Belief Elicitation as Behavioral Design

This experiment relies on the elicitation of subjects' beliefs, specifically, what they believe others do, before making their decision in a similar decision environment.

2025-07-28

2025-09-15

Using the between subjects design, our main outcome of interest for the moral wiggle room game is the ignorance rate and elicited belief regarding the ignorance rates about other subjects across the different treatment arms. Ignorance rate is calculated as a proportion of subjects within a treatment arm who did not reveal information regarding the recipient's payoffs. Elicited beliefs on ignorance will be quantified between 0 to 100 percent.

In the dice rolling game, the main variable of interest is the distribution of dice reports and a similarly elicited belief on whether or not others misreported or truthfully reported the dice roll. This will be compared between the treatments and with a uniform distribution (denoting truthful reporting).

In a between subjects design, subjects are asked to play either the moral wiggle room game or the dice rolling game. Within each game, depending on the treatment arm, subjects' beliefs about what others do is elicited ex-ante or ex-post their own decision. Afterwards, subjects complete a questionnaire.

There are two decision making tasks that compose of this study: the moral wiggle room or the dice rolling game.

In the moral wiggle room game, the experiment is divided into a belief elicitation stage, a decision stage, and a questionnaire. Treatment varies conditions of when subjects' beliefs about what others do are elicited. In the Pre-Belief treatment, subjects first estimate the percentage of subjects who revealed the payoffs in the belief elicitation before entering the decision stage. In the Post-Belief treatment, the ordering of the belief elicitation and decision stages are flipped with subjects beginning with the decision stage first. Lastly, in the Placebo condition, subjects estimate an unrelated statistic about others.

Amendment 8.7.2025: The Placebo condition is being removed. Instead, a full information condition focusing on the conflicting interest game will be included. A Self/Self condition in which a subject chooses whether to reveal the payoff for themselves rather than a second player is also included.

The dice rolling game follows the same procedure as the moral wiggle room game, including the Pre-Belief, Post-Belief, and Placebo conditions. However, a second dimension of variation is included in terms of framing, either framed as asking if subjects believe others misreported their dice rolls or framed as asking if others truthfully reported their dice rolls.

In all treatment conditions, subjects will complete a questionnaire after the belief elicitation and decision stages.

Amendment 8.20.2025: A binary dictator game with the same payoffs as from the full information condition will be included to evaluate the effects of belief elicitation outside of an information avoidant environment.

Computer randomization and balanced assignment for treatment arms. Subjects are assigned randomly to each treatment within each decision making task.

Individual

No

N/A

Moral wiggle room: 460 to 800 Dice rolling game: 600 to 900 Total: 1060 - 1700 Binary Dictator Game: 320 to 720

At least 170 subjects for the two main treatment arms Pre-Belief and Post-Belief conditions in the moral wiggle room game. At least 60 in the Full Information and Self/Self condition.
At least 150 subjects per treatment arm in the dice rolling game with 4 treatment arms.
Higher N depends on budget constraints

At least 320 subjects for the binary dictator game with at least 80 for the 2 by 2: Belief First / Belief After and Option A and Option B framing. Recruitment dependent on stopping rules (depending on if effect size is a null or sufficiently large)

Moral Wiggle Room Game In line with Dana, Weber, and Kuang 2007, with a conservative assumption of a 20 percentage point treatment effect (e.g. 60% versus 40% ignorance), then a power analysis for a two-sided test with an alpha of 0.05 and a power of 0.80 indicates about 97 participants per group. However, based on a previous study's exploratory findings, the difference may be as much as 30 percentage point, allowing for reliable detection with about 50 participants. A total of 3 treatment arms between experiments approximated to a target of about 100 to 125 participants per arm (300 to 375 total), depending on the power. Amendment 8.7.2025: A 15 percentage point treatment effect (e.g. 50% ignorance versus 35% ignorance), then a power analysis for a two-sided test with an alpha of 0.05 and a power of 0.80 indicates about 169 participants per group. Dice Rolling Game The goal is to test whether the distribution of reported outcomes in each group differs from the uniform distribution, and whether treatment affects that distribution. Based on Fischbacher and Föllmi-Heusi 2013 who recruited 265 subjects, a Chi-square test with a medium effect size between of 0.20 requires a minimum sample size of about 198 participants per treatment arm, rounding up to 200 in case of missing data or incomplete subject responses. Amendment 8.20.2025 Based on a .6 prosocial rate from the Full Info condition from the Moral Wiggle Room game, to detect a 10pp gap (0.7 prosocial rate), a total of about 180 subjects per treatment and frame is expected at a power of 0.80.

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