Does Increasing Numeracy Reduce Probability Weighting?

The treatment group will undergoe a numeracy intervention involving arithmetic exercises (addition, subtraction, multiplication, and division) using a number line. Specifically, they will be asked to compute arithmetic questions involving listed operations and place the correct answer on a number line. The difficulty of the arithmetic questions adapts dynamically based on performance: correct answers increase the difficulty, while incorrect answers reduce it. Participants should answer at least 25 questions (and at most 125) to complete the training. This adaptive approach prevents highly skilled participants from becoming disengaged and ensures that lower-skilled participants do not become discouraged. Responses are submitted by marking the result on a number line, which enhances numerical reasoning by reinforcing relative magnitude comparisons.

The control group will receive an active placebo intervention consisting of 30 trivia questions (sport, history, geography, etc.) which should not affect the numeric abilities of the participants. This active control intervention will help us keep the effort level and time spent constant across two groups.

2025-11-11

2025-11-14

We are interested in the probability weight parameters and numeracy scores of participants. Specifically, we are studying whether these two variables change or not after the intervention.

Probability weights are estimated within the framework of Cumulative Prospect Theory. We first elicit participants’ certainty equivalents and then use these values to estimate individual probability-weighting parameters via nonlinear regression (Kahneman and Tversky, 1992). Numeracy is measured using the 8-item Objective Numeracy Scale developed by Weller et al. (2013), which yields scores ranging from 0 to 8 based on the number of correctly answered items.

This experimental design is implemented through Prolific. We recruit participants with approval ratings of at least 95% and aim for a sample balanced by gender. We will also use Prolific’s demographic information to control for income, educational background, socioeconomic status, neurodiversity, and dyslexia/dyscalculia status.

The experiment consists of a single session with five stages and is expected to last approximately one hour. Participants receive a $10 show-up fee plus any earnings from their decisions; all five stages are eligible for bonus payments.

In Stages 1 and 4, participants’ numeracy levels are assessed before and after the intervention using the 8-item Objective Numeracy Scale (ONS) developed by Weller et al. (2013). If one of these stages is selected for bonus payment, a single question from the set of eight will be randomly drawn, and participants will earn a $3 bonus if their answer is correct.

In Stages 2 and 5, we elicit certainty equivalents using Multiple Price Lists (MPLs) administered before and after the intervention. Each lottery is paired with a descending list of certain outcomes via a computerized interface. Certainty equivalents are necessary for estimating value and probability-weighting functions, following Tversky and Kahneman (1992) and Prelec (1998). Bonus payments for these stages are determined based on a randomly selected lottery question from a randomly selected MPL. This procedure ensures accurate elicitation of certainty equivalents and robust estimation of probability-weighting parameters.

Stage 3 constitutes the intervention. Participants are randomly assigned to either the treatment or control group. The treatment group completes a numeracy training intervention involving arithmetic exercises—addition, subtraction, multiplication, and division—answered by placing solutions on a number line. The control group receives an active placebo consisting of trivia questions unrelated to numerical ability.

In Stages 1 and 4, numbers are randomly drawn from predefined sets chosen to resemble those used in the main study (Weller et al., 2013) while still introducing random variation.

In Stages 2 and 5, participants complete eight distinct multiple price lists (MPLs), each containing 15 rows. The MPLs are presented twice and in randomized order, yielding a total of 16 MPLs per stage.

In Stage 3, the difficulty of the arithmetic questions adapts dynamically to participants’ performance: correct answers increase the difficulty, while incorrect answers decrease it. This adaptive design prevents highly skilled participants from disengaging and ensures that lower-skilled participants are not discouraged. Responses are submitted by marking the result on a number line, which reinforces numerical reasoning through relative magnitude comparison. The control group receives an active placebo intervention consisting of trivia questions (e.g., on social media trends) that are not expected to influence numerical ability. This active control helps keep effort levels comparable across groups.

Randomization is implemented through Prolific by recruiting treatment and control samples separately but randomly. Prolific assigns eligible participants to the study based on predefined screening criteria, without disclosing any identifying information to researchers. Individuals allocated to the treatment group are automatically excluded from the pool eligible for control-group recruitment, ensuring that no participant appears in both conditions.

Individual: Participants are randomly assigned to control and treatment groups.

No

The study is clustered at the subject level and there will be 200 subjects in total.

Each person will have 2 (pre and post treatment) numeracy scores, 32 certainty equivalent value and a manipulation score. These are the variables we elicit through the experiment. So in total (per participant) we elicit 35 observations. Also, through prolific we collect demographic data for each participant. However, these are provided by Prolific, not elicited through the experiment.

100 assigned to the treatment group and 100 to the control group.

Main outcomes