Abstract: Risky choice (RC) and intertemporal choice (IC) are two fundamental decision-making categories essential to people's daily life. The former involves selecting among outcomes with varying probabilities, whereas the latter requires making decisions across different time points. These domains share similarities regarding theoretical developments, behavioral effects, and neural bases. A critical challenge persists because, although previous studies have revealed that RC and IC involve similar cognitive processes, findings remain inconsistent regarding their precise underlying mechanisms. Examining the similarities and differences between RC and IC from a decision process perspective contributes to the development of a generalized decision-making framework and clarifies the boundaries of its applicability. However, existing studies lack direct comparisons and converging process evidence between these two decision types. Given that probability and time parameters influence decision preferences and processes, ensuring their comparability is essential when comparing RC and IC. Previous research has often used fixed parameters, neglecting the conversion between probability and time, as well as individual differences; such an approach potentially introduces biases in experimental results due to parameter effects and individual variability.
To address these limitations, the present study initially developed a novel paradigm that subjectively equates probability to time and generates a unique set of parameters for each participant. Then, by incorporating eye-tracking technology, the research systematically investigated the cognitive mechanisms underlying RC and IC during single-outcome (Study 1) and dual-outcome (Study 2) tasks. Each study consisted of two phases. In Study 1 (N = 41, M_age = 27.14), each participant first generated pairs of approximately equivalent RC and IC options. Following the adaptive design optimization method, participants made choices between an RC and IC option possessing similar payoffs. The IC option was fixed, whereas the probability of the RC option was adjusted according to user responses until reaching an indifference point. Second, the study used these equivalent options to construct single-outcome RC and IC tasks and examined their underlying processes via eye-tracking technology. In Study 2 (N = 37, M_age = 26.31), the equivalence conversion paradigm operated in the opposite manner. That is, the RC option remained fixed, whereas the time parameter of the IC option was adjusted. The research then extended these findings by constructing double-outcome options, focusing on compensatory versus noncompensatory and alternative-based versus attribute-based rules. By integrating eye-tracking and hierarchical Bayesian modeling, the analysis examined local and holistic decision processes.
The entire set of analyses aimed to (1) determine whether the decision processes of RC and IC are similar and (2) identify the computational model most suitable for both decisions. Regarding the first aim, results indicated that RC and IC share equivalence conversion points and comparable local decision processes, which reflect noncompensatory and attribute-based rules. However, RC and IC differ in holistic process characteristics, as IC undergoes a relatively more deliberate and deeper fashion than RC. Furthermore, as task complexity increased from single-outcome to dual-outcome scenarios, the process similarity between RC and IC increased, suggesting the adoption of more parallelized and simplified decision strategies. Regarding the second aim, computational modeling of process characteristics suggests that both types of decisions are consistent with nondiscounting models. Altogether, these results reveal that participants more likely follow the noncompensatory, attribute-based rule rather than the alternative-/attribute-based rule when deciding for RC and IC.
To conclude, the present study demonstrates several key findings. (1) The equivalence conversion paradigm confirmed the existence of subjective equivalence points between probability and time. (2) After equivalence conversion, despite process-level differences, RC and IC exhibited consistency in core cognitive mechanisms. In both decision types, and contrary to classic discounting models, individuals seem not to follow compensatory, attribute-based rules, which undergo a “weighting and summing” or “time discounting” process. Instead, they more likely use simple heuristic rules hypothesized by nondiscounting models. (3) RC and IC demonstrated distinct behavioral preferences, process characteristics, and underlying mechanisms, such as differences in processing complexity and overall eye-movement dynamics. Overall, the research provides new perspectives on theoretical and methodological comparisons across different decision-making tasks and offers empirical support for the development of a more unified decision-making theory.

Key words: risky choice, intertemporal choice, eye-tracking, hierarchical Bayesian modeling