Persistence1Waiting and delay lead naturally to the concept of persistence. It is interesting that waiting to or delaying before making a decision is procrastination, while waiting for a reward after you make the decision is persistence.  Procrastination is generally panned while persistent is typically praised.

On July 5, 2014, during a repeat of the “Prairie Home Companion,” 40th anniversary celebration show, Dwayne’s mother called him about dumping his novel after only three years. She said:  “You give up so fast. That is why you have never gotten married…You are addicted to new beginnings… And did you hear about that man who has been on the same radio show for forty years?” They go back and forth for a couple of minutes when she says: “Well at least he stuck with something” and her son replies that: “the key there is stuck as in unable to move.”  Dwayne goes on to note that the guy has been married five or six times and his mom answers: “At least he kept trying.”  We all know that the correct amount of persistence is a virtue.

This post is based on a 2013 paper: “Rational Temporal Predictions Can Underlie Apparent Failures to Delay Gratification,” by Joseph T. McGuire and Joseph W. Kable that appeared in Psychological Review Vol. 120, No. 2, 395–410. An important category of seemingly bad decisions involves failure to postpone gratification. A person pursuing a desirable long-run outcome may abandon it in favor of a short-run alternative that has been available all along. The authors’ account recognizes that decision makers generally face uncertainty regarding the time at which future outcomes will materialize. When timing is uncertain, the value of persistence depends crucially on the nature of a decision maker’s prior temporal beliefs–the expected distribution of waiting times. If you expect an exponential or normal distribution of waiting times, you will not typically expect your waiting time to increase. However, in fat tailed distributions once you have waited a while, a delay’s predicted remaining length increases as a function of time already waited. In this type of situation, the rational, utility-maximizing strategy is to persist for a limited amount of time and then give up. They conclude that delay-of-gratification failure, generally viewed as a manifestation of limited self-control capacity, can instead arise as an adaptive response to the perceived statistics of one’s environment.

Rachlin in the Science of Self Control(2000) eloquently expressed the intuition that McGuire and Kable develop:

In a normal situation, where buses come on a fixed schedule, the time
left until the coming of the bus would vary inversely with the time
elapsed. But a New York street corner at eleven o’clock on a cold
night is far from normal. . . . Where waiting time is completely
unpredictable, as at the bus stop and in delay-of-gratification experiments,
we would expect estimates of time left to vary directly with
time elapsed. The longer you have already waited for the bus, the
longer you expect to wait. As time goes by, therefore, the larger
reward recedes farther and farther into the distance . . . Children with
flatter discount functions delay gratification longer than those with
steeper discount functions, and people waiting for the bus hail taxis
one by one in order of the flatness of their discount functions.

Waiting for a cab is an example that I have experienced. Seeking a second opinion at the USF Cancer Center we were easily transported by cab for a 2 pm appointment. When we emerged about 4pm, we had the hospital concierge call us a cab. By about 5:30pm we had waited at several streets. My inclination was to wait at one spot until one came.  My sister for whom the second opinion had been sought and who had planned the venture, was more impatient, she had a steeper discount function. It was a Friday evening, a Giants playoff baseball game was along our path, and something big was apparently at the Mosconi Convention Center. We called cabs. Other people called cabs. We saw cabs. We tried to hail cabs. Apparently my sister soon saw that this was a very fat tailed distribution. Extreme values like 4-6 hours needed to be assigned greater probability. In fact, the Black Swan (see post Dancing with Chance) should have used cab waiting times as an example to help us all see the error of believing that the world is Gaussian. She called her friend whom as I recall managed to pick us up within about 45 minutes. I note that this trip is 4.3 miles by car according to Google maps and is about an 18 minute trip under normal circumstances.  Public transportation takes about an hour if you can figure out the convoluted route. You can walk in about 1 hour and 12 minutes over the 3.6 mile trip. Walking was the only choice left without my sister’s friend.

Figure 2A shows an example of a fat tailed distribution as included in the paper by McGuire and Kable. The distribution shown is parameterized to predict a 5-min delay initially. The predicted remaining delay increases linearly as time passes (see Figure 2C).  The anticipated wait is longer after some time has passed than when the interval began.

McGuire and Kable show that time intervals associated with many real-world human activities are well fit by heavy-tailed functions. A real-life situation that might be characterized by heavy-tailed beliefs is waiting for a reply to an e-mail. You might initially expect a very quick reply, but if it does not come quickly you might infer that it will take substantially longer. Other examples include the interval between successive mentions of the same name in a newspaper,  between hospital admission and discharge, and predictions of how long you would remain on hold on a phone call. Heavy-tailed prior beliefs have also been recommended, on theoretical grounds, as appropriate defaults when an event’s timing is unknown.

The authors  propose that apparent delay-of-gratification failures in many contexts can emerge from a rational and self-consistent decision process. When the timing of events is uncertain, the expected remaining length of a delay can increase with time waited. This means that persistence is not beneficial under all circumstances. Adaptive behavior requires not maximizing one’s level of persistence but calibrating it appropriately to one’s environment. McGuire and Kable propose that waiting is difficult not just because people have self-control deficiencies but because calibrating persistence is a genuinely complex problem. Rather than assuming that persistence is generally adaptive, the issue should be conceptualized as making judgments about when persistence will be effective and when it will be useless or even self-defeating.