Abstract
Individual valuation of a binary lottery at values less than the lottery’s worst outcome has been designated as the “uncertainty effect”. Our paper aims to explore the boundary conditions of the uncertainty effect by investigating a plausible underlying process and proposing two possible methods. First, we examine how providing an exogenous evaluation opportunity prior to judging the value of the lottery affects individuals’ judgments, and find that first valuing the worst outcome and then the lottery eliminates the uncertainty effect. Second, we explore whether introducing additional cognitive load dampens how far decision makers correct their initial evaluations, and find that additional cognitive load is able to eliminate the uncertainty effect.
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Acknowledgments
We thank the Editors and an anonymous referee for the Journal of Risk and Uncertainty and participants in our seminars for helpful comments. Tianjun Feng is the corresponding author for inquiries on the published paper (TFeng@Fudan.edu.cn). Portions of this work were supported by grants to Yitong Wang for his dissertation on “Decision Research on Time, Risk, and Ambiguity” from a National Science Foundation Dissertation Grant to the University of California, Irvine, and the National Natural Science Foundation of China (Grant 71201091, Grant 71361130017), and Tianjun Feng from the National Natural Science Foundation of China (Grant 70901022, 71371057), the Shanghai Philosophy and Social Science Planning Funds (Grant 2012BGL014), and the Ministry of Education of China (Grant for Overseas-Returnees).
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Appendices
Appendix A
1.1 The questionnaire of Study 2
1.1.1 Scenario 1: Barnes and Noble gift certificate
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Certainty condition:
We are interested in how much you would be willing to pay for two different items. In particular we will ask you how much you would be willing to pay for a \$50 gift certificate or a \$100 gift certificate for Barnes and Noble, which are good for use within the next two weeks.
If you could only buy the \$50 gift certificate, what is the highest amount of money you would pay for it? \$____
If you could only buy the \$100 gift certificate, what is the highest amount of money you would pay for it? \$____
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Uncertainty condition:
We are interested in how much you would be willing to pay for a lottery ticket that will for sure pay one of two possible rewards (both are equally likely).
The lottery will either pay a \$50 gift certificate or a \$100 gift certificate for Barnes and Noble, each of which is good for use within the next two weeks.
What is the highest amount of money you would pay for this lottery? \$____
1.1.2 Scenario 2: time preference
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Certainty condition:
Imagine that we offer you \$100 or \$200 one year from today. What is the highest amount of money you would be willing to pay for one of them now?
If we could only offer you \$100 one year from today, what is the highest amount of money you would be willing to pay for this now? \$____
If we could only offer you \$200 one year from today, what is the highest amount of money you would be willing to pay for this now? \$____
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Uncertainty condition:
We are interested in how much you would be willing to pay for a lottery ticket that will for sure pay one of two possible rewards (both are equally likely). The lottery winnings you earn will be paid to you one year from today.
The lottery will either pay you \$100 cash or \$200 cash. The lottery winnings you earn will be paid to you one year from today.
What is the highest amount of money you would be willing to pay for this lottery ticket now? \$____
1.1.3 Scenario 3: boring tasks
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Certainty condition:
Consider a boring and tedious task (like sorting file folders). We will offer you two different payments (\$25 or \$50). What is the longest amount of time you would be willing to spend on this task for one of these payments?
Imagine that your payment for this task is \$25. What is the longest amount of time you would be willing to spend on this task for this payment? ____minutes
Imagine that your payment for this task is \$50. What is the longest amount of time you would be willing to spend on this task for this payment? ____minutes
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Uncertainty condition:
Consider a boring and tedious task (like sorting file folders). Imagine that your payment for this task is a lottery ticket that will for sure pay one of two possible rewards (both are equally likely).
The lottery will either pay you \$25 cash or \$50 cash.
What is the longest amount of time you would be willing to spend on this task for this payment?
_____minutes
1.1.4 Scenario 4: products
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Certainty condition:
We are interested in how much you are willing to pay for the following two products currently being sold in the market.
Product 1 (MSRP \$75.99)
Product 2 (MSRP \$169.99)
Black & Decker Toast-R-Oven 4-Slice Toaster Oven
Panasonic Full-Size 1250-Watt Microwave Oven
Description: This versatile toaster oven toasts, cooks, broils and reheats a variety of foods. Enjoy your favorite muffins, individual pizzas, casseroles or small chicken parts—cooked to perfection right on your countertop.
Description: With a 1-3/5-cubic-foot capacity and 1250 watts of power, this full-sized microwave oven provides quick and easy meal preparation. Its one-touch sensor cooking adjusts power levels automatically, making cooking a variety of foods easier than ever.
If you could only buy product 1 (Black & Decker Toast-R-Oven 4-Slice Toaster Oven), what is the highest amount of money you would pay for it? \$____.
If you could only buy product 2 (Panasonic Full-Size 1250-Watt Microwave Oven), what is the highest amount of money you would pay for it? \$____.
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Uncertainty condition:
We are interested in how much you would be willing to pay for a lottery ticket that will for sure pay one of two possible rewards (both are equally likely).
The lottery will either give you a Black & Decker Toast-R-Oven 4-Slice Toaster Oven or a Panasonic Full-Size 1250-Watt Microwave Oven. (See more information about these two products below.)
Product 1 (MSRP \$75.99)
Product 2 (MSRP \$169.99)
Black & Decker Toast-R-Oven 4-Slice Toaster Oven
Panasonic Full-Size 1250-Watt Microwave Oven
Description: This versatile toaster oven toasts, cooks, broils and reheats a variety of foods. Enjoy your favorite muffins, individual pizzas, casseroles or small chicken parts—cooked to perfection right on your countertop.
Description: With a 1-3/5-cubic-foot capacity and 1250 watts of power, this full-sized microwave oven provides quick and easy meal preparation. Its one-touch sensor cooking adjusts power levels automatically, making cooking a variety of foods easier than ever.
What is the highest amount of money you would be willing to pay for this lottery ticket now? \$____.
Appendix B
2.1 Cumulative distributions for the three scenarios in Study 2
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Wang, Y., Feng, T. & Keller, L.R. A further exploration of the uncertainty effect. J Risk Uncertain 47, 291–310 (2013). https://doi.org/10.1007/s11166-013-9180-x
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DOI: https://doi.org/10.1007/s11166-013-9180-x