N.B. This manuscript is a work in progress.
This study was originally conceived, designed, and analyzed in 2015 with the substantial involvement of Howard Rachlin (1935 – 2021).
Task code, raw data, and data-analysis code can be found at http://arfer.net/projects/pattern.
The core task of the study was a computer-based gambling task adapted from Luhmann, Ishida, and Hajcak (2011). The first 110 subjects were paid their winnings in cash, but our funds were limited, so the remaining 67 completed the task with hypothetical gambles instead.
On each trial of the task, subjects chose between two gambles, which were displayed graphically as in Figure 1. The immediate choice I had a 60% chance of paying the subject 4 cents, whereas the delayed choice D had a 70% chance of paying the subject 4 cents. Since D provides a higher probability of winning the same amount, it dominates I. However, D wasn't available at the start of each trial whereas I was. The wait until D could be chosen was 5 s plus an random exponentially distributed amount of time with median 5 s (or equivalently, mean ). The use of an exponential distribution ensured that after the initial fixed 5 s, the expected remaining wait time remained constant, so waiting provided no new information about the time remaining to wait.
When the subject chose a gamble, they were immediately told whether they'd won ("WIN! 4 cents") or lost ("0 cents"). However, if they chose I, they had to wait until the next trial. The duration of this wait was the same as the wait for D to become available, minus any time they'd already spent waiting for D. Thus, choosing I only let the subject end the trial and see whether they'd won sooner. It didn't let them complete the whole task sonner.
Trials were grouped into 3-trial blocks. Even-numbered blocks (counting the first block as block 1) were shown with a yellow background, and odd blocks used a blue background. The significance of the blocks varied according to which of four conditions the subjects was randomly assigned to. Conditions were assigned by building a sequence of randomly permuted four-condition subsequences and then assigning each subject the last unused condition. Thus we ensured that each subject was equally likely to receive each condition, while maximizing the equality of sample sizes between conditions.
- In the Control condition, subjects could choose freely on all trials.
- In the Within-Pattern condition, subjects could choose freely on trial 1 of each block, but had to choose the same option on trials 2 and 3 of the same block.
- In the Across-Pattern condition, subjects could choose freely in odd-numbered blocks, but had to make the same sequence of choices in each even-numbered block as they had in the previous block.
- In the Force-D condition, subjects could choose freely in odd-numbered blocks, but could only choose D in even-numbered blocks.
In each case, a reminder of the rules for the current trial were shown on screen, above the options. Trials on which the subject was not forced to choose a given option due to condition-specific rules are termed "free" trials henceforth.
We expected that in the two pattern conditions, compared to Control, we would see a greater rate of free choices for D, especially on later blocks (after sufficient opportunity for learning). We expected a greater such effect in Across-Pattern, because it enforces a larger-scale pattern. Finally, we expected that free choices under Force-D would be similar to those in Control, showing that it isn't merely being forced to make choices but pattern-setting that increases free choices for D.
Undergraduate students in the psychology department of Stony Brook University were run in September, October, and November of 2015. After providing informed consent, subjects read detailed instructions for the task (see appendix). A four-item quiz tested the subject's understanding and reinforced it by telling them the correct answer immediately after each question. Next subjects were shown their condition-specific instructions. Subjects completed 20 blocks of 3 trials. Finally, subjects were debriefed. Some subjects were compensated with cash, and all received course credit.
Demographic information was obtained from screener forms the subjects filled out as part of registering for the department's subject pool. Of 177 subjects, 65% were female. Ages ranged from 17 to 49, with 95% of subjects being 22 or younger. In terms of ancestry, one item allowed the respondent to choose one of "African American/Black", "American Indian or Alaska Native", "Asian", "Caucasian/White", "Multiple Ethnicity", "Native Hawaiian or Other Pacific Islander", or "Other", and another item asked if the respondent was Hispanic. Thus 45% of subjects indicated they were white, 24% Asian, 12% black, 11% "Other", and 8% multi-ethnic, while 16% were Hispanic. All subjects indicated they were native speakers of English. Finally, 10% were left-handed.
Subjects initially had some trouble understanding the task instructions. Only 53% answered all 4 quiz questions correctly, and 20% answered 2 or less correctly. Since the right answer was shown to subjects immediately after they responded, ideally correcting any misconceptions, we don't omit any subjects on the basis of quiz performance.
While observing the gambling task, experimenters noticed 3 subjects who appeared to be inattentive: one seemed to fall asleep, one frequently yawned, and one frequently checked her phone. An additional 6 subjects, on 3 or more trials, chose I after D had been available for 2 s or longer. With these 9 subjects excluded, 168 remained: 41 Control, 43 Within-Pattern, 42 Across-Pattern, and 42 Force-D. Completion times for the gambling task (not including the instructions and quiz) ranged from 13 to 23 min, with a mean of 16 min 57 s.
Table 1 shows that in the first half of trials, between 58% and 69% of free choices were for D. Such proportions, being neither near 0 nor near 1, are helpful in that they provide room to show learning effects. However, the rate of free D choices is similar in the second half. Looking at mean differences between the first and second halves (see also Figure 2), we see little evidence of change over the course of the study, or of per-condition effects on such change. The mean differences of greatest magnitude are for Control, in which subjects chose D slightly more often later in the experiment, and Within-Pattern, in which subjects chose D slightly less often later (contrary to hypothesis). Any effect by which Within-Pattern or Across-Pattern help subjects learn to choose D is small, not exceeding 6 percentage points.
|Condition||1st||2nd||2nd − 1st|
|Control||.58||.60||+.025 [−.020, +.069]|
|Within-Pattern||.69||.67||−.019 [−.086, +.040]|
|Across-Pattern||.69||.69||+.006 [−.037, +.056]|
|Force-D||.59||.59||+.006 [−.052, +.068]|
The initial instructions and the quiz were as follows:
Some quick notes before we begin:
- Please give the experiment your undivided attention. Doing something else (like checking your phone) during a waiting period would interfere with the purpose of the experiment.
- This experiment uses timers to make you wait for certain things. Don't use your browser's back button or refresh button on a page with a timer, or the timer may restart (in which case it will have the same length as before).
In this study, you'll complete a number of trials which will allow you to choose between two gambles, A or B. You can win real money from the gambles, which will be paid to you at the end of the study. You can't lose money from gambles. Right after you choose each gamble, I'll tell you whether or not you won the gamble.
[For unpaid subjects, the above instead read "In this study, you'll complete a number of trials which will allow you to choose between two gambles, A or B. You can win (imaginary) money from the gambles. You can't lose money from gambles. Right after you choose each gamble, I'll tell you whether or not you won the gamble. At the end of the study, I'll tell you your total winnings. Although no real money will be involved in this study, please try to make your decisions as if the gambles were for real money."]
Here's what the gambles look like:
[An example similar to Figure 1 of the main manuscript.]
The colored bars are just graphical representations of the chance of winning.
Notice that B has a higher chance of paying out. However, B isn't immediately available at the beginning of each trial. It will show as "[Not available yet]". You'll have to wait a random, unpredictable amount of time (sometimes short, sometimes long) for B to become available.
Choosing A will allow you to receive an outcome (either winning or not winning) without waiting, because A is available from the start of each trial. But choosing A won't let you complete the study any faster, because the time you would have waited for B, had you waited for it, will be added to the time you have to wait to get to the next trial (or to the end of the study). Any time you spend waiting before choosing A (although you don't need to wait before choosing A, as you do for B) will be credited towards reducing this wait.
Let's test your understanding.
- Compared to B, A's chance of paying out is
- lower [correct]
- the same
- Which gamble gives you more money when you win the gamble?
- They give the same amount of money [correct]
- Which option can you choose as soon as a trial starts?
- A [correct]
- Either A or B
- Which option will allow you to complete the study faster?
- Neither; it makes no difference [correct]
Okay, one more thing before we begin.
You'll complete trials in blocks of 3.
[On a blue background:] In odd-numbered blocks (the 1st, 3rd, 5th, and so on), you'll see this background.
[On a yellow background:] In even-numbered blocks (the 2nd, 4th, 6th, and so on), you'll see this background.
The final line of the instructions varied by condition:
- Control: "The task works the same whether you're in an odd block or an even block."
- Within-Pattern: "Within each block, whether even or odd, you can choose either A or B on trial 1, but the task will force you to repeat that choice on trial 2 and trial 3."
- Across-Pattern: "In odd blocks, you can choose either A or B. In even blocks, the task will force you to repeat the series of choices you made in the previous block. So if in the 1st block you chose A, then B, then A, the task will force you in the 2nd block to choose A, then B, then A."
- Force-D: "In odd blocks, you can choose either A or B. In even blocks, the task will force you choose B on every trial."
Luhmann, C. C., Ishida, K., & Hajcak, G. (2011). Intolerance of uncertainty and decisions about delayed, probabilistic rewards. Behavior Therapy, 42, 378–386. doi:10.1016/j.beth.2010.09.002. Retrieved from http://www.psychology.stonybrook.edu/cluhmann-/papers/luhmann-2011-bt.pdf