Subjective Probability and Prizes

Last registered on May 22, 2023


Trial Information

General Information

Subjective Probability and Prizes
Initial registration date
July 23, 2020

Initial registration date is when the trial was registered.

It corresponds to when the registration was submitted to the Registry to be reviewed for publication.

First published
July 23, 2020, 9:42 AM EDT

First published corresponds to when the trial was first made public on the Registry after being reviewed.

Last updated
May 22, 2023, 11:46 AM EDT

Last updated is the most recent time when changes to the trial's registration were published.



Primary Investigator

ESMT Berlin

Other Primary Investigator(s)

PI Affiliation
University of California at Los Angeles
PI Affiliation
Queen Mary University of London

Additional Trial Information

Start date
End date
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
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. 2023. "Subjective Probability and Prizes." AEA RCT Registry. May 22.
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.

Update on May 22, 2023: We will run a third robustness check in which the same prize is offered three times (i.e., instead of varying the prize).
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].

Institutional Review Boards (IRBs)

IRB Name
University of Oxford Economics Departmental Research Ethics Committee
IRB Approval Date
IRB Approval Number


Post Trial Information

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Is the intervention completed?
Data Collection Complete
Data Publication

Data Publication

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Program Files

Program Files
Reports, Papers & Other Materials

Relevant Paper(s)

Reports & Other Materials