Sequence effects in taxi driver decision making

Subjects will be randomly assigned in proportions 1:1 to two conditions---control group and treatment (tutorial) group. All subjects (both control and treatment groups) will be asked to predict the outcome of a computer generated sequence of 20 random coin tosses. In addition, treatment (tutorial) subjects will be taught that the probabilities of all sequences of 20 coin tosses are equal. The control group will not receive the tutorial.

Next, all subjects will be presented a scenario in which the previous job was a booking and the outcome is randomly posed as either completed or cancelled. Then they will be presented a request for a new booking 5 minutes away and must bid an estimated time of arrival (2, 4, 6, or 8 minutes) for the booking.

2024-07-02

2025-06-30

(1) All subjects: Proportion of subjects who believe in the gambler's fallacy.
(2) All subjects: Estimated time of arrival (2, 4, 6, or 8 minutes) for a new booking request 5 minutes drive away.
(3) Subjects in the control group: (i) If they were posed the previous job as a cancelled booking: The reason for their ETA bid---whether disappointment at cancellation or belief that the next booking is less likely to be cancelled. (ii) If they were posed the previous job as a completed booking: The reason for their ETA bid---whether gladness with success or belief that the next booking is more likely to be cancelled.

This research follows up on an earlier study on the effect of the gambler's fallacy on bidding for taxi bookings among Singapore taxi drivers (https://osf.io/hjgq2).

In the previous study, subjects were randomly assigned to three conditions---a control group, treatment 1 (placebo), and treatment 2 (tutorial). Subjects in treatment 1 (placebo) and treatment 2 (tutorial) were asked to compare the probabilities of pairs of sequences of five random coin tosses. In addition, treatment 2 (tutorial) subjects were taught that the probabilities of the two sequences are equal. The control group will not be asked the coin toss question.

Next, subjects in all three conditions were presented a scenario in which the previous job was a booking which was randomly posed as either completed or cancelled. Then they were presented a new booking 5 minutes away and asked to bid an estimated time of arrival (2, 4, 6, or 8 minutes) for the booking.

The previous study found that the debiasing tutorial mitigated the effect of previous cancellation on the ETA bid on the next booking. However, owing to small sample size based on a pilot with unusually large effect size, the estimated effect was not significant at conventional levels.

Also, the previous study did not register an examination of the effect of the extent of gambler's fallacy beliefs on bookings. Based on comments from the behavioral economics community, this is an issue of first-order importance and actually the more important question.

Like the previous study, the present study will recruit Singapore taxi drivers as subjects. By contrast with the previous study, the present study will apply just two conditions---control and treatment (tutorial). The main analysis will focus on subjects who believe in the gambler's fallacy (as revealed by their answers to a revised coin toss question). The analysis will test the effect of a previous cancellation on the ETA bid on the next booking. The secondary analysis will also focus on subjects who believe in the gambler's fallacy and examine the moderating effect of the debiasing tutorial on the effect of previous cancellation on the ETA bid on the next booking.

The hypotheses to be tested:

Hypothesis 1 (Gambler's fallacy). If the driver believes in the gambler's fallacy and if their previous booking was cancelled, they will bid more aggressively on the next booking job.

Hypothesis 2 (Gambler's fallacy). If the driver believes in the gambler's fallacy and if their previous booking was cancelled, they will explain their bid as due to the next booking being less likely to be cancelled.

Hypothesis 3 (Tutorial). The sequence effect in Hypothesis 1 will be attenuated among drivers who are educated about the gambler's fallacy.

To conserve economic resources, this study will re-use the data collected in the previous study.

The main analysis (test of Hypothesis 1) will be a Poisson regression of the ETA bid on three explanatory variables---belief in the gambler's fallacy, previous booking cancelled, and their interaction---on the sample of subjects in the control condition. The coefficient of main interest is that of the interaction, belief in the gambler's fallacy x previous booking cancelled.

The secondary analysis (test of Hypothesis 3) will be a Poisson regression of the ETA bid on three explanatory variables---tutorial indicator, previous booking cancelled, and their interactions---on the sample of subjects who believe in the gambler's fallacy. The coefficient of main interest is that of the interaction, previous booking cancelled x tutorial.

Randomization by online Qualtrics system: (i) Assignment to conditions---control and treatment (tutorial); (ii) Posing the previous booking as completed or cancelled.

Individual driver.

No

Not clustered: Please refer to Planned Number of Observations below.

Main analysis The main analysis will be a Poisson regression in which the main coefficient of interest is an interaction. For Poisson regressions, GPower provides power analysis only for a single non-interacted variable. Accordingly, we calculated the required sample size as follows: (a) OLS regression with three explanatory variables, focusing on the interaction, belief in the gambler's fallacy x previous booking cancelled: 658 (b) OLS regression limited to believers in the gambler's fallacy with one explanatory variable, focusing on the previous booking cancelled: 80; (c) Poisson regression limited to believers in the gambler's fallacy with one explanatory variable, focusing on the previous booking cancelled: 90. Poisson inflation factor = (c)/(b) = 90/80. Poisson with interaction = OLS with interaction x Poisson inflation factor = (a) x (c)/(b) = 658 x 90/80 = 741. Secondary analysis The secondary analysis will be a Poisson regression in which the main coefficient of interest is an interaction. For Poisson regressions, GPower provides power analysis only for a single non-interacted variable. Accordingly, we calculated the required sample size as follows: (a) OLS regression with three explanatory variables, focusing on the interaction, tutorial x previous booking cancelled: 69 (b) OLS regression limited to previous booking cancelled with one explanatory variable, focusing on tutorial: 59; (c) Poisson regression limited to previous booking cancelled with one explanatory variable, focusing on tutorial: 90. Poisson inflation factor = (c)/(b) = 90/59. Poisson with interaction = OLS with interaction x Poisson inflation factor = (a) x (c)/(b) = 69 * 90/59 = 312. Based on the previous study, 0.34 of subjects believe in the gambler's fallacy. Accordingly, the required sample for the secondary analysis is 312/0.34 = 882. Considering both the main and secondary analyses, the required sample size is the larger of the required sample size for the two analyses, i.e., 882. In addition, we must allow for subjects not completing the survey . Based on the previous study, 0.2 of subjects did not complete the survey. Accordingly, the required sample (Planned Number of Observations) is 882/0.80 = 1102.

Randomize into control and treatment (tutorial) in the ratio 1:1.

Please refer to Planned Number of Observations above.