Comparison of risky and intertemporal choice processes: An equivalent conversion paradigm of probability and time

doi:10.3724/SP.J.1041.2026.1213

Abstract

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 the two types of choice. 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 participants’ 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 equivalent 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 dual-outcome options, focusing on compensatory versus noncompensatory and alternative-based versus attribute-basedrules. 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 types of choice. Regarding the first aim, results indicated that RC and IC share equivalent conversion points and comparable local decision processes, which reflect noncompensatoryand attribute-based rules. However, RC and IC differ in holistic process characteristics, as IC is processed in a relatively more deliberate and deeper manner 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 choice are consistent with nondiscounting models. Altogether, these results reveal that participants more likely follow the noncompensatory, attribute-based rules rather than the compensatory, alternative-basedrules when deciding for RC and IC.

To conclude, the present study demonstrates several key findings. (1) The equivalent conversion paradigm confirmed the existence of subjective equivalent options between probability and time. (2) After equivalent 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, alternative-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 holistic 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, equivalent conversion, eye-tracking, hierarchical Bayesian modeling

ZHOU Lei, LI Litong, LIANG Zhuyuan, LI Shu, HUI Qingshan, ZHANG Lei. (2026). Comparison of risky and intertemporal choice processes: An equivalent conversion paradigm of probability and time. Acta Psychologica Sinica, 58(6), 1213-1236.

Figures/Tables 27

References 135

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Model category	Fitted model	Risky choice			Intertemporal choice
Model category	Fitted model	elpd (SE)	elpd-diff(SE)	Predictive accuracy	elpd (SE)	elpd-diff(SE)	Predictive accuracy
Discounting model	Exponential model	-1253.6 (31.2)	-602.3 (59.2)	69.98%	-903.8 (56.2)	-237.5 (37.7)	70.31%
Discounting model	Hyperbolic model	-1439.9 (10.1)	-788.5 (72.6)	72.54%	-824.8 (55.4)	-158.5 (28.5)	71.18%
Nondiscounting model	ITCH heuristic model	-651.4 (68.4)	0 (0)	86.83%	-666.3 (43.1)	0 (0)	81.75%

Model category	Fitted model	Risky choice			Intertemporal choice
Model category	Fitted model	elpd (SE)	elpd-diff(SE)	Predictive accuracy	elpd (SE)	elpd-diff(SE)	Predictive accuracy
Discounting model	Exponential model	-1253.6 (31.2)	-602.3 (59.2)	69.98%	-903.8 (56.2)	-237.5 (37.7)	70.31%
Discounting model	Hyperbolic model	-1439.9 (10.1)	-788.5 (72.6)	72.54%	-824.8 (55.4)	-158.5 (28.5)	71.18%
Nondiscounting model	ITCH heuristic model	-651.4 (68.4)	0 (0)	86.83%	-666.3 (43.1)	0 (0)	81.75%

Dependent variable	Predictor	b	SE	z	p	95% CI
Risky choice: proportion of choosing the LH option	Intercept	0.97	0.22	4.33	< 0.001	[0.53, 1.41]
	Decision time	0.02	0.08	0.31	0.760	[-0.13, 0.18]
	Mean fixation duration per fixation	0.12	0.12	0.96	0.339	[-0.12, 0.35]
	Proportion of long fixations	-0.06	0.11	-0.59	0.556	[-0.28, 0.15]
	SM value	-0.21	0.07	-3.06	0.002	[-0.35, -0.08]
	Fixation coverage	0.12	0.07	1.85	0.064	[-0.01, 0.25]
Intertemporal choice: proportion of choosing the LL option	Intercept	-1.32	0.29	-4.57	< 0.001	[-1.89, -0.76]
	Decision time	0.20	0.08	2.37	0.018	[0.04, 0.37]
	Mean fixation duration per fixation	0.03	0.13	0.25	0.802	[-0.22, 0.28]
	Proportion of long fixations	-0.25	0.13	-2.02	0.044	[-0.50, -0.01]
	SM value	-0.04	0.09	-0.44	0.658	[-0.22, 0.14]
	Fixation coverage	-0.06	0.10	-0.65	0.516	[-0.25, 0.12]

Dependent variable	Predictor	b	SE	z	p	95% CI
Risky choice: proportion of choosing the LH option	Intercept	0.97	0.22	4.33	< 0.001	[0.53, 1.41]
	Decision time	0.02	0.08	0.31	0.760	[-0.13, 0.18]
	Mean fixation duration per fixation	0.12	0.12	0.96	0.339	[-0.12, 0.35]
	Proportion of long fixations	-0.06	0.11	-0.59	0.556	[-0.28, 0.15]
	SM value	-0.21	0.07	-3.06	0.002	[-0.35, -0.08]
	Fixation coverage	0.12	0.07	1.85	0.064	[-0.01, 0.25]
Intertemporal choice: proportion of choosing the LL option	Intercept	-1.32	0.29	-4.57	< 0.001	[-1.89, -0.76]
	Decision time	0.20	0.08	2.37	0.018	[0.04, 0.37]
	Mean fixation duration per fixation	0.03	0.13	0.25	0.802	[-0.22, 0.28]
	Proportion of long fixations	-0.25	0.13	-2.02	0.044	[-0.50, -0.01]
	SM value	-0.04	0.09	-0.44	0.658	[-0.22, 0.14]
	Fixation coverage	-0.06	0.10	-0.65	0.516	[-0.25, 0.12]

Dependent variable	Predictor	b	SE	z	p	95% CI
Risky choice: LH option	Intercept	-1.57	0.61	-2.55	0.011	[-2.77, -0.36]
	Decision time	-0.10	0.15	-0.69	0.492	[-0.40, 0.19]
	Mean fixation duration per fixation	-0.24	0.16	-1.46	0.143	[-0.56, 0.08]
	Proportion of long fixations	0.05	0.15	0.33	0.740	[-0.24, 0.34]
	SM value	-0.18	0.14	-1.27	0.205	[-0.45, 0.10]
	Fixation coverage	-0.28	0.13	-2.16	0.031	[-0.53, -0.03]
Intertemporal choice: LL option	Intercept	0.49	0.43	1.14	0.256	[-0.36, 1.34]
	Decision time	-0.16	0.13	-1.25	0.212	[-0.40, 0.09]
	Mean fixation duration per fixation	-0.25	0.14	-1.81	0.071	[-0.52, 0.02]
	Proportion of long fixations	0.11	0.13	0.89	0.375	[-0.13, 0.36]
	SM value	0.11	0.11	0.99	0.322	[-0.11, 0.33]
	Fixation coverage	-0.04	0.10	-0.43	0.670	[-0.24, 0.15]