BY: SYON BHANOT (SWARTHMORE COLLEGE) AND ZACH SPECTOR (BROWN UNIVERSITY, CLASS OF 2018)
Sitting in the waiting room at the dentist’s office, you feel some spare change clang around in your pocket. With nothing better to do, you decide to give a coin a few flips to see what happens. After tossing it into the air and clapping it onto the back of your hand five times, you record the following results: THTHT. Unamused by such reasonableness, you give it another go, flipping the coin another five times. This time, your eyes grow wide in response to the wildly different results: TTTTT. What are the odds?
Actually, the likelihood of both of these outcomes is the same (about 3.1%). In fact, that’s the case for any sequence of five flips of a fair coin. Yet, for some reason, seeing alternating heads and tails seems more “normal” to us than a string of all tails. But why? Behavioral science icons Daniel Kahneman and Amos Tversky address this question in a 1974 paper, noting that “after observing a long run of red at the roulette table...most people erroneously believe that black is now due.” This phenomenon is known as the gambler’s fallacy, and it helps to explain why THTHT looks “more correct” to us than TTTTT. That is, when we flip a coin multiple times, we expect to get roughly the same number of heads and tails because we know the odds for each are fifty-fifty. So a string of tails seems bewildering, when in actuality, any specific series of five outcomes of a coin flip is just as likely as any other.
When it comes to decision making, feeling that a certain outcome is “due,” despite the statistical independence of a process, can significantly affect our perceptions. This perceptional bias can then influence ensuing decisions, purely due to the previous results. The idea that the outcomes in a series of independent events can be affected by earlier outcomes in that series is known as autocorrelation (it can be either positive or negative, depending on how the decisions sway). In a recent NBER working paper, “Decision-Making Under the Gambler’s Fallacy: Evidence from Asylum Judges, Loan Officers, and Baseball Umpires”, researchers from the Toulouse School of Economics and the University of Chicago set out to find evidence of autocorrelation by analyzing decisions in real-world settings.
Specifically, they looked at three types of decision makers: 1) judges determining whether or not an applicant seeking asylum can remain; 2) loan officers evaluating loan applications; and 3) umpires deciding whether a pitch was a ball or a strike. In the latter two cases, the researchers were able to compare the groups’ judgments to a standard. For loan officers, they used a previous assessment of each loan by another officer, and for umpires, they used data provided by PITCHf/x, a computer system that tracks the direction and position of a baseball when it crosses home plate.
Importantly, there was a lot on the line for both the affected parties and the decision makers. The researchers wanted to know - could the gambler’s fallacy strike in these real-world, high-stakes scenarios? To determine this, they looked for “negative autocorrelation” in decisions; in other words, instances where one decision was followed by the opposite decision in an ensuing similar case.
The researchers found significant evidence of negative autocorrelation in each decision scenario. Specifically, they found that asylum judges were 3.3 percentage points more likely to deny a case if they had accepted the previous case, allowing them to infer that 1.6 percent of the cases were turned down strictly due to negative autocorrelation. Meanwhile, loan officers were 23 percentage points more likely to deny a loan if they had accepted the previous loan, meaning that 9 percent of loans were turned down due to negative autocorrelation. The authors also found that umpires were 0.9 percentage points more likely to call a pitch a ball if the previous pitch had been called a strike, and 2.1 percentage points more likely if the previous two pitches had been called strikes. While these numbers may seem small, their impact on both decision making and people’s lives is significant.
Ultimately, this research gives us a lot to think about when it comes to making our own decisions. We like to believe that we are objective, fair, and immune to distortions in our judgment caused by unrelated past events. But when we play one more hand of poker or pull one more lever at the slots - all because “I’m bound to win this time!” - we fall prey to our own biases. Perhaps our gut feeling isn’t always right, and we should listen to our logic and reason over what we feel is supposed to happen. Although that’s pretty hard to do when the coin is in the air, isn’t it?