Are You Smarter Than Other New York Times Readers?
Because unfortunately I’m not.
The New York Times interactive article linked in this post allows the reader to pick a number that they think will be “two-thirds of the average of all numbers.” For instance, if everyone were to pick the value 50, you would win by picking 33. However, keep in mind that if everyone were to think that everyone else is picking 50 and picks 33, the real average would be dependent on that mode of thinking, and so on. As someone who has reading skills that leave much to be desired, I picked the number I thought would be the “average of all numbers” chosen by readers, which would be generally around the right number if everyone were picking random numbers. Nearly 4% of readers, myself included, thought that this was the correct answer. Unfortunately, we’re both incorrect in reading the problem statement and analyzing the problem, but someone has to lost for others to win. The article categorizes people as “k-step thinkers,” k being the number of steps you think ahead. (I would be a 0-step thinker. Oh well.)
Say for instance, I were to read the problem statement correctly. Since 50 would be a good guess of what the average random person would pick, it seems logical that 33 would be the answer. And accordingly, well over 9% of people guessed 33 was the correct number. However, this shifted the average down from 50 and so those people were wrong as well, forward thinking only 1 step. If you were a 2-step thinker, you’d repeat this way of thinking, using 33 as the predicted average and you’d get 22 (6% of people thought this was the answer), which is still not the correct answer. To save you from the anticipation I’m sure you have, I’ll tell you that the answer is actually 19 and only about 1.5% got the answer correct.
Two important answers that I haven’t mentioned yet are 0 and 1, both of which had approximately 6% choosing them as the answer. These people chose what would be the Nash Equilibrium for this situation, “a number that if everyone guessed it, no one would want to change their guess” as Richard Thaler said. With more rationalization, people would have continued to apply the idea that 2/3 of the average is some number over and over again and eventually reach the number 0. Unfortunately, most of us don’t think nearly as far and choose to stop after only one or two steps (1-step or 2-step thinkers), leaving us with an actual result that is a combination of everyone’s predictions: 19.