Comparison of processes of risky choice and intertemporal choice: Based on equivalence conversion paradigm

Abstract: Risky choice (RC) and intertemporal choice (IC) are two fundamental types of decision-making that are vital to human’s everyday life. The former involves selecting among outcomes with varying probabilities, while the latter requires making decisions across different time points. They share similarities regarding theoretical development, behavioral effects, and neural basis. One critical challenge is that, 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 can contribute to the development of a generalized decision-making framework and clarify the boundaries of its applicability. However, existing studies lack direct comparisons and converging process evidence between these two decision types. Since decision preferences and processes are influenced by probability and time parameters, 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, which may introduce biases in experimental results due to parameter effects and individual variability.
To address these limitations, the present study first developed a novel paradigm which subjectively equivalent probability to delay and generate a unique set of parameters for each participant. Then by incorporating eye-tracking technology, we 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, Mage = 27.14), pairs of approximately equivalent RC and IC options were first generated for each participant. Following the Adaptive Design Optimization (ADO) method, participants made choices between an RC and IC option, which have the similar payoffs. IC was fixed, while the probability of RC was adjusted according to their response until reaching an indifference point. Second, we used these equivalent options to construct single-outcome options RC and IC tasks and examined their underlying process of by eye-tracking technology respectively. In study 2 (N = 37, Mage = 26.31), the equivalence conversion paradigm was utilized in the opposite way. That is, the RC option was fixed, and delay of IC was adjusted. Then we extended our research by constructing double-outcome op. We focused on compensatory/non-compensatory and alternative based/attribute based rule. By integrating eye-tracking and hierarchical Bayesian modeling, we analyzed both local and holistic decision processes, focusing on the differences between compensatory versus non-compensatory and alternative-based versus attribute-based decision rules.
Our entire set of analyses aimed to (1) determine whether the decision processes of RC and IC are similar and (2) identify the best computational model that is more suitable for both decisions. For the first aim, results indicated that RC and IC indeed share equivalence conversion points and comparable local decision processes, which reflected non-compensatory and attribute based rule. However, RC and IC differ in holistic process characteristic, as IC is processed in 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. For the second aim, computational modeling of process characteristics suggests that both types of decisions are consistent with non-discounting models. Altogether, these results reveal that participants are more likely to follow the non-compensatory, attribute-based rule rather than the alternative-based/attribute-based rule when deciding for both RC and IC.
To conclude, the present study shows that: (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 types of decisions, contrary to classic discounting models, individuals seem not to follow compensatory, attribute-based rules, which undergoes a “weighting and summing” or “delay discounting” process. Instead, they are more likely to use simple heuristic rules hypothesized by non-discounting 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, our 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.