1. Toward a Method for Measuring the Influence of Multiple Outcomes on Discounting
David J. Cox & Jesse Dallery
Behavioral Health & Technology Research Clinic
University of Florida

2. Multiple Outcomes

3. Multiple Outcomes Smoking Cigarette: Immediate relief from withdrawal
Delayed and uncertain adverse health outcomes.

4. Multiple Outcomes Smoking Cigarette: Abstaining:
Immediate relief from withdrawal
Delayed and uncertain adverse health outcomes.
Abstaining:
Immediate discomfort
Delayed and uncertain positive health outcomes.

5. Multiple Outcomes Balanced Nutrition, Other Substance Use,
Physical Exercise, Risky Sexual Behavior

6. Discounting: Equations
Delay
V = 𝐴 1+𝑘D
Probability
V = 𝐴 1+ℎθ 𝜃= (1−𝑝) 𝑝

7. Discounting: Equations
Delay
V = 𝐴 1+𝑘D
Probability
V = 𝐴 1+ℎθ 𝜃= (1−𝑝) 𝑝

8. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:

9. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure: X

10. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:
100% Chance of
Getting $500
40% Chance of
Getting $1000 OR X

11. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:
100% Chance of
Getting $500
40% Chance of
Getting $1000 OR X

12. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:
100% Chance of
Getting $500
40% Chance of
Getting $1000 OR X

13. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:
100% Chance of
Getting $500
40% Chance of
Getting $1000 OR X

14. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:
100% Chance of
Getting $750
40% Chance of
Getting $1000 OR
100% Chance of
Getting $250
40% Chance of
Getting $1000 OR X

15. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:

16. Discounting: Obtaining k or h
Odds Against
Certain Value ($)
Adjusting Amount Procedure:
Subjective Value ($)

17. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:

18. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:

19. Discounting: Obtaining k or h
Odds Against
Subjective Value ($)
Adjusting Amount Procedure:
5 Prob. x 5 Trials = 25 Total Trials

20. Discounting: Obtaining k or h
Adjusting Amount Procedure:
100% Chance of
Getting $500
Immediately
40% Chance of
Getting $1000
In 6-Months OR
Vanderveldt, A., Green, L., & Myerson, J. (2015). Discounting of monetary rewards that are both delayed and probabilistic: delay and probability combine multiplicatively, not additively. Journal of Experimental Psychology. Learning, memory, and cognition, 41,

21. Discounting: Obtaining k or h
Adjusting Amount Procedure:
Delay or Probability:
5 Prob. x 5 Trials = 25 Total Trials
Delay and Probability:
5 Delays x 5 Prob. x 5 Trials = 125 Total Trials
Vanderveldt, A., Green, L., & Myerson, J. (2015). Discounting of monetary rewards that are both delayed and probabilistic: delay and probability combine multiplicatively, not additively. Journal of Experimental Psychology. Learning, memory, and cognition, 41,

22. Discounting: Obtaining k or h
OPTION A: Smoke
100% chance of short delay to relief from withdrawal
p chance delayed negative health impact
OPTION B: Other Behavior
100% chance of short delay to experience withdrawal
p chance of delayed positive health impact

23. Discounting: Obtaining k or h
OPTION A: Smoke
100% chance of short delay to relief from withdrawal
p chance delayed negative health impact
OPTION B: Other Behavior
100% chance of short delay to experience withdrawal
p chance of delayed positive health impact
125 Trials for Outcome-One x 5 Delays Outcome-Two X 5 Prob. Outcome-Two
= 3,125

24. Discounting: 5-Trial Adjusting Delay
Koffarnus & Bickel (2014)
Koffarnus, M.N., & Bickel, W.K. (2014). A 5-Trial Adjusting Delay Discounting Task: Accurate Discount Rates in Less Than One Minute. Experimental and Clinical Pharmacology, 22,

25. Discounting: 5-Trial Adjusting Delay
Koffarnus & Bickel (2014)
Subjective Value ($)
Delay (Days)

26. Discounting: 5-Trial Adjusting Delay
Koffarnus & Bickel (2014)
Subjective Value ($)
Delay (Days)
Delay (Days)

27. Discounting: 5-Trial Adjusting Delay
Koffarnus & Bickel (2014)
Subjective Value ($)
Delay (Days)
Delay (Days)

28. Discounting: 5-Trial Adjusting Delay
Koffarnus & Bickel (2014)
Subjective Value ($)
Delay (Days)
Delay (Days)

29. Discounting: 5-Trial Adjusting Delay
Koffarnus & Bickel (2014)
Subjective Value ($)
Delay (Days)
Delay (Days)

30. Discounting: 5-Trial Adjusting Delay
Koffarnus & Bickel (2014)
Effective Delay 50% (ED50)
Yoon, J.H., & Higgins, S.T. (2008). Turning k on its head: Comments on use of an ED50 in delay discounting research. Drug and Alcohol Dependence, 95,

31. Discounting: 5-Trial Adjusting Delay
Koffarnus & Bickel (2014)
Effective Delay 50% (ED50) = 1/k
Yoon, J.H., & Higgins, S.T. (2008). Turning k on its head: Comments on use of an ED50 in delay discounting research. Drug and Alcohol Dependence, 95,

32. Discounting: Adjusting Delay/Probability
Koffarnus & Bickel (2014)
Effective Delay 50% (ED50) = 1/k
5-trial adjusting delay tasks provide similar ks for delayed monetary gains.
Cox & Dallery (in review)
Delayed monetary losses (5-trials)
Probabilistic monetary gains (5-trials)
Probabilistic monetary losses (5-trials)
Delayed & Probabilistic monetary losses (10-trials)
Delayed & Probabilistic monetary gains (10-trials)
Cox, D.J., & Dallery, J. (in review). Effects of delay and probability combinations on discounting in humans.
Behavioural Processes.

33. Multiple Outcomes

34. Multiple Outcomes
Influence of second outcome of equal value

35. Multiple Outcomes Influence of second outcome of equal value
Outcome Combinations
Gain-Gain
Gain-Loss
Loss-Gain
Loss-Loss

36. Multiple Outcomes Influence of second outcome of equal value
Outcome Combinations
Model comparison

37. Method ]

38. Method Participants 185 Psychology Participant Pool
AVG. Age = 18.60, range 18-25
74% female

39. Method Participants Randomly Assigned Hypothetical Money
GG, GL, LG, or LL

40. Method Participants Randomly Assigned Hypothetical Money
GG, GL, LG, or LL

41. Method
Tasks

42. Method Tasks 1-Outcome: 10-Trial Monetary Gains
1-Outcome: 10-Trial Monetary Losses

43. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay

44. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

45. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

46. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

47. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

48. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

49. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

50. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

51. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

52. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

53. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

54. Method Tasks 1-Outcome: 10-Trial 5-Trial Adjusting Probability
5-Trial Adjusting Delay
Subjective Value ($)

55. Method
Tasks
1-Outcome: 10-Trial
Gains
Losses

56. Method
Tasks
1-Outcome: 10-Trial
Gains
Losses
2-Outcomes: 10-Trial

57. Method OPTION A: Smoke OPTION B: Other Behavior
100% chance of short delay to relief from withdrawal
Smaller-Sooner-Certain Gain
p chance delayed negative health impact.
Larger-Later-Uncertain Loss
OPTION B: Other Behavior
p chance of delayed positive health impact.
Larger-Later-Uncertain Gain
100% chance of short delay to experience withdrawal
Smaller-Sooner-Certain Loss

58. Method Smaller-Sooner-Certain Gain Larger-Later-Uncertain Loss
Larger-Later-Uncertain Gain
Smaller-Sooner-Certain Loss

59. Method Smaller-Sooner-Certain Gain Larger-Later-Uncertain Loss
Larger-Later-Uncertain Gain
Smaller-Sooner-Certain Loss

60. Method Tasks 1-Outcome: 10-Trial 2-Outcomes: 10-Trial Gains Losses
100%, 0-Day Delay
75%, 0-Day Delay
45%, 0- Day Delay
100%, 6-Month Delay
75%, 6-Month Delay
45%, 6-Month Delay
100%, 2-Years Delay
75%, 2-Years Delay
45%, 2-Years Delay

61. Method Tasks 1-Outcome: 10-Trial 2-Outcomes: 10-Trial Gains Losses
100%, 0-Day Delay
75%, 0-Day Delay
45%, 0- Day Delay
100%, 6-Month Delay
75%, 6-Month Delay
45%, 6-Month Delay
100%, 2-Years Delay
75%, 2-Years Delay
45%, 2-Years Delay

62. Results

63. If 2-outcome ↑ = Value of Target Outcome Decreases More Rapidly

64. If 2-outcome ↑ = Value of Target Outcome Decreases More Rapidly

65. If 2-outcome ↑ = Value of Target Outcome Decreases More Rapidly

66. If 2-outcome ↑ = Value of Target Outcome Decreases More Rapidly

67. If 2-outcome ↑ = Value of Target Outcome Decreases More Rapidly

68. Results
Model

69. Results 𝑉= 𝐴 1+𝑘D 1+ℎƟ Model
Vanderveldt, A., Green, L., & Myerson, J. (2015). Discounting of monetary rewards that are both delayed and probabilistic: delay and probability combine multiplicatively, not additively. Journal of Experimental Psychology. Learning, memory, and cognition, 41,

70. Results
Model
𝑉= 𝐴 1+𝑘D 1+ℎƟ
How do these combine?
𝑉= 𝐴 1+𝑘D 1+ℎƟ

71. Subtractive-Independent Model
Results
Model
𝑉= 𝐴 𝑡 1+ 𝑘 𝑡 𝐷 𝑡 1+ ℎ 𝑡 𝜃 𝑡 − 𝐴 𝑠 1+ 𝑘 𝑠 𝐷 𝑠 1+ ℎ 𝑠 𝜃 𝑠
Subtractive-Independent Model

72. Results
Model
𝑉= 𝐴 𝑡 𝑘 𝑡 ∗ 𝐷 𝑡 𝐴 𝑠 + 𝑘 𝑠 ∗ 𝐷 𝑠 ℎ 𝑡 ∗ 𝜃 𝑡 𝐴 𝑠 + ℎ 𝑠 ∗ 𝜃 𝑠
Multiplicative-Interactive Model

73. Results Interactive Model Independent Model Model Gain-Gain Loss-Loss
Median VAC (Min, Max)
Independent Model
Gain-Gain
0.99 (0.99, 1.00)
0.02 (-1.86, 0.99)
Loss-Loss
0.99 (0.99, 1.00)
(-3.86, 0.98)
Gain-Loss
0.99 (0.89, 1.00)
0.74 (-1.73, 0.99)
0.63 (-2.07, 0.96)

74. Gain-Gain Multiplicative-Interactive Model
Subtractive-Independent Model

75. Gain-Loss Multiplicative-Interactive Model
Subtractive-Independent Model

76. Summary

77. Summary
Research on more complex choice scenarios is beginning to occur.
Reliable and efficient methods are needed.
10-trial adjusting delay and probability tasks are one method.
1-Outcome vs. 2-Outcome:
Delay, probability, & similarity
Model Comparison:
Outcomes interact to influence choice.

78. Future Directions Methods Second Outcome Amount Across Commodity
Money vs. cigarette
Money vs. salad
Money vs. steps
Etc.

79. Acknowledgements: Dr. Jesse Dallery Phillip Erb Brantley Jarvis
Sarah Martner
Triton Ong
Tia Bolivar
Molly Barlow
Lisa Stedman-Falls
Nick Green
Andrea Villegas
I’d like to acknowledge the many individuals who have provided tremendous amounts of helpful feedback on this line of research from its initial inception.