Using eye-tracking to examine strategies for evaluating compound lotteries

A compound lottery is a lottery where the outcomes themselves are lotteries, adding multiple stages of risk. Reducing such compound lotteries to simpler ones—the Reduction of Compound Lotteries (ROCL) axiom—is a central tenet of expected utility theory. ROCL axiom posits that a compound lottery can be simplified into an equivalent simple lottery, preserving the same expected utility. This reduction is based on the expected utility theory, where decision-makers rely on the final-stage outcomes and their probabilities akin to a forward induction approach to problem-solving. On the other hand, the Compound Independence (CI) axiom proposes an alternative approach to simplifying compound lotteries, where each stage is evaluated independently. CI axiom, compatible with many decision theories, suggests that people first evaluate the final-stage lotteries separately and use those evaluations to simplify the overall lottery process like backward induction (Segal, 1990). Eye-tracking data can help determine which strategy participants predominantly follow by analysing the sequence and timing of their visual fixations. Participants will complete the main experimental tasks while their eye movements will be recorded with a Tobii Pro Fusion eye-tracker (120 Hz). Participants will evaluate both simple and compound lotteries by entering their certainty equivalents (CEs). Lotteries appear as horizontal decision trees randomized in order and orientation, being displayed in either a standard (straight) or mirrored (flipped) position on the screen.

2025-11-01

2026-12-31

Behavioural outcomes are the following:

- Certainty equivalents (CEs) for compound lotteries, their actuarially equivalent lotteries, and their embedded simple lotteries.
- Accuracy in valuation tasks, defined as the percentage of CEs consistent with stochastic dominance and dominance orderings.
- Response times.

The following eye-tracking measures are analyzed as averages across trials:

- First fixation location and time-to-first-fixation (TTFF).
- Fixation order – the sequence of attention between probabilities and outcomes, allowing comparison of fixation order patterns.
- Temporal attention distribution – each trial is divided into 10 equal intervals, and time spent on each area of interest (AOI) is measured across these intervals.
- Proportion of total trial time spent on different AOIs.
- Fixation duration and pupil size.

Trial-Level Outcome:

- Order of fixations within each trial.

Constructed Outcomes

- The use of Forward induction strategy is identified if fixation sequences prioritise initial first stage probabilities, consistent with ROCL axiom.
- Backward induction strategy is identified when fixation sequences emphasise the final-stage lotteries, consistent with the CI axiom.

This is a within-subjects laboratory experiment with lottery evaluation task incentivised with BMD procedure. Each participant will complete the tasks in a controlled lab setting with eye-tracking throughout.

To test the ROCL and CI axioms, we elicit certainty equivalents of compound lotteries (two-stage lotteries), their corresponding actuarially equivalent lotteries, and the embedded second-stage lotteries in compound lotteries on their own (simple lotteries). We used two sets of compound lotteries, A and B, where A had a greater expected value than B. Each lottery was presented separately, and participants indicated their certainty equivalent by typing the amount in a text box below the lottery description. Trials had no time limit, and a one-second fixation screen appeared between trials to reset attention.

The eye-tracking data allows comparison of forward vs. backward induction strategies within each trial and as averages across trials. The use of forward induction strategy is identified if fixation sequences prioritise initial first stage probabilities, consistent with ROCL axiom. Backward induction strategy is identified when fixation sequences emphasise the final-stage lotteries, consistent with the CI axiom.

Not available

The order and orientation of the lotteries are randomised by a computer.

NA

No

There is no cluster

We have 54 trials for each subject.

A sample size of 70 participants was determined, consistent with typical eye-tracking studies (Zhang et al., 2024; Alós-Ferrer & Ritschel, 2022).