I was originally planning on writing my closing thoughts on Trump and the election, but I have decided to do that later (or maybe never). Instead, I’m writing a post based on a “quiz” I took in my IR class last year. Go ahead and take it, and then I’ll discuss the questions below.
1. Imagine that the US is preparing for the outbreak of a rare disease expected to kill 900 people. Which option would you choose:
A) A program that will save 200 people.
B) A program that has a 1/3 chance of saving 900 people, and a 2/3 chance that no one will be saved?
2. In four pages of a novel (about 2000 words), how many seven letter words would you expect that end in “ing”?
E) Over 160
3. What percentage chance do you think there is that a bomb will go off in Washington D.C. in the next year?
E) Over 16%
4. Let’s go back to the question on the expected outbreak of a disease anticipated to kill 900 people. Which option would you choose:
A) A program in which 400 people will die.
B) A program with a 1/3 chance that no one will die, and a 2/3 chance that 900 people will die.
5. In four pages of a novel (about 2000 words), how many seven letter words would you expect that have the letter “n” as their second-to-the-last letter?
E) Over 160
6. Donald Trump wants to increase the size of the navy by building one extra Arleigh Burke Class Destroyer per year. My sister, who knows nothing about naval procurement, guesses an extra destroyer would cost $120 million. How much do you think the destroyer will cost?
A) $105 million
B) $120 million
C) $300 million
D) Over $300 million
7. If I flip an ordinary coin seven times, which of the following sequences of Heads (H) and Tails (T) is least likely?
A) H H H H H H
B) H T H H T T
8. What do you think are the percentage chances that terrorists will detonate a bomb in Washington over the next year, killing at least 5 people?
E) Over 16%
9. Choose a number between one and one hundred that is one-third of the average of the numbers that all the students in this class will choose.
10. For each of the following, without peeking at the internet, write down your best estimate, and then give an upper and lower bound such that you are 98 percent sure the actual number is within the range you have given:
A) What was the population of the US in 1700?
B) What is the year in which Isaac Newton was born?
C) How many emails did Bill Clinton send while he was president?
D) How much did Americans spend on pets in 2015?
So, now that you’ve thought about your answers, let’s discuss them.
Questions 1 and 4 concern a principle known as prospect theory. Prospect theory argues that people are more risk sensitive when considering gains than when considering losses. In other words, people are willing to gamble more to prevent a loss than they are to achieve a gain. I imagine that many of you picked A for question 1 and B for question 4. What’s interesting, however, is that these are clearly the wrong answers. The reason that many people get these questions wrong is the wording. Question 1 is framed in terms of gains. As explained previously, people are less willing to take risks when seeking new gains. Instead, they tend to take the guaranteed payoff, even if it actually has a lower value. The opposite is true for question 4, which is framed in terms of loss. In that case, people are willing to role the dice even though they know the likely payoff is worse. This kind of cognitive bias explains why Japanese policymakers sanctioned the attack on Pearl Harbor even though they knew they would lose a protracted war with the U.S. It is also why, I believe, Trump won this election. People were so desperate to arrest the perceived decline of the United States that they were willing to gamble big league on a questionable payoff.
Questions 2 and 5 feature retrievability bias. This is a concept based on the availability heuristic: “the tendency to judge the frequency or likelihood of an event by the ease with which relevant instances come to mind.” Many of you probably picked a higher probability for question 2 than 5, but this is obviously absurd because the scenario described in question 2 is a subset of the question 5 scenario. Every word that ends in “ing” has an “n” in the second to last place, but not every word with an “n” in the second to last place is one that ends in “ing.” Nevertheless, because it is easier to think of words ending in “ing,” many of you probably evaluated question 2 to have a higher probability.
Questions 3 and 8 are also very interesting, and they demonstrate the biases found in questions of contingent probability. Contingent probability argues that the more specific the scenario, the less likely it is to occur. This is because highly specific scenarios require a greater number of low-probability events to occur. To use the question above as an example, question 3 should be assigned a higher probability than question 8 because every bomb in DC killing 5 people is also just a bomb in DC. In other words, question 8 is a subset of question 3. Nevertheless, people tend to evaluate the risk of highly specific scenarios to be higher than vague scenarios. Why this occurs is unclear, but many psychologists believe it’s because more concrete details allow people to better visualize a situation, thus leading them to inflate the likelihood of it occurring relative to a more generalizable situation.
Question 6 involves the concept of anchoring, which argues that people tend to base their assessments around an anchor point provided by someone else. What’s interesting is that this occurs even when the decider of the initial anchor point has no qualifications. I imagine many of you picked A or B for question 6 despite my explicit disclaimer that my sister knows absolutely nothing about naval procurement. In fact, Arleigh Burke destroyers cost about $1.8 billion, so guesses around $120 million are way off the mark.
Question 7 is a trick question. They are equally likely events, but many of you probably picked B. This is due to representativeness bias. You know that getting straight heads is unlikely, so you pick B because your expectations are of some kind of mixed result that has both heads and tails.
Question 9 is interesting because it involves game theory and empathy. Obviously the answer can’t be above 33% because the average could only ever be 100, and 1/3*100 is 33.333333. The trick to this question is that nobody will pick a number above 33 because this is the upper bound. This pushes down the average, and this logic continues until the average approaches the value of one. Thus, the correct answer is A.
Question 10 is not really about the questions themselves, but rather the degree of confidence you had in your answers. People constantly overestimate their ability to predict things. As another example, consider that almost all drivers think they are above average, even though this is statistically impossible because some have to be below average. I’m sure many of you assigned extremely high confidence levels to your predictions (maybe even 80%-90%) despite having absolutely no idea what the answers were. This is known as the illusory superiority bias, and, unfortunately, it affects almost everyone, leading to gross overestimations of ability and accuracy.