Projective Measurements in the Elicitation of Preferences

Last registered on October 20, 2021

Pre-Trial

Trial Information

General Information

Title
Projective Measurements in the Elicitation of Preferences
RCT ID
AEARCTR-0005005
Initial registration date
November 07, 2019
Last updated
October 20, 2021, 8:47 AM EDT

Locations

Primary Investigator

Affiliation
DICE, University of Duesseldorf

Other Primary Investigator(s)

PI Affiliation
DICE, University of Duesseldorf
PI Affiliation
DICE, University of Duesseldorf

Additional Trial Information

Status
In development
Start date
2019-11-14
End date
2021-11-01
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
Abstract
Economic preferences are a fundamental aspect of economic modeling but their measurement presents a number of puzzles such as order and framing effects, and paradoxes like the lack of additivity. This study focuses on how to understand such behavioral patterns as a natural construct of the measurement process itself, and not as an undesirable anomaly. We propose a model that departs from standard probability theory by including projective measurements that do not require a certain boolean structure in the underlying space of events. Instead, we rely on a more general condition of orthomodularity.

In order to illustrate the working of this theoretical setting, we propose a stylized laboratory experiment with three treatments. In all treatments, subjects will first face the same choice task regarding time preferences and they will finish facing the same choice task (Lottery A vs. Lottery B) regarding risk preferences with a neutral frame. There will be no other intermediate steps in baseline Treatment 1. In addition, Treatments 2 and 3 will include an intermediate elicitation task. Subjects will also make a choice between a safe option and a lottery, framed as a gain or a loss: Safe+ vs. Lottery+ in Treatment 2 and Safe- vs. Lottery- in Treatment 3, respectively. We will collect additional control variables in a questionnaire at the end of the sessions.

Comparing the choices in the final task in Treatments 2 and 3 to the outcomes in the final task in Treatment 1 will allow us to identify a potential lack of additivity as a result of order effects. Comparing Treatment 2 to Treatment 3 will allow us to formally include framing as part of a projective measurement. Finally, we aim at assessing the validity of our theoretical framework as a descriptive tool for the measurement of individual preferences by producing a model that incorporates all these building blocks from the experiment in one unified setting, and testing it against the data.
External Link(s)

Registration Citation

Citation
Martínez Martínez, Ismael, Hannah Schildberg-Hörisch and Chi Trieu. 2021. "Projective Measurements in the Elicitation of Preferences." AEA RCT Registry. October 20. https://doi.org/10.1257/rct.5005-1.1
Experimental Details

Interventions

Intervention(s)
Intervention Start Date
2019-11-14
Intervention End Date
2020-07-31

Primary Outcomes

Primary Outcomes (end points)
Fraction of subjects that select Lottery A or Lottery B in the last measurement (neutral frame) of the three treatments.
Primary Outcomes (explanation)
Comparing the choices in the final task in Treatments 2 and 3 to the choices in the final task in Treatment 1 will allow us to identify a potential lack of additivity as a result of order effects. Comparing choices in Treatment 2 to those in Treatment 3 will allow us to formally include framing as part of a projective measurement.

Secondary Outcomes

Secondary Outcomes (end points)
Fraction of subjects that select Lottery- or Lottery+ instead of the Safe options in the intermediate measurements of the two framed Treatments 2 and 3.
Secondary Outcomes (explanation)

Experimental Design

Experimental Design
We propose a stylized laboratory experiment with three treatments. In all treatments, subjects will first face the same choice task regarding time preferences and they will finish facing the same choice task (Lottery A vs. Lottery B) regarding risk preferences with a neutral frame. There will be no other intermediate steps in baseline Treatment 1. In addition, Treatments 2 and 3 will include an intermediate elicitation task. Subjects will also make a choice between a safe option and a lottery, framed as a gain or a loss: Safe+ vs. Lottery+ in Treatment 2 and Safe- vs. Lottery- in Treatment 3, respectively. We will collect additional control variables in a questionnaire at the end of the sessions.
Experimental Design Details
We implement a between-subject treatment design with three treatments, namely Treatment 1–Baseline, Treatment 2–GainFrame, and Treatment 3–LossFrame. In all treatments, subjects make a sequence of decisions and answer a questionnaire. The sequence includes two decisions in Treatment 1—Baseline, and three decisions in Treatments 2–GainFrame and 3–LossFrame.

The first decision (task T) in the three treatments is a choice between 14 Euro to be paid today and 17 Euro to be paid in five weeks.

The last decision in the three treatments is a choice between two lotteries (task R’). These two lotteries will be expressed in neutral terms, without emphasizing gains or losses. We adapt this task from a comparable one in Brown and Healy (EER, 2018). For example, the first lottery pays 18 Euro and 9 Euro, each with 50% probability. The second lottery pays 22 Euro with 75% probability, and 0 Euro with 25% probability.

The intermediate task that is only present in Treatments 2 and 3 but not in the baseline Treatment 1. This task is about making a choice between a safe payment and a lottery with loaded framing. We will use positive framing (emphasizing gains) in Treatment 2 and call it “task R+” and negative framing (emphasizing losses) in Treatment 3 and call it “task R-”. We adapt the two wording for the two frames directly from an experiment by De Martino et al. (Science, 2006).

For instance, each subject in Task R+ is endowed with 20 Euro and makes a choice between keeping 12 Euro for sure and a lottery with 75% probability of keeping all of the 20 Euro and 25% probability of keeping nothing. On the other hand, each subject in Task R- is endowed with 20 Euro and makes a choice between losing 8 Euro for sure and a lottery with 75% probability of losing nothing and 25% probability of losing all of the 20 Euro.

Summary of treatment design:
Treatment 1 (Baseline): First T, then R’.
Treatment 2 (Gain Frame): First T, then R+, then R’.
Treatment 3 (Loss Frame): First T, then R-, then R’.

A final questionnaire will include control variables such as measures of cognitive ability (Raven Matrices and Cognitive Reflection Test), trust, patience, engagement in risky behaviors, and socio-economic background.

For each subject, one of the choice-making tasks will be randomly selected to be paid. Payments will be made via bank transfers. This is communicated to the subjects in advance when sending the invitation emails.

Within the general research question whether the structure of projective measurements is a good description for the elicitation of individual preferences, we will focus on three specific questions of interest based on the experimental data. (1) Do we find statistical differences in the outcomes of the first task T? (2) Are there statistical differences between the fraction of subjects choosing the lottery in tasks R+/R- in treatments 2 and 3? (3) Do we find significant differences in the final task R’ across the three treatments? If so, can the projective model explain them as a result of the inclusion of the intermediate framed tasks R+ and R-? (4) Finally, can we conclude positively in favor of a model of projective measurement testing its goodness of fit? (This step is likely to require a simulation exercise).
Randomization Method
Invitation of subjects with standard ORSEE procedures. When arriving in the lab, participants will select one computer randomly, by drawing a cabin number blindly. Treatments will also be assigned to each computer randomly at the beginning of the session.
Randomization Unit
Each subject will be one observation.
Was the treatment clustered?
No

Experiment Characteristics

Sample size: planned number of clusters
We aim at a balanced sample with at least 60–80 subjects per treatment.
Sample size: planned number of observations
We aim at a balanced sample with at least 60–80 subjects per treatment.
Sample size (or number of clusters) by treatment arms
We aim at a balanced sample with at least 60–80 subjects per treatment.
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
IRB

Institutional Review Boards (IRBs)

IRB Name
IRB Approval Date
IRB Approval Number

Post-Trial

Post Trial Information

Study Withdrawal

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Intervention

Is the intervention completed?
No
Data Collection Complete
Data Publication

Data Publication

Is public data available?
No

Program Files

Program Files
Reports, Papers & Other Materials

Relevant Paper(s)

Reports & Other Materials