Hoping the loan application you submitted to the bank, or your application to the college of your dreams is approved? Your chances will be better if the applications that came immediately before yours were turned down.

Why should the sequence of decisions matter for whether an application is approved or denied? It appears to be one of the unexpected results of the "gambler's fallacy." This is the tendency for people to believe it's more and more likely a streak will end the longer it goes on, even though the probability of the streak ending hasn't changed.

For example, the probability that the next flip of a coin is a head or a tail doesn't depend on the sequence of past flips. Nevertheless, people are more likely to expect the next flip to be tails if the sequence of flips has been HHHHHH than if the sequence had been THTTHH.

Similarly, whether the spin of a roulette wheel comes up red or black doesn't depend on the outcome of past spins. Even so, the more times in a row the spin comes up black, the more people will wager that the next spin is red.

The reason for this is a miscalculation of the odds of sequences containing streaks versus sequences that appear more random. The sequence HHHHHH has exactly the same probability of occurring as the sequence THTTHH, yet most people believe the first sequence is less likely. Because they expect sequences to look random, they mistakenly believe a T is more likely than an H if the flips so far have been HHHHH.

One famous example of this happened in Monte Carlo on Aug. 18, 1913. The roulette wheel landed on black 26 time in a row, and bettors lost millions betting on red based on their belief the odds were changing the longer the streak went on.

Recent research finds that this bias extends beyond predictions about games of chance. In particular, when people make yes-no decisions, they're more likely to say yes if their previous decision was no, and vice-versa. Economists Daniel Chen, Tobias J. Moskowitz and Kelly Shue looked at three different cases and found a bias against consecutive decisions in the same direction.

First, they examined U.S. refugee asylum cases. Even though the cases are assigned randomly to judges so there's no reason to expect any relationship between the merits of successive cases, "judges are up to 3.3 percentage points more likely to reject the current case if they approved the previous case."

In addition, the effect is stronger when there's a sequence of recent decisions in one direction or the other (i.e., if the past three applications were denied, it's even more likely that the current application will be approved).

The second set of decisions they examined comes from an experiment involving loan applications in India. In the experiment, the applications given to loan officers were randomized so that, once again, there's no reason to expect any correlation in the quality of successive applications. Yet once again, the chance that an application is approved is higher if the previous application was denied, and the effect is stronger if the sequence of previous denials is longer.

Finally, the researchers look at calls of balls and strikes by umpires in professional baseball games. As the researchers explain:

"An advantage of the baseball umpire data is that it includes precise measures of the three-dimensional location of each pitch. Thus, while pitches may not be randomly ordered over time, we can control for each pitch's true "quality" or location and measure whether mistakes in calls conditional on a pitch's true location are negatively predicted by the previous call. We find that umpires are 1.5 percentage points less likely to call a pitch a strike if the previous pitch was called a strike, holding pitch location fixed. This effect more than doubles when the current pitch is close to the edge of the strike zone (so it is a less obvious call) and is also significantly larger following two previous calls in the same direction. Put differently, MLB umpires call the same pitches in the exact same location differently depending solely on the sequence of previous calls."

The authors considered several explanations for these results and concluded that the gambler's fallacy is the most likely explanation for these results.

There is, however, a mitigating factor. In their results, the more experience a decision maker has, the smaller the bias. Thus, if you're given a choice of who'll make a decision about you with important consequences, and you're unwilling to roll the dice hoping the cases immediately before yours are denied, the fairest evaluation is likely to come from someone who has considerable experience.

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