Belief Updating, Cognitive Noise and Order Effects

Last registered on January 28, 2026
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Pre-Trial

Trial Information

General Information

Title
Belief Updating, Cognitive Noise and Order Effects
RCT ID
AEARCTR-0017473
Initial registration date
January 22, 2026

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
January 28, 2026, 7:06 AM EST

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

Locations

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Primary Investigator

Name
Filippo Chilò
Affiliation
Università degli Studi di Milano-Bicocca
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Other Primary Investigator(s)

PI Name
Arianna Galliera
PI Affiliation
Università Cattolica del Sacro Cuore
PI Name
Fabrizio Panebianco
PI Affiliation
Università Cattolica del Sacro Cuore

Additional Trial Information

Status
In development
Start date
2026-01-23
End date
2027-01-23
Keywords
Behavior
Additional Keywords
Belief Updating, Bayesian Updating, Cognitive Noise, Cognitive Uncertainty, Order Effects
JEL code(s)
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
Abstract
We study how cognitive noise shapes belief updating from sequences of signals and generates order effects.
We extend a Bayesian model of cognitive noise to a sequential environment in which agents noisily integrate new evidence relative to their previous belief rather than pooling all signals together, producing primacy or recency depending on the relative effective weights on past beliefs and new information. The magnitude of such order effects is instead dependent on the cognitive noise experienced when decoding the signals, which is the main hypothesis we plan to test via an online balls-and-urns experiment with repeated belief elicitation under a binarized scoring rule, complemented by a within-task measure of cognitive uncertainty. We plan to explore whether the latter, together with additional measures of cognitive/numerical abilty, can explain the magnitude of order effects at the individual level.

Two additional treatments (Treatment 1 and 2) aimed at independently manipulate the salience of prior beliefs (to shift reliance on past beliefs) and signal diagnosticity (to shift the weight on new information) will be pre-registered separately. The aim of such treatments is to assess the model's ability to predict the direction of order effects.
External Link(s)

Registration Citation

Citation
Chilò, Filippo, Arianna Galliera and Fabrizio Panebianco. 2026. "Belief Updating, Cognitive Noise and Order Effects." AEA RCT Registry. January 28. https://doi.org/10.1257/rct.17473-1.0
Sponsors & Partners
Experimental Details

Interventions

Intervention(s)
Intervention Start Date
2026-01-23
Intervention End Date
2027-01-23

Primary Outcomes

Primary Outcomes (end points)
Stated Beliefs (b), Cognitive Uncertainty (p^CU)
Primary Outcomes (explanation)
- Stated Beliefs: these are the beliefs stated during the decision-making task, one per round: b_(1,i), ..., b_(7,i). Beliefs are in log-odds form, and refer to the two possible urns (Blue urn, Red urn).

- Cognitive Uncertainty: this is a measure of cognitive noise experienced during the task (see Enke & Graeber, 2023). One data point per round, but the measure is considered as their average. The variable ranges from 0 (complete cognitive uncertainty) to 1 (the participant is completely sure that their beliefs is correct).

Secondary Outcomes

Secondary Outcomes (end points)
Order Effects (γ), Coefficient of cognitive precision (λ), Weight on Past Belief (a), Weight on New Evidence (c)
Secondary Outcomes (explanation)
These varaibles are estimated (that is, not directly measured) starting from the Primary Valuables (beliefs, cognitive uncertainty), but are are expected to change under the non-baseline treatment (according to the model's predictions):

- Order Effects: an unbounded measure of the relationship between weights over time (recency, primacy). One per individual: γ_i (affected by all treatments);

- Coefficient of cognitive precision (λ): bounded in [0,1], describing how much the updating process of the participant reflects Bayesianism. One per individual: λ_i;

- Weight on Past Belief: bounded in [0,1], it's the weight attributed to the previous belief during belief updating. One value per individual: a_i (affected by Treatment 1);

- Weight on New Evidence: bounded in [0,1], it's the weight attributed to new information during belief updating. One value per individual: c_i (affected by Treatment 2).

Experimental Design

Experimental Design
The study is conducted online with participants recruited via Bilendi and completing the task individually on a computer. Each participant plays seven rounds of a balls-and-urns task with two possible states: a Blue urn containing 5 blue and 4 red balls and a Red urn containing 4 blue and 5 red balls, with the true urn chosen with 50/50 probability (but not shown to the participant). In each round, participants observe a simultaneous draw of four balls from the unknown urn and then make three decisions: (1) they guess which urn the draw came from (Blue vs. Red); (2) they report the probability (from 50% to 100% on a 50-step slider) that their guess is correct, and this report is incentivised using a Binarized Scoring Rule that converts the stated probability and correctness of the guess into a lottery win probability for a fixed reward; and (3) they report their cognitive uncertainty by stating how likely it is that the computer’s Bayesian probability lies within ±5 percentage points of their own reported probability, using a 0–100% slider (not incentivised). Tokens are used as the unit of account and later converted to payments.
Experimental Design Details
Not available
Randomization Method
Participants are assigned to treatment depending on the enrollement wave (one for baseline treatment, one for treatment 1 and one for treatment 2). Participants are recruited from the Bilendi platform via randomised invites. The first wave of participants will be attributed to the baseline treatment (125 participants), the one described in this pre-registration.

Treatment 1 and 2 will both feature 125 participants. In total, the whole experiment will recruit around 375 participants.
Randomization Unit
There's no further randomisation unit than that of the treatments.
Was the treatment clustered?
No

Experiment Characteristics

Sample size: planned number of clusters
No clusters.
Sample size: planned number of observations
375 valid observations (125 baseline treatment; 125 treatment 1 and 125 treatment 2)
Sample size (or number of clusters) by treatment arms
125 per treatment arm (125 baseline, 125 Treatment 2, 125 Treatment 3)
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
The following power calculation refers to a 0.05 significance level and 0.8 power. Our hypotheses for treatment effects allow us to work with one-sided tests. The sample size used is N = 125; this refers then to pair-wise comparison between treatments). For unbounded variables (order effects γ, past belief weighting a, new evidence weight c), the minimum detectable effect size is: - 0.031 if SE = 0.1; - 0.063 if SE = 0.2; - 0.094 if SE = 0.3; - 0.126 if SE = 0.4; We keep SE under 0.4 according to the survey in Benjamin (2019): both a and c are generally estimated to fall into a realtively small range (c in [0.25, 1.23] and a in [0.51, 1.88]) with particularly small SE (in the [0.013, 0.133] range). For proportions (e.g., the percentage of the treatment population that shows recency/primacy effects), the minimum detectable effect size falls within the [0.063-0.158] range, depending on the starting point of the proportion within the [0,1] support.
Supporting Documents and Materials

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IRB

Institutional Review Boards (IRBs)

IRB Name
German Association for Experimental Economic Research (GfeW)
IRB Approval Date
2025-06-12
IRB Approval Number
h2YY8F7j
Analysis Plan