Belief Updating under an Ambiguous and Asymmetric Information Structure: An Experimental Study

To investigate the belief updating rule an individual adopts in the presence of ambiguity in a signal structure, we plan to implement different values of the accuracy of true news and the bias of fake news across rounds, and different ranges of pervasiveness of fake news across treatments in our experiment.

2022-10-28

2023-06-30

A subject's matching probability for a bet on one state (i.e., subjective belief about one state) in each decision task

We will examine how often a subject updates away from a signal, i.e., how often a subject (1) reports a matching probability lower than 50% when (the color assigned to) Option A is the same as the hint (i.e., state = signal), and (2) reports a matching probability higher than 51% when Option A is different from the hint. We will also examine if the reported matching probability is lower when Option A and the hint are the same than when Option A and the hint are different.

Such reverse belief updating behavior can be an indicator of whether a subject has a good understanding of the experimental environment.

Each experimental session include a series of decision tasks. In each task, we use a choice list to elicit a subject's matching probability for a bet on one state. We incentivize subjects using the random incentive system: At the end of the experiment, (only) one line in the choice list among all decision tasks will be randomly selected for payment.

We also include comprehension checks in our experiment to make sure that participants read and understand the instruction. The participants can proceed to the decision tasks only after they pass the comprehension quiz.

In a decision task, a subject needs to choose between a bet on the color of an unknown box (Option A) and a bet with an objective winning probability (Option B) for each line of the choice list. Specifically, in each task, there is a collection of (red and blue) boxes, and one color is assigned to Option A. The computer randomly selects one box (unobserved by subjects) from this collection of boxes. A subject choosing Option A wins a bonus if the selected box has the color assigned to Option A. A subject choosing Option B wins a bonus with a given chance. In a choice list, the winning probability of Option B in each line increases from 0% to 100% in steps of one percent. A subject needs to specify at which line she would like to switch from Option A to Option B in each choice list by reporting her probability assessment of the color of the selected box. In a basic task, a subject does not observe any signal and we elicit his/her unconditional matching probability; in a main task, a subject observes a "hint" before making his/her decision, as explained below.

In each main task, a box contains a number of "hint balls", and a subject observes one ball randomly drawn from the selected box before making a decision. There are two possible compositions of balls in a box. In the first composition, which corresponds to true news, there are more red balls in a red box and more blue balls in a blue box. In the second composition, which corresponds to fake news, the number of red (and blue) balls is fixed and not related to the color of the box. Depending on the treatment, subjects may or may not know how likely is each composition. We adopt the strategic method to elicit a subject's conditional matching probability on both possible signals.

We employ a between-subject design with two treatments: Fully Ambiguous treatment and Partially Ambiguous treatment. In each treatment, a subject faces decision tasks under both the ambiguous scenario (i.e., the pervasiveness of fake news is unknown) and under the non-ambiguous scenario (i.e., the pervasiveness of fake news is known). Within each scenario, we vary the proportion of red balls to blue balls in each composition across decision tasks.

Under the ambiguous scenario in the Fully Ambiguous treatment, a subject has no information about how likely is each composition. Under the ambiguous scenario in the Partial Ambiguous treatment, a subject is informed that the first composition (i.e., true news) is more likely to be the composition of balls in a box. Under the non-ambiguous scenario in the Fully Ambiguous treatment, a subject is informed that both compositions have equal chance. Under the non-ambiguous scenario in the Partial Ambiguous treatment, a subject is informed that there is a 25 out of 100 chance that the second composition (i.e., fake news) is the composition of balls in a box.

Randomization done by computer program.

A subject will be assigned to one treatment (session). In each session, we randomize the order of two scenarios and the order of tasks within each scenario at individual level.

No

200 subjects

200 subjects

100 subjects per treatment