How does uncertainty influence moral behaviors?

We will conduct two experiments, where we manipulate the level of uncertainty associated with potential payoffs and observe participants’ choices in a subsequent moral decision. The first experiment is a replication of Chen and Zhong (2025)'s main experiment, but with a US-based sample recruited via Prolific. In the replication experiment, the moral decision is the same as the decision that determines the uncertain payoff. In the second experiment, we relax the direct connection by separating the moral decision and the decision that determines the uncertain payoff, but still keep both decisions in the same choice environment.

2025-08-10

2025-10-31

The primary outcome variable is a dummy which equals 1 if subject i choose the box with additional money in choice problem c and 0 otherwise.

This can be directly observed from the collected data. When the selected box is the same as the box with additional money in that round, the variable equals 1, otherwise it equals 0.

-Belief about winning the high bonus in the lottery when the person conducted moral or immoral behaviors
-Survey questions about the perception of the connection between moral behaviors and outcome of uncertainty.

We will conduct two experiments, where we manipulate the level of uncertainty associated with potential payoffs and observe participants’ choices in a subsequent moral decision. The first experiment is a replication of Chen and Zhong (2025)'s main experiment, but with a US-based sample recruited via Prolific. In the replication experiment, the moral decision is the same as the decision that determines the uncertain payoff. In the second experiment, we relax the direct connection by separating the moral decision and the decision that determines the uncertain payoff, but still keep both decisions in the same choice environment.

1. Replication Experiment

In this experiment, we replicate the main experiment (“Dice Game Experiment”) of Chen and Zhong (2025) using a US sample. Participants will be recruited from the United States via the online platform Prolific (prolific.com). The sample size will be 120, which is calculated based on our power analysis and consistent with Chen and Zhong (2025) who had 107 subjects in their main experiment.
The experiment closely follows the design of Chen and Zhong (2025), with the primary modification being the conversion of all payments to USD using an appropriate exchange rate. The experiment consists of three parts.

Part 1
In Part 1, subjects participate in 21 rounds, each involving six boxes numbered 1 to 6. Each box may contain two independent bonuses: Bonus 1 and Bonus 2. Bonus 1 is a lottery (h, n/6 ; l) designed to induce uncertainty: n boxes contain a high payoff h, and 6 − n boxes contain a low payoff l. Subjects are informed of the composition (how many boxes contain h and how many contain l), but not the specific allocation of payoffs to boxes. Uncertainty is present when n != 0, 6. Bonus 2 is an additional bonus of $1 placed in one randomly selected box, providing an incentive to lie.

At the start of each round, subjects are asked to choose a box and record their choice on paper (with the understanding that this record will not be collected). After making their choice, they are informed which box contains Bonus 2. Subjects are then asked to report their initial box selection to receive the corresponding payoffs (Bonus 1 and, if applicable, Bonus 2) in that box. Reporting the box containing Bonus 2 may reflect either honesty (if their initial choice coincidentally matches the Bonus 2 box, with probability 16 ) or dishonesty (if they change their report to maximize payoffs). While individual lying cannot be detected, aggregate dishonesty can be inferred by comparing the observed proportion of Bonus 2 claims to the expected 1/6 rate.

The 21 rounds vary the uncertainty associated with Bonus 1. There are three payoff structures for Bonus 1: (10, n/6 ; 0), (7.5, n/6 ; 2.5), and (5.5, n/6 ; 4.5), and seven levels of winning probability, p ∈ {0, 1/6, 2/6, 3/6, 4/6, 5/6,1}. All payoffs are denominated in USD.
The allocation of Bonus 1 and the placement of Bonus 2 are determined randomly and independently. The box containing Bonus 2 in each round is predetermined using Excel’s RANDBETWEEN(1,6) function. The distribution of Bonus 1 among the boxes is determined after all decisions are made using random number generator: one round is randomly selected for payment, and the experimenter uses random numbers from 1 to 6 to assign high and low payoffs to boxes according to the relevant probability, in full view of the subjects. All procedures and randomization methods are explained to subjects before the experiment begins.

Part 2
In Part 2 of the experiment, we elicit subjects’ belief about winning the high bonus in the lottery under different occasions. We ask the subjects to consider the decision scenario, where participants in group 1 lied in the experiment to receive Bonus 2 and participants in group 2 did not lie, reporting the previously recorded box truthfully and did not receive Bonus 2. We then ask the subjects which group if participants they believe is more likely to win the high bonus 1 in the lottery. If people behave more morally under uncertainty because they perceive a connection between their moral behaviors and the outcome of uncertainty, we should expect people to believe that the more honest group is more likely to win the high bonus. This question is not incentivized to avoid unnecessary complication. And since the question is about other subjects instead of the subjects themselves, we tend to believe that the subjects will answer truthfully even without incentives.

Part 3
In Part 3, we conduct a survey to assess participants’ perceptions regarding the connection between moral behavior and uncertain outcomes. We intentionally avoid using specific terms such as “karma” or “immanent justice reasoning” in the survey. First, we describe the belief in a link between uncertainty and morality and provide an explicit example: Anna receives extra change at the supermarket. Although she is certain no one will discover the error, she decides to return the money after recalling that she is awaiting the result of her dream school application.

We then ask participants whether they know anyone who holds such a belief (“Do you know anyone in your life who holds this kind of belief?”) and what proportion of people they think share this belief (“What proportion of people do you think hold this kind of belief?”). We also ask if they personally hold this belief (“Do you hold this kind of belief yourself?”), the extent to which this belief influences their daily actions (“To what extent does this kind of belief influence your actions and choices in daily life?”), and how true they believe this notion to be (“To what extent do you think this kind of belief is true? That is, how likely is it that the world actually works according to this kind of belief?”). Additionally, we ask about their belief in a just world (“To what extent do you believe that the world is a just place, i.e., people get what they deserve?”) and their general risk attitude (“How willing or unwilling are you to take risks in general?”).

2. Bracketing Experiment

The sample of the Bracketing Experiment depends on whether we can replicate Chen and Zhong (2025)'s result with the US prolific sample. If we can successfully replicate, we will run the Bracketing Experiment with the US sample on Prolific. If we can not replicate Chen and Zhong (2025)'s result, we will conduct the Bracketing Experiment with Chinese university students through the Weikeyan platform, a social science experimental platform in Wuhan University, China. This sample is chosen to ensure comparability with Chen and Zhong (2025), who used the same platform and subject pool in their study. Our previous experiments using this sample successfully replicated their findings in the main experiment and found null results in the separation experiment. Based on power analysis and to maintain consistency with the original study (which included 107 subjects in the main treatment), we plan to recruit 120 participants for the experiment.

This experimental design eliminates potential confounders stemming from regret aversion and the “law of small numbers” bias, while removing the direct link between moral decisions and uncertain outcomes. At the same time, it ensures that uncertainty and the moral decision remain bracketed together, so that participants continue to perceive uncertainty when making their moral choice.

Part 1
The general experimental design closely mirrors that of the replication experiment: we manipulate the level of payoff uncertainty and examine participants’ moral decisions under varying degrees of uncertainty. As in the original experiment, subjects face 21 rounds, each involving six boxes with Bonus 1 and Bonus 2, and the structure of payoffs and uncertainty for Bonus 1 is identical to the replication experiment.
The key difference in this design is that subjects now make two independent choices: one for Bonus 1 and another for Bonus 2. Specifically, in each round, participants first select a box to receive Bonus 1; this choice is final and cannot be changed. Next, they are asked to (privately) select a box for Bonus 2 and record this choice on paper (with the understanding that this record will not be collected or checked). After both choices are made, participants are informed which box actually contains Bonus 2. They are then asked to report which box they initially selected for Bonus 2, and their payment for Bonus 2 depends on this report.

This design allows participants to receive Bonus 1 and Bonus 2 from different boxes, thereby eliminating the direct link between the moral decision (reporting the box for Bonus 2) and the resolution of uncertainty (the outcome of Bonus 1). This also get rid of the potential concerns from the “law of small numbers”, where people avoid lying because they mistakenly believe that the box selected for Bonus 2 is less likely to contain Bonus 1 as well. Meanwhile, the two choices are still bracketed together in the same set of boxes, making sure that participants still perceive corresponding uncertainty when they make moral decisions. Since they do not need to change their choice of box for Bonus 1 even if they decide to lie, regret aversion will not play a role. At the end of the experiment, one round will be randomly selected to be payoff-relevant, and the subject will get Bonus 1 in the first chosen box and Bonus 2 in the second chosen box.

As in the replication experiment, the allocation of Bonus 1 and the placement of Bonus 2 are determined randomly and independently, and this is known to all subjects before the start of the experiment.

Part 2 & 3

Part 2 and 3 are exactly the same as in the replication experiment. We elicit subjects’ belief about winning the high bonus in the lottery under different occasions, and we ask the same survey questions about the subjects’ opinions on the perceived connection between moral behaviors and uncertainty.

The lottery randomization within each subject was coded in Qualtrics. The box containing Bonus 2 in each round is predetermined using Excel’s RANDBETWEEN(1,6) function. The distribution of Bonus 1 among the boxes is determined after all decisions are made using a random number generator: one round is randomly selected for payment, and the experimenter uses random numbers from 1 to 6 to assign high and low payoffs to boxes according to the relevant probability.

In the replication experiment, these random numbers will be generated by the random number generator in Qualtrics (online). In the Bracketing Experiment, the round selected for payment will always be determined by Qualtrics. The box or boxes containing uncertain payments will be determined by Qualtrics if the experiment is conducted on Prolific, and by the experimenter throwing five dice if the experiment is conducted on the Weikeyan platform.

Round level. Each subject goes through 21 rounds. The payoff uncertainty differs across the rounds. One round is randomly selected to be payoff-relevant.

Yes

240 subjects in total (120 subjects per experiment, 21 rounds for each individual, cluster at individual level).

5040 observations in total (21 rounds per subject, 120*21 = 2520 observations per experiment).

120 subjects per experiment, 240 subjects in total.

The minimum detectable effect size is 0.12, which means that when there is no uncertainty in their payment, participants report the box containing additional money (+4) 12 percentage points more often. Given a baseline reporting rate of 59.1% for +4 in uncertain environments (Chen and Zhong (2025)), this corresponds to a 20.3% relative increase in the proportion of reporting +4.