Balancing Risk and Reward: Cognitive Processes in Decision-Making Explored Through the Modular Serial-Parallel Network

doi:10.21203/rs.3.rs-4999384/v1

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Balancing Risk and Reward: Cognitive Processes in Decision-Making Explored Through the Modular Serial-Parallel Network

https://doi.org/10.21203/rs.3.rs-4999384/v1

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The Modular Serial-Parallel Network (MSPN) framework provides a robust approach to understanding the cognitive mechanisms underlying decision-making, particularly in risk-reward scenarios exemplified by the classical gamble task. By facilitating the diagnosis of processing order (serial or parallel), stopping rules (exhaustive or self-terminating), and the interdependency of mental processes, the MSPN model bridges the gap between two prominent theoretical approaches: utility-based models and heuristic-based models. Our study utilized the MSPN to explore how participants navigate decisions involving risk, revealing diverse strategies—some participants relied on serial processing, others on parallel processing, and many exhibited a dynamic mix of both depending on the trial. Notably, individual subject analysis highlighted significant variability, with some participants showing consistent preferences for one processing style, while others flexibly switched between strategies. These findings challenge the dominance of pure utility-based models and underscore the importance of considering heuristics and individual differences in decision-making. Furthermore, the MSPN’s capability to validate or falsify cognitive assumptions enhances our understanding of the risk-reward calculus in human judgment. This dual role positions the MSPN as a pivotal tool in advancing both theoretical insights and practical applications in cognitive research.

Biological sciences/Psychology/Human behaviour

Health sciences/Risk factors

Risk-reward decision-making

Modular Serial-Parallel Network

cognitive processes

utility-based models

heuristic-based models

gamble task

In everyday life, individuals frequently face preferential choices that involve weighing risks and rewards between various options or courses of action. Whether deciding between faster but more expensive air travel versus slower, more economical driving, or choosing between a risky medical procedure and managing a chronic condition, these decisions are ubiquitous and carry significant consequences. Understanding the cognitive processes that underpin these risk-reward evaluations has been a central focus of research. A common experimental method for studying preferential choice is the lottery gamble task, where participants must choose between options defined by potential outcomes and their associated probabilities. Each gamble represents a decision-making scenario where an individual can gain or lose a certain amount of money (V) with a known probability (p), for example, gamble₁ = <V₁, p₁> and gamble₂ = <V₂, p₂>. These tasks are designed to mirror real-life decisions that balance potential rewards against associated risks. Two dominant theoretical approaches have emerged to explain decision-making in these contexts. The first, grounded in rational choice theory, centers on the concept of utility. This approach posits that individuals assign psychological value to observed properties, integrating these into a single metric—utility—that guides decision-making. According to this model, a decision-maker compares the utility values of different options, such as evaluating whether the potential benefits of a medical procedure outweigh the risks, and selects the option with the higher utility^1,2.

Utility-based models have profoundly influenced decision-making research, forming the foundation of many subsequent computational models. These models share key premises:

Psychological utility is an integral concept, where properties are multiplicatively combined into a single dimension, rendering the original attributes inseparable once the utility is calculated.
The scope of information search is unrestricted, allowing all relevant properties to be integrated into a single utility value.
These models typically do not specify the order in which properties are processed, leaving it unclear whether attributes are combined sequentially or in parallel when determining utility.

In contrast, the second major theoretical approach is rooted in the concept of heuristics—mental shortcuts or simple decision-making strategies. Far from being mere practical tools, heuristics address the limitations of human cognition, which often deviate from the principles of rationality^2,3. Heuristics, such as the Take-The-Best (TTB) heuristic⁴, involve sequentially comparing attributes based on their importance, stopping as soon as a decisive difference is found. For instance, when deciding on surgery, a patient might first compare the potential outcomes and, if a clear difference emerges, make a decision without considering other factors.

Heuristic-based models adopt the following core premises:

The properties of gambles, such as p and V, are independent, meaning they can be separated and individually assessed during decision-making.
The scope of information search is often limited, with not all properties being considered.
Attribute comparisons typically occur in a strict serial order.

These contrasting approaches—utility-based and heuristic-based—have shaped our understanding of decision-making processes, each offering unique insights into how individuals navigate complex choices involving risk and reward. This research aims to further explore and clarify these cognitive processes, providing a deeper understanding of how people make decisions in real-world scenarios.

Model validation and falsifiability and its challenges

Both classes of models, heuristic- and utility-based, are grounded on strong and falsifiable premises, which means that their predictions are constrained by critical assumptions, ensuring model validity and identifiability. Consequently, falsification of any of these premises would directly falsify one class of models and could be utilized to validate the other class. For instance, if it can be demonstrated that cognitive processes only consider one attribute in a decision-making task while disregarding other attributes, it would directly falsify the utility-based models in relation to premises 1 and 2. In contrast, the theoretical stance regarding premise 3 differs asymmetrically between proponents of the utility-based and heuristic-based approaches. While this premise is seldom explicitly stated in the theoretical framework, the proponents of fast and frugal heuristics (such as TTB⁴) offer a notable exception by clearly defining the serial property (referred to as lexicographic property) in attribute inspection⁴. Falsifying the third premise, by revealing a sequential processing order of attributes, may not provide strong evidence for falsifying utility-based models, but it can serve as robust evidence supporting heuristic-based approaches.

Three Key Challenges

Despite decades of research, the field of decision-making continues to grapple with significant challenges, particularly in achieving clear model identifiability. These challenges stem from several factors:

First, much of the historical research on preferential choices has focused primarily on predicting outcomes rather than dissecting the cognitive processes underlying these decisions. This "outcome-based" approach has prioritized forecasting behavior over understanding the mental mechanisms at play. By emphasizing the relationship between input variables and output decisions, these models often treat the cognitive system as a "black box," neglecting the intricacies of the mental processes that drive decisions. This has led to the development of what Gigerenzer terms "As-If" models—models that predict decision outcomes without fully exploring the cognitive systems responsible for generating them, thereby limiting their falsifiability and explanatory power⁵. However, the past two decades have seen considerable progress in investigating the mental processes involved in decision-making. This progress includes the development of sophisticated methodologies such as hierarchical Bayesian modeling and individual subject analysis. These advancements go beyond mere outcome prediction, enabling more precise predictions of joint response times and choice preferences. Additionally, process tracing methods have become increasingly refined, offering deeper insights into the covert cognitive processes that underlie decision-making^6,7,8.

Second, the challenge of model mimicking presents a significant obstacle to distinguishing between competing decision-making models. Model mimicking occurs when different models predict identical outcomes, whether at the choice level or across both choice and response time distributions. This complicates the task of differentiating between models, even when additional variables like response times are considered. For example, Fifić, Houpt, and Rieskamp demonstrated that two distinct models could yield identical response time distributions, underscoring the difficulty of distinguishing between them⁹.

Third, there is a notable lack of a unified theoretical framework that integrates the diverse processes underlying these models. Both utility-based and heuristic-based approaches are often used interchangeably, as highlighted by Lee and Gluck and Diederich^10,11. This aligns with the concept of hierarchical representations, a dominant paradigm in perception and neural organization^12,13,14. Within this framework, decision-making attributes can be hierarchically structured, allowing decision-makers to access both individual properties and their combinations, such as utility and separate attributes. This hierarchical flexibility enables decision-makers to apply heuristic approaches when appropriate, while also leveraging utility-based representations for more comprehensive analyses when needed.

The solution to the challenges: Modular Serial-Parallel Networks (MSPN) as a Full Computational Processing Model for Cognitive and Perceptual Operations

In summary, the MSPN model is a powerful tool that addresses the key challenges in decision-making research. It moves beyond outcome-based models by offering a detailed analysis of cognitive processes, mitigates model mimicking by integrating multiple cognitive approaches, and provides a unified theoretical framework that can incorporate both heuristic and utility-based strategies. Through its modular and hierarchical organization, MSPN enhances our understanding of the cognitive mechanisms underlying decision-making and offers a versatile platform for exploring and validating different cognitive theories.

The Modular Serial-Parallel Network (MSPN) computational model serves as a comprehensive stochastic framework that can accurately account for both response accuracy (choice preferences) and response times in binary task conditions. The model is built around four core components: (a) representational, (b) decisional, (c) logical-rule implementation, and (d) modular stochastic accrual of information. The formal mathematical representation is provided in Supplementary Appendix A. Detailed parametric properties of the MSPN’s computational framework are provided in Supplementary Appendix B. The structure and flow of the MSPN model are visually presented in Figure 1.

(a) Representational Level: Memory plays a pivotal role in cognitive and perceptual processes at this level, where the properties of various decision-making scenarios are stored and organized. These properties include the basic features and attributes of the stimuli, represented as point values (M) on independent stimulus dimensions, with associated internal noise N(M, σ) (see Figure 1, Left). Understanding this foundational representation is crucial, as it influences higher-order cognitive operations. Each attribute is encoded as an independent feature, allowing the cognitive system to process and manipulate them individually. The presence of perceptual noise in these representations highlights the complexities of memory encoding, reflecting the inherent variability in our perceptual experiences. Similar to how neurons in the brain are tuned to specific features, this perceptual noise stems from the dynamic and context-dependent nature of cognitive processes^12,13.

(b) Decisional Level: At this stage, the cognitive system establishes stimulus-response associations and determines how to classify property representations based on task requirements. In the MSPN model, a decision rule is represented by a single criterion value that divides a property dimension into two response regions, each corresponding to a different binary decision outcome. For example, in the stimulus scenario illustrated in Figure 1, if a property activation is observed to the right of the decision value on the V1 dimension (dotted line), it generates evidence favoring Gamble A (Decision A); otherwise, it supports Gamble B (Decision B). When a property is activated in memory, it automatically produces evidence that is labeled according to the decision rule, supporting one of the two binary outcomes.

(c) Logical Rule Implementation:In this stage, the system determines how to combine multiple sources of independently stored properties activated by the task^15,16. The decision-making process involves logically integrating these activated properties, considering the scope of evidence from various attributes. This integration allows the system to make well-informed decisions. If all attributes need to be analyzed, the cognitive system employs a conjunctive rule (AND gate), requiring exhaustive evidence collection. If only one attribute is necessary, a disjunctive rule (OR gate) is used, allowing the decision to be made based on a single attribute, regardless of others.

(d) Modular Stochastic Accrual of Information:The MSPN model integrates two successful approaches to modeling response time (RT) data and choice outcomes: the random-walk and mental-architecture approaches^16,17. The random walk is a stochastic process that accumulates noisy evidence over discrete time steps, with the observer setting criteria that determine the amount of evidence needed to choose either Gamble A or Gamble B. The sampling process continues until one of the criteria is reached, with the number of steps determining the decision time, as shown on Fig.1, the boxes at the top right.

Figure 1. A schematic illustration of the stimulus structure in a binary gamble task and the MSPN model. The stimuli consist of two dimensions: X (v1, the maximum gain value in Euros) and p1 (the probability of maximum gain). These dimensions are orthogonally combined to produce 16 different gamble sets. In this task, Gamble A = <vA1, pA1; 0, 1-pA1> and Gamble B = <200€, 1>. To make a preferential choice for Gamble A, participants must consider both v1 and p1, representing a classification problem where membership in category A follows a conjunctive rule (both v1 and p1 must exceed certain criterion values). In contrast, membership in category B follows a disjunctive rule, where at least one property is below its criterion. The decision boundaries for these rules are illustrated as dotted lines. The marginal dimensions depict the memory status of the gamble properties, represented as normal distributions of activation. In a single trial, two gambles are displayed (e.g., v1=700 and p1=0.9 for the gamble A and v2=200 and p=1.0 for the gamble B). To determine the preferential choice, the system accesses the underlying perceptual representations on each property dimension, sampling noisy evidence bounded by the decision criteria. Before evidence accumulation, the system decides to use either the serial or parallel modular system, with the modular gate probabilistically switching between them on a trial-by-trial basis, as governed by the p_Mod parameter, indicated by the three circles and arrow. In the example, the parallel interactive model is selected, where evidence is exchanged between two concurrent random walks, resulting in joint accumulation. This interaction, driven by the p_Cross parameter, allows the two random walks to act as a third combined process, facilitating a faster response by reaching the decision boundary more quickly, as shown by the superimposed random walk (bolded random walk) in the accumulation box belonging to the parallel module. At the bottom right, popular schematics of serial and parallel systems are shown to illustrate the information processing flow for decision-making, highlighting where p_Cross parameter influences the process, indicated as the “Process communication gate”.

The overall response is determined by the mental architecture, which governs the processing order of multiple random walks, each analyzing a different property. The serial and parallel processing modules are separated at the module gate, depicted in the middle of Fig. 1, indicated by the circles and the arrow. In serial processing, properties are analyzed sequentially, with the total response time being the sum of the accumulation times for each random walk (AND rule) or the time taken by the first random walk to reach a criterion (OR rule). In parallel processing, properties are analyzed simultaneously, with the response time being determined by the longest (AND rule) or shortest (OR rule) random walk.

The MSPN model also accounts for process dependency, where the time needed to process one attribute depends on the time needed to process others. This concept has been explored in various cognitive models¹⁸. The nature and extent of interaction in these models are often determined by free parameters, such as in the stochastic General Recognition Theory¹⁸. Other models fix the type of interaction based on assumptions, such as the relationship between facilitatory inputs and inhibitory lateral connections between accumulators¹⁹. In this model, the two parallel random walks exchange sampled evidence toward one of the two response boundaries at each step during accumulation. The concept of cross-channel interaction is implemented as a lateral connection between the two random walk accumulators, serving as a gate that allows the processes to share evidence. When the gate is open, both channels exchange their accumulated evidence at that time step.

When the random walks exchange congruent evidence, the accumulation rate for each channel increases, potentially leading to faster boundary crossing—this is identified as a facilitatory process interaction. Conversely, when they exchange incongruent evidence, the accumulation rate decreases, potentially slowing the boundary crossing—this is identified as an inhibitory process interaction. The example of two random walks exchanging information in a parallel system during accumulation can be represented as a superimposed random walk. This is depicted in Fig. 1 as a third, bolded accumulation line, which results from summing the evidence from the two parallel random walk accumulators, as displayed in the last to the right rectangular area of the parallel interactive module.

Interpreting MSPN Model Parameters and Validating/Falsifying Heuristic and Utility Approaches

The Modular Serial Parallel Network (MSPN) model offers a robust framework for interpreting decision-making strategies by evaluating specific model parameters. These parameters provide insight into whether a decision-making process aligns more closely with heuristic-based or utility-based approaches. The detailed parameter formalization of MSPN is described in Supplementary Appendix B.

Process Interdependence (p_Cross):The interdependence of gamble properties—such as values v1, v2 and probabilities p1, p2—is assessed using the parameter p_Cross within the parallel processing module. A p_Cross value greater than zero (p_Cross > 0) indicates process dependency, suggesting that the properties are being combined during a single trial. This interdependence strongly supports utility-based models, which rely on the integration of multiple attributes to form a single decision metric.
Scope of Information Search:The scope of information search is explored by comparing different variants of the MSPN model that engage stopping rules consistent with either limited or unlimited search scopes. This allows for the evaluation of whether a decision-making process is exhaustive—considering all available information—or self-terminating, focusing only on key attributes before making a decision. The scope of search can differentiate between strategies that are more heuristic-based (limited scope) versus those that are more utility-based (unlimited scope).
The modularity gate parameter (p_Mod):The processing module used to combine retrieved individual task properties from memory, using the serial or processing, order is evaluated using the parameter p_Mod. A p_Mod value of 0 indicates a pure heuristic-based approach, where properties are processed sequentially and often independently, while the value of 1 indicates pure parallel processing, and thus more utility based. Values between 0 and 1 (0 ≤ p_Mod < 1) suggest a combination of heuristic and utility-based processing, with the degree of utility-based processing increasing as p_Mod approaches 1. This parameter helps in determining whether the decision-making process relies more on quick, rule-based judgments or on the comprehensive integration of information.

To assess these components, we designed a study using the MSPN model to analyze decision-making in a gambling task. By manipulating the values of two key attributes and collecting data on both response times and preferential choices, we aim to uncover the underlying cognitive mechanisms at play.

Following the model selection procedures²⁰, we tested four computational models, each a special case of the MSPN: (1) Serial, a stochastic version of the Take-The-Best model or Priority Heuristic (with specified order of search across attributes); (2) Parallel interactive, a version of the utility decision making model that combines the properties of variables; and (3) MSPN model. To further evaluate the model's validity, we also fitted the data using an unconstrained (4) Free-drift model. This model is highly parameterized, allowing each stimulus condition to have a unique evidence accumulation process with free stepping probabilities toward a decision boundary. Unlike the MSPN model, which calculates step probabilities based on stimulus configuration and decision criteria, the free-drift model treats these probabilities as free parameters, unconstrained by any mechanistic assumptions. It serves as a statistical benchmark to compare the fit quality of the MSPN's parameter-constrained approach. The quantitative model-fitting procedures are detailed in Supplementary Appendix C. The results of the model fitting are presented in Table 1, showing the negative log likelihood (-LL) and the related Bayesian information criterion (BIC) associate the best model fit.

Each model predicts a specific pattern of response times distributions for both preferential gamble choice (A and B). Overall, considering the average BIC score, MSPN is preferred over the serial and parallel interactive models, respectively, but individual differences in decision-making strategies were evident: three participants (2, 5, and 10) were more likely to adopt parallel interactive processing, two participants were more likely to accept the serial self-terminating strategy (1 and 9), and five participants (3, 4, 6, 7, and 8) were more likely to rely on the MSPN model, which means that these five participants were likely mixing serial and parallel process across experimental trials.

Table 1

The best fitting Log Likelihood and BIC values of the considered models for each participant. The best model's BIC scores, accounting for model complexity, are bolded in the table.
		Parallel Interactive	Serial	MSPN	Saturated
Participants
1	-LL	659	649	639	613
1	BIC	1390	1378	1417	1655
2	-LL	697	728	686	669
2	BIC	1466	1535	1510	1767
3	-LL	779	780	709	714
3	BIC	1631	1640	1556	1858
4	-LL	684	685	639	590
4	BIC	1440	1450	1417	1609
5	-LL	569	571	550	527
5	BIC	1211	1221	1238	1483
6	-LL	1152	1136	1039	1039
6	BIC	2377	2352	2217	2509
7	-LL	747	762	711	608
7	BIC	1567	1603	1560	1647
8	-LL	801	788	729	708
8	BIC	1674	1657	1596	1847
9	-LL	722	716	699	580
9	BIC	1517	1512	1536	1590
10	-LL	691	700	671	584
10	BIC	1456	1480	1480	1598
Mean	-LL	750	751	707	663
	BIC	1573	1583	1553	1756

When compared to the saturated model, the MSPN model fits come very close to the benchmark values. However, the average BIC scores are smaller for the MSPN than that of the free-drift model for all ten subjects. Surprisingly, in 2 out of 10 comparison cases (Table 1), the best-fitting MSPN log-likelihood values are lower or equal than those of the free-drift model. This means that the parameter-constrained MSPN model provides a better fit to the data than the free-drift model, with fewer parameters (MSPN: 19 vs Free-drift: 59).

To explore the specific cognitive properties of the decision-making process, we analyzed the recovered best MSPN parameters reported in Supplementary Table 1. The parameters are divided between two modules, the serial and parallel modules, and the shared parameters. We used the MSPN recovered parameter values to investigate the cognitive properties of the decision-making process, looking for evidence to validate or falsify one of the two major classes of decision-making models: the utility-based and heuristic-based models. The diagnostic evidence is drawn from the models’ parameter values, particularly (1) the modularity gate parameter, which indicates the likelihood of trial-to-trial switching between serial and parallel modules (p_Mod), and (2) the parameter of cross-featural interaction (p_Cross), only for the parallel model. The two best-fitting parameter values are presented in the Supplementary Table 1. In general, the MSPN’s best parameter values are interpretable, showing values within acceptable ranges. The MSPN model provided satisfactory fits to both preferential choice and response time distributions (see Supplementary Fig. 1). Note that the MSPN model is able to capture the complex response patterns of individual subjects’ response time distributions.

The MSPN Model-Based Evidence Supporting Utility and Heuristic Approaches

Analysis of the MSPN model parameters showed that participants used parallel processing 67% of the time and serial processing 33%, with an average p_Mod value of 0.67 (Supplementary Table 1). Even though two participants (1 and 9) were primarily identified as serial processors based on BIC model fits Table 1, the MSPN model indicated a general preference for parallel processing across all subjects, with even these 'serial' participants showing p_Mod values above 0.4, within the MSPN framework. Conversely, those identified as parallel interactive processors (2, 5, and 10) were accurately reflected in the MSPN model, with p_Mod values above 0.88, the highest in the group. The p_Cross parameter, which measures cross-feature interaction, averaged 0.48 in the MSPN model. This indicates that in 48% of all parallel trials, there was interaction between processes analyzing gamble properties, strongly supporting utility-based decision-making. Specifically, 32% (.67 x .48 = .32) of all trials involved utility-based processing.

The data also revealed clear patterns of serial processing, supporting heuristic-based decision-making. Approximately one-third of trials (.33) involved a strictly sequential analysis of gamble properties, sometimes terminating early after considering just one property, suggesting the use of heuristic strategies. On the other hand, the presence of parallel processing without process interaction challenges the traditional view of heuristic decision-making, which often assumes strict serial processing. Around one-third of trials involved parallel processing of independent attributes (.67 x .52 = .35), where decisions could be made as soon as the 'right' property was identified, aligning more closely with heuristic-based approaches. In summary, the study provides evidence for both serial and parallel processing, with a stronger inclination toward parallel processing, and also to parallel interactive processing. These findings contribute to the ongoing debate between heuristic and utility-based decision-making approaches, demonstrating that both strategies are used. The results support the modularity of decision-making processes and highlight the hierarchical organization of gamble representations in the cognitive system.

The Modular Serial-Parallel Network (MSPN) model builds on key foundations in cognitive research by integrating several dominant approaches, including signal detection theory, stochastic evidence accumulation, and mental architectures. This synthesis not only enables the diagnosis of essential cognitive concepts through parameter estimation and computational modeling but also provides a powerful framework for disentangling the contributions of serial and parallel processes in decision-making tasks. By analyzing detailed patterns of response times and accuracies, the MSPN model effectively distinguishes between different cognitive architectures and validates specific theoretical predictions about cognitive processing. The MSPN model advances the study of rule-based architectures by offering a unified framework that accommodates both utility-based and heuristic-based decision-making strategies. Utility-based models, such as Expected Utility Theory, Prospect Theory, and Decision Field Theory, suggest that decision-making involves the comprehensive integration of all relevant information to compute a psychological utility value, often implying parallel processing and interdependence of attributes. In contrast, heuristic-based models, like the Take-The-Best heuristic, propose that decision-making relies on simpler rules and sequential processing, often ignoring some attributes altogether. By estimating key parameters—such as process dependency, the scope of information search, and processing order—the MSPN model can determine whether a particular decision-making task aligns more closely with a utility-based or heuristic-based approach. For instance, if data indicate strong process interdependency and comprehensive information integration, this would support utility-based models. Conversely, if data show a limited scope of information search and sequential processing, this would validate heuristic-based models. Our computational modeling analysis revealed that decision-making often involves both utility- and heuristic-based approaches. This dual presence suggests that decision-makers can switch between different processing systems, supporting the notion of a flexible and adaptive cognitive architecture. While the MSPN model describes this switching mechanism with a probability parameter, further research is needed to explore the conditions under which such switching occurs. This aligns with the work of Lee and Gluck¹⁰, who also emphasize strategy switching in decision-making, allowing transitions between different cognitive strategies based on task demands. Both the MSPN model and Lee and Gluck model¹⁰ underscore the importance of strategy switching and modular cognitive structures. However, while the MSPN model uses a probability parameter to describe switching, Lee and Gluck’s model provides a more detailed account of the conditions and factors that influence this process. Additionally, their model places greater emphasis on heuristic-based decision-making, particularly in multi-cue decision tasks, whereas the MSPN model more comprehensively integrates both utility-based and heuristic-based approaches. When compared with Diederich’s Multiattribute Dynamic Decision Model (MADD)¹¹, the MSPN model shows both similarities and differences. While MADD is more general and flexible, the MSPN model contributes by constraining evidence accumulation rates, enhancing falsifiability, and explicitly defining process dependency through cross-accumulator evidence exchange. These distinctions make the MSPN model a more structured approach, while MADD offers broader flexibility¹¹.

In conclusion, the Modular Serial-Parallel Network (MSPN) model offers valuable insights into the cognitive mechanisms underlying risk and reward decision-making. By dissecting the decision-making process into modular components, the MSPN model elucidates how individuals balance the potential risks and rewards in scenarios such as the gamble task. The model’s ability to capture both heuristic-based and utility-based strategies reflects the complexity and adaptability of human cognition in the face of uncertainty. For instance, when participants engage in parallel processing, they are likely weighing multiple aspects of a gamble simultaneously, integrating probabilities and potential outcomes to arrive at a utility-based decision. Conversely, the presence of serial processing suggests that individuals may sometimes rely on simpler, rule-based approaches, focusing on the most salient aspect of the gamble—such as the potential reward—before making a decision. This duality in cognitive processing highlights how individuals navigate the inherent tension between risk and reward, optimizing their choices based on the specific context and the cognitive demands of the task. The MSPN model not only advances our theoretical understanding of decision-making processes but also provides a practical framework for analyzing how people assess and respond to risk and reward in real-world situations.

Participants:
Ten students (6 females, 4 males; age range 20-27 years) were recruited from several Berlin universities. The experiment took place at the Max Planck Institute for Human Development, Berlin, Germany.

Ethics Approval and Consent to Participate:
The study was approved by the Ethics Committee of the Max Planck Institute for Human Development, Berlin, Germany. All procedures involving human participants were performed in accordance with the relevant guidelines and regulations outlined by the committee. Informed consent was obtained from all participants prior to their inclusion in the study.

Apparatus:
The experiment was conducted using Pentium II computers running DMDX software. Visual stimuli were presented on monitors with a resolution of 1024 x 768 pixels and a refresh rate of 60 Hz. Responses were recorded via mouse clicks.

Design and Stimuli:
Participants engaged in a binary choice task designed to evaluate decision-making under uncertainty with non-negative prospects. The task required selecting between two gambles: Gamble A (a risky option) and Gamble B (a sure gain). Gamble A was characterized by two properties: the potential value (v1) and the probability of earning that value (p1). The properties of Gamble B were fixed at a value of €200 with a probability of 1.0 (i.e., a guaranteed gain). The possible outcomes for Gamble A were defined as Gamble A = <vA1, pA1; 0, 1-pA1>, while Gamble B was defined as <200 €, 1>.

The study included 54 unique trial conditions, derived from the orthogonal combination of six probabilities of maximum gain for Gamble A (p1 = 0.1, 0.2, 0.3, 0.5, 0.7, 0.9) and nine values of maximum gain for Gamble A (v1 = €1, €100, €200, €300, €500, €600, €700, €900, €1000).

Procedure:
Participants were instructed to make a decision between the two options, A and B, by pressing one of two mouse buttons. The left button indicated a preference for Gamble A, and the right button indicated a preference for Gamble B. Trials began with an 800 ms delay, followed by a central fixation point for 1280 ms, and a 680 ms warning signal. The two gamble options were then displayed until a response was made. No feedback was provided after trials.

Each participant completed three sessions, each consisting of 8 practice trials and 486 experimental trials, spread across different days. Participants rested after every 100 trials. This resulted in 27 repetitions per factorial condition (v1 × p1).

Compensation:
Participants were compensated at a rate of €10 per hour. Additionally, a bonus was awarded based on a random selection of trials. The chosen gamble was played out, and the average outcome was converted into cash (at a rate of 100:1). On average, participants received an additional €4. Each session took approximately 55 minutes to complete.

Competing interests

The authors declare no competing interests.

Author Contribution

M.F. and J.H. conceived the experiment(s) and contributed equally to the project. M.F. and C.K. collaborated on the design and analysis. M.F., C.K., and J.H. analyzed the results. All authors reviewed and approved the manuscript

Acknowledgments

This work was supported by grant from the National Science Foundation (NSF SES-1854762 & 1854763 to Mario Fifić and Joseph W. Houpt.

Data Availability

The study’s data is available for this paper at: https://osf.io/v5jwr/files/osfstorage/66d0a1e7eec96e4b5e89bba8

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Balancing Risk and Reward: Cognitive Processes in Decision-Making Explored Through the Modular Serial-Parallel Network

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Abstract

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Introduction

Results: Quantitative Model Fitting

The MSPN Model-Based Evidence Supporting Utility and Heuristic Approaches

Discussion

Method

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Competing interests

Author Contribution

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References

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