Subjective Probability and Prizes
Last registered on August 14, 2020


Trial Information
General Information
Subjective Probability and Prizes
Initial registration date
July 23, 2020
Last updated
August 14, 2020 6:11 PM EDT
Primary Investigator
ESMT Berlin
Other Primary Investigator(s)
PI Affiliation
Queen Mary University of London
PI Affiliation
University of California at Los Angeles
Additional Trial Information
In development
Start date
End date
Secondary IDs
We collect experimental evidence to examine the descriptive validity of Anscombe & Aumann's (1963) definition of subjective probability. We document the proportion of subjects in our sample who give responses consistent with the definition and explore the responses of those who violate it. We also report at how violations co-vary with measures including competency in dealing with probabilities and demographic information.
External Link(s)
Registration Citation
Ronayne, David, Roberto Veneziani and William Zame. 2020. "Subjective Probability and Prizes." AEA RCT Registry. August 14.
Experimental Details
Subjects choose between various risky choices in a way designed to test whether they behave consistently with Anscombe & Aumann's (1963) definition of subjective probability. A within-subject treatment will provide data for us to examine how the prize level of the risky choices affects responses.
Intervention Start Date
Intervention End Date
Primary Outcomes
Primary Outcomes (end points)
The proportion of subjects who have the same switch point between choosing an ambiguous (for which the probability of winning a prize is unknown) vs. an uncertain (for which the probability of winning a prize is known) option, across scenarios that differ by payoff level.
Primary Outcomes (explanation)
Our primary outcome is a function of the point at which subjects switch from choosing the ambiguous option to choosing the uncertain option. This measure is a natural number (including zero), where the highest value possible is defined by the number of choices a subject makes per prize level. We want to know whether each subject has the same switch point across different prize levels.
Secondary Outcomes
Secondary Outcomes (end points)
Probability competency questions formed of the first five items of the "Expanded numeracy scale" of Lipkus et al. (2001).

Demographics: Age, gender, race, mother tongue, income, education, and political affiliation.

Reference: Lipkus, I. M., Samsa, G., & Rimer, B. K. (2001). General performance on a numeracy scale among highly educated samples. Medical decision making, 21(1), 37-44.
Secondary Outcomes (explanation)
We will investigate associations between these secondary measures and our primary measure.
Experimental Design
Experimental Design
Subjects make multiple choices between an ambiguous option (for which the probability of winning a prize is unknown) and an uncertain option (for which the probability of winning a prize is known). For each subject and prize level we vary the attractiveness of the uncertain option while keeping the ambiguous option fixed.

We will run two robustness checks of the main design. One will have exactly the same design but will use a pool of workers with Amazon's "Masters" qualification. The other will present the same choices as the main design, but in a different layout/format.
Experimental Design Details
Subjects have one of their choices selected at random to determine their payoff. Each choice alternative is a lottery that can gives either a positive payoff level (in USD) or nothing. In order to make incentive payments to subjects for whom an ambiguous choice was selected, we fixed the probability of winning a prize from that option. Via a random process, we fixed this once and for all, at 40%, for all subjects. (Subjects of course do not know this because the ambiguous option must appear with an unknown chance of paying off.)
Randomization Method
Within-subject randomization (of the order in which each subject sees the different prize levels) is conducted by the software Qualtrics.
Randomization Unit
Randomization is within-subject.
Was the treatment clustered?
Experiment Characteristics
Sample size: planned number of clusters
No clustering.
Sample size: planned number of observations
1200 for the main wave 100-125 per robustness wave
Sample size (or number of clusters) by treatment arms
Randomization is within-subject.
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
We aim for a 95% confidence interval on our primary outcome measure (a proportion) with +/- 3 percentage points. Assuming a proportion of 0.5 (which generates the widest possible confidence interval), n=1200 provides a 95CI = [0.472,0.528].
IRB Name
University of Oxford Economics Departmental Research Ethics Committee
IRB Approval Date
IRB Approval Number
Post Trial Information
Study Withdrawal
Is the intervention completed?
Is data collection complete?
Data Publication
Data Publication
Is public data available?
Program Files
Program Files
Reports, Papers & Other Materials
Relevant Paper(s)