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Negative correlation (gambler’s fallacy) in decisions under uncertainty erodes productivity: Retrospective study and intervention

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Ivan Png & Song Wang

National University of Singapore

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Decision biases

  • Path dependence: Decisions affected by irrelevant past outcomes
    • Positive serial correlation (assimilation): Jury decisions (Bindler and Hjalmarsson, 2019); food safety inspections (Ibanez and Toffel, 2020); emergency room treatment (Jin et al., 2023).
    • Negative serial correlation
      • Gambler's fallacy: Tendency to underestimate likelihood of streaks (Clotfelter and Cook, 1993; Rabin and Vayanos, 2010)
    • Contrast effects
      • Personal: Speed dating (Bhargava and Fisman 2014)
      • Work: Interviews for study grants and jobs (Radbruch and Schiprowski 2024)

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Gambler’s fallacy

  • Gambling, laboratory experiments: fun or low even zero consequences
  • Work: MBA admission interviewers (Simonsohn and Gino, 2013); asylum judges, loan officers, baseball umpires (Chen et al., 2016)
    • Decision-maker only bears indirect consequences
    • Observe only choices, cannot observe beliefs
    • Confounds---quotas, learning about standards, preference for fairness, contrast effects
    • Difficult to quantify cost of bias

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Research questions

  • Do seasoned decision makers (face same choices repeatedly) suffer from negative serial correlation in choices?
  • How is negative serial correlation related to Gambler’s Fallacy beliefs?
  • Can mistaken beliefs be corrected?

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Setting: Singapore taxi drivers

  • Job choice
    • Street hail
    • Booking---broadcast to nearby drivers, assigned by fastest ETA
      • Longer distance + booking fee => higher fare
      • Possibly cancelled
  • Residual claimant: Fully responsible for consequences
  • Can quantify the loss (in expectation)
  • No confounds due to quotas, learning about standards, preference for fairness, contrast effects

​

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Two studies

  • Retrospective study of administrative data
    • If previous job cancelled, next job more likely to be booking (implicitly, driver bid faster ETA)
      • Reversals: longer streak of cancellations attenuated the effect of previous cancellations
      • Multi modality (Bordalo et al.): short streaks---discrete fallacy, long streaks---cumulative fallacy
  • [In progress] Experiment---Debiasing intervention [AEARCTR-0013808]
    • Hypothesis 1: Gambler’s Fallacy beliefs => stronger effect of previous cancellation on ETA bid
    • Hypothesis 3: Mistaken beliefs can be corrected

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Outline

  • Introduction
  • Setting
  • Retrospective study
  • Experiment
  • Discussion

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Setting

  • Singapore—city-state
    • 55 planning zones
    • 311 subzones
  • December 2016:
    • 5.6 million population
    • 100,000 drivers and 27,500 taxis
  • Booking procedure
    • Passenger makes request
    • Dispatch system broadcasts request to nearby drivers
    • Drivers bid (ETA)---2, 4, 6, or 8 minutes---through a dedicated terminal
    • System assigns booking to driver who bids soonest ETA.

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Outline

  • Introduction
  • Setting
  • Retrospective study
  • Experiment
  • Discussion

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Models

  •  

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Estimate

  • Sample
    • Exclude first and last trips of shift
    • Exclude drivers who never take booking (< 3%).
  • Controls
    • Region: Fixed effects by subzone (311 subzones)
    • Time: Fixed effects by date-hour (31 days x 24 hours)
    • Driver’s job preference (Nickell, 1981; Chen et al., 2016):
      • Moving average of proportion of bookings in 5 trips
      • Proportion of bookings in previous shift
    • Market conditions: Numbers of idle vehicles, street hails, and bookings nearby (500m radius and 5 mins of trip start)

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Identification

  • Conditional on time and location, customer cancellation is
    • Exogenous to driver
    • Not negatively correlated
  • Correlation of cancellations
    • Driver-trip: Subsample of successive bookings, correlation of completion = 0:023 (se 0:002); positive not negative
    • Aggregated by region and time: Completion rates positively correlated.

​

​

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<Supplement>

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Data

  • December 2016
    • 9,211,035 jobs
    • 32,750 drivers
  • Trip dataset: Jobs served by taxi and vehicle and driver identifiers
    • Origin and destination: 6-digit postal code (building)
    • Booking status---completed, cancelled
  • Location dataset: GPS location of taxi at 15-30 second intervals and vehicle identifier
  • Driver dataset: Driver identifier and personal characteristics

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Summary statistics

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VARIABLE

Unit

Obs

Mean

Std. dev.

A. Drivers

Male

Indicator

32,750

0.98

0.15

Age (as of 2016)

Year

32,383

55.47

9.09

Years since joining (as of 2016)

Year

32,383

13.26

9.01

B. Shifts

Shift duration

Hour

742,672

7.75

3.43

Shift revenue

Dollar

742,672

165.73

79.32

Shift profit

Dollar

742,672

152.75

73.42

C. Trips

Booking job

Indicator

9,211,035

0.23

0.42

Cancelled booking

Indicator

2,043,679

0.08

0.27

Completed booking jobs: distance

Kilometer

1,879,248

12.42

8.34

Completed booking jobs: duration

Minute

1,879,248

19.39

9.48

Completed booking jobs: trip fare

Dollar

1,879,248

17.27

7.50

Completed booking jobs: trip profit

Dollar

1,879,248

15.99

6.77

Street-hail jobs: distance

Kilometer

7,167,356

9.76

7.84

Street-hail jobs: duration

Minute

7,167,356

15.77

9.15

Street-hail jobs: trip fare

Dollar

7,167,356

12.64

7.15

Street-hail jobs: trip profit

Dollar

7,167,356

11.64

6.43

D. Market

Idle taxis

Count

9,211,035

0.06

0.28

Street hail in progress

Count

9,211,035

8.54

10.80

Booking in progress

Count

9,211,035

1.50

2.99

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Booking: Discrete model

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 VARIABLES

(a)

(b)

(c)

(d)

(e)

(f)

​

Basic

Exclude last trip and never booker

Controlling for job preference

Time & region FE

Controlling for market thickness

Preferred specification

Previous trip was booking

0.174***

0.166***

0.039***

0.113***

0.158***

0.019***

(0.016)

(0.016)

(0.008)

(0.009)

(0.011)

(0.003)

Previous trip was

booking x cancelled

0.121***

0.119***

0.111***

0.089***

0.090***

0.068***

(0.011)

(0.011)

(0.011)

(0.007)

(0.006)

(0.005)

Controls

No

No

Job preference

No

Market

Job preference and market

Time FE

No

No

No

Yes

No

Yes

Region FE

No

No

No

Yes

No

Yes

Observations

9,211,035

8,290,871

8,035,218

9,211,034

9,211,035

8,035,217

R-squared

0.035

0.032

0.077

0.165

0.099

0.208

Sample

Full

Excl last trip and never-bookers

Full

Full

Full

Excl last trip and never-bookers

Economic effect (%)

33.91

33.19

31.10

25.16

25.43

18.95

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Robustness

  • Moderate preference drivers (Chen et al. 2016)
  • Driver FE
  • Streaks (two completions)
  • Logit

​

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Heterogeneity

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Booking: Cumulative model

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 VARIABLES

(a)

(b)

​

Cumulative model (first order)

Cumulative model (second order)

Cum(Street Hail)

-0.004***

-0.007***

​

(< 0.001)

(< 0.001)

Cum(Street Hail) ^2

 

<0.001***

 

 

(< 0.001)

Cum(Completed Booking)

0.007***

0.011***

​

(0.001)

(0.002)

Cum(Completed Booking) ^2

 

>-0.001***

 

 

(< 0.001)

Cum(Cancellation)

0.017***

0.022***

​

(0.001)

(0.002)

Cum(Cancellation)^2

​

-0.002***

​

​

(< 0.001)

Controls

Yes

Yes

Time FE

Yes

Yes

Region FE

Yes

Yes

Observations

8,035,217

8,035,217

R-squared

0.209

0.209

Economic effect: cum(cancellation) (%)

3.51

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Economic effect: cum(cancellation) + cum(cancellation)^2 (%)

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Fit: Discrete, cumulative

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Outline

  • Introduction
  • Setting
  • Retrospective study
  • Experiment
  • Discussion

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Retrospective study: Limitations

  • Data only on outcome (street hail or booking)
    • No information on bids
    • No information on beliefs (in common with almost all other studies)
    • Cannot completely rule out loss aversion, disappointment, income targeting, income effect, fatigue
  • [In progress] Lab-in-field experiment with taxi drivers
    • Elicit beliefs about sequences of coin tosses
    • Apply debiasing tutorial on gambler’s fallacy
    • Incentivized---based on prediction tasks
    • Registered, AEARCT 13808, 15 August 2024

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Experimental design

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Scen-ario

Bid ETA

Predict & recognize coin toss

Tutorial

Treatment

Scen-ario

Bid ETA

Predict & recognize coin toss

Control

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Elicitation of beliefs: Prediction task

  • Four prediction tasks (2 x 2nd order + 2 x 4th order)

​

​

​

​

​

​

​

​

​

  • Randomly interspersed with four decoy tasks

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Elicitation of beliefs: Recognition task

  • Randomized (3H or 3T) + (5H or 5T)

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Gambler’s fallacy: Definitions

  • Prediction task: all 4 of 4 predictions in line with GF
  • Recognition task: all 3 of 3 judgments of 3 coin tosses in line with GF
  • Correlation: 0.12
    • Different biases?

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Debiasing intervention

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Summary statistics

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VARIABLE

All subjects

Control group

Treatment group

t-test

 

N

Mean

(SE)

N

Mean

(SE)

N

Mean

(SE)

p-value

Male

37

0.973

19

0.947

18

1.000

0.337

 

​

(0.027)

​

(0.053)

​

(0.000)

​

Age

37

60.595

19

61.526

18

59.611

0.593

 

​

(1.757)

​

(2.091)

​

(2.905)

​

Taxi experience

37

14.081

19

14.684

18

13.444

0.739

(years)

​

(1.823)

​

(2.591)

​

(2.630)

 

Major taxi company

37

1.000

19

1.000

18

1.000

NA

 

​

(0.000)

​

(0.000)

​

(0.000)

 

Earnings per shift

37

106.973

19

113.316

18

100.278

0.599

 

​

(12.154)

​

(19.257)

​

(14.948)

​

Income targeter

37

0.541

19

0.579

18

0.500

0.641

 

​

(0.083)

​

(0.116)

​

(0.121)

 

GF belief

37

0.135

19

0.158

18

0.111

0.688

(prediction task)

​

(0.057)

​

(0.086)

​

(0.076)

​

GF belief

37

0.189

19

0.211

18

0.167

0.742

(recognition task)

​

(0.065)

​

(0.096)

​

(0.090)

​

ETA bid if previous

18

5.444

11

5.273

7

5.714

0.625

cancelled (minutes)

​

(0.422)

​

(0.488)

​

(0.808)

​

ETA bid if previous

19

5.579

8

5.000

11

6.000

0.310

completed(minutes)

​

(0.473)

​

(0.756)

​

(0.603)

​

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GF (prediction task): Control group---Non-believers vis-à-vis believers

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GF believers (prediction task): �Debiasing intervention

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GF (recognition task): Control group---Non-believers vis-à-vis believers

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GF believers (recognition task): �Debiasing intervention

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Outline

  • Introduction
  • Setting
  • Retrospective study
  • Experiments
  • Discussion

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Findings

  • Retrospective study
    • On average, drivers were 14.2% less likely to serve another booking after completing a booking.
    • Longer in shift, more likely to follow cumulative than discrete model of gambler’s fallacy
  • [In progress] Experiment

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Contributions

  • Gambler’s fallacy in context not confounded by quotas, learning about standards, preference for fairness, contrast effects.
    • Reversal
    • Multi-modality
    • Quantified loss: Driver would have earned $67.50 (6.2%) more per week if they served bookings and street hail without regard for the outcome of previous bookings.
  • [In progress] Related beliefs to future behavior: Only previous study related beliefs to past behavior (Dohmen et al. 2009).
  • [In progress] Showed debiasing intervention.

​

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Thanks!

iplpng@gmail.com

WangSong9771@gmail.com

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Cancellation (individual drivers)

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VARIABLES 

(a)

​

Cancellation

Previous trip was booking x cancelled

0.023***

 

(0.002)

Control

Yes

Time FE

Yes

Region FE

Yes

​

​

Observations

691,158

Drivers

28,329

R-squared

0.013

Notes: Estimated by ordinary least squares. Sample includes all successive booking jobs for the same driver. Dependent variable: indicator of whether the job was a cancelled booking. Control variables include moving average of the fraction of bookings in the last five jobs the driver served within the same shift, the driver’s proportion of bookings during the previous shift, and nearby supply and demand for taxis (number of idle vehicles, number of street-hail jobs in progress, and number of booking jobs in progress). Constant included but not reported. Robust standard errors in parentheses, clustered multi-way by date, hour, and region (*** p<0.01, ** p<0.05, * p<0.1).

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Cancellation (region)

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(a)

(b)

(c)

VARIABLES

Time interval:

15 mins

Time interval:

30 mins

Time interval:

60 mins

Booking cancellation rate

0.022***

0.014***

0.022***

(region r, period t-1)

(0.002)

(0.003)

(0.004)

Constant

0.073***

0.074***

0.074***

 

(< 0.001)

(< 0.001)

(< 0.001)

Time of day FE

Yes

Yes

Yes

Region FE

Yes

Yes

Yes

Observations

429,925

275,058

164,681

R-squared

0.030

0.034

0.041

Notes: Estimated by ordinary least squares. In each column, the sample is a panel of booking cancellation rate by region and specified time interval. Dependent variable is the booking cancellation rate in the region and time interval. Column (a): time interval, 15 minutes; Column (b): time interval, 30 minutes; Column (c): time interval, 60 minutes. Standard errors in parentheses, clustered multi-way by date, hour, and region (*** p<0.01, ** p<0.05, * p<0.1).

<Main narrative>

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Model: Discrete/cumulative

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Exploratory experiment

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Scen-ario

Bid ETA

Bid ETA

Booking completed

Booking cancelled

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Exploratory experiment

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Findings

  • Retrospective study
    • On average, drivers were 14.2% less likely to serve another booking after completing a booking.
    • Longer in shift, more likely to follow cumulative than discrete model of gambler’s fallacy
  • Experiment
    • Effect of cancellation on bidding more pronounced among drivers who believed in gambler’s fallacy
    • Effect corrected by debiasing tutorial

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