not occur, especially if the set in which it might have occurred is large and if there is no response category in which to place a non-occurrence. Only one out of 99 students (rationally) placed Drews nowhere. All the others placed Drews in one of the three theoretical bins. Without any Drews-related recall, placement should be random, resulting in an equal distribution over categories. Indeed, this was so. The frequencies of placement were 39, 25, and 34 respectively for cognitive, social, and learning. These numbers do not significantly depart from the expected equal distribution (Χ-square(2)= 3.08, p = .21).
Accepting the null hypothesis (gasp!), we conclude that the students were rationally indifferent. They assumed that Drews was in the book, and they placed her (him?) randomly. This makes sense if points are given for correct responses, and no points are subtracted for incorrect responses. Again, the moral of the story is that rationality is a matter of person-situation interaction, much like any type of human behavior.
