Multifactorial effects on bounded rational decision-making

The complexities of decision-making processes have garnered considerable interdisciplinary attention, intersecting domains such as psychology, economics, machine learning, and game theory [1–6]. Conventional decision-making paradigms posit that individuals operate as agents of rationality, optimizing self-interest aligned choices [7]. Nonetheless, this paradigm has been rigorously challenged by emergent research underscoring the salient influence of bounded rationality on decisional conduct [8]. Introduced by Arrow and subsequently expounded upon by Simon, bounded rationality acknowledges the propensity for rational action yet concedes the presence of inherent constraints [9]. This concept occupies the theoretical middle ground between perfect rationality and complete irrationality, adapting to the confines of cognitive, informational, and temporal limitations.

The construct of bounded rationality within decision theory and behavioral economics encapsulates the encumbrances faced during decision-making, attributable to the finitude of information processing, time, and cognitive capacity [10]. This framework not only mirrors the intricate nature of real-world decision-making but also captures the sway of psychological biases [11]. These biases are paramount in understanding decision-making within the bounds of rationality, providing profound insights into the management of complexity and limitations in real-life contexts [12]. They are equally critical for the development of decision-support mechanisms, the formulation of policy, and the creation of marketing strategies. The bounded rationality paradigm challenges the traditional tenets of rational choice theory by positing that the ideal of optimal decision-making is often elusive, constrained by cognitive limitations, information availability, and temporal pressures [13]. Confronted with multifaceted decisions, individuals resort to heuristic approaches, enabling expedited decision-making amidst a deluge of information and inherent uncertainty.

Exploring the concept of bounded rationality is pivotal for a deeper comprehension of decision-making within constraints. Close analysis of the factors influencing choice allows researchers to develop more accurate models of human behavior. Such research can enhance decision-support systems and inform policy-making to more faithfully reflect genuine human thought processes and actions. This area of study is essential for bridging the gap between theoretical predictions and actual decision-making practices. Furthermore, investigating bounded rationality offers substantial advantages to cutting-edge scientific disciplines. In the field of artificial intelligence (AI), for example, incorporating bounded rationality into AI models marks a substantial progression [14–17]. These models strive to replicate human decision-making by recognizing and integrating the same limitations that humans encounter. The ambition is to evolve AI systems to process decisions more intelligently and aligned with the nuanced ways that humans approach decisions amid constraints.

Based on the above analysis, the present research aims to show the substantial impact of bounded rationality on the decision-making process. It involves a close look at many factors that shape how one make decisions, including, but not limited to, cognitive biases such as anchoring, availability heuristics, the decoy effect, herd behavior, and the interplay between rewards and punishments, along with weighting and framing effects. The aim is to contribute to the discourse on individual decision-making by offering a refined understanding of bounded rationality's role. The investigation concludes by highlighting current research gaps and proposing future areas to investigate the impact of bounded decision-making on choice processes.

Within the domain of decision-making research, the anchoring effect serves as a notable example of bounded rationality, significantly influencing cognitive processing during decision-making [18–21]. This cognitive bias describes the tendency to overly rely on the first piece of information —termed the “anchor”— when making decisions [22]. The introduction of an anchor at the early stages of contemplation establishes a psychological benchmark that can skew subsequent judgments and choices, regardless of the anchor's contextual pertinence or factual correctness [23]. Adjustments in subsequent judgments are often made relative to this anchor, leading to a consistent deviation in the interpretation of incoming information [24]. The anchoring effect can manifest in both positive and negative forms, influencing the evaluation and preference for different types of information and frequently resulting in outcomes that diverge from normative predictions of rationality, thus underscoring the substantial impact of cognitive biases in decision-making [25].

The anchoring effect was first identified by researchers Amos Tversky and Daniel Kahneman [26]. In a seminal experiment, participants were asked to quickly estimate the product of the numbers one through eight, either in ascending $(1\,\times2\,\times3\,\times4\,\times5\,\times6\,\times7\,\times8)$ or descending order $(8\,\times7\,\times6\,\times5\,\times4\,\times3\,\times2\,\times1)$. Due to time constraints preventing accurate calculation, participants’ estimates were influenced by the initial numbers, leading to median estimates of 512 for ascending and 2250 for descending sequences, showcasing the anchoring effect (the actual product is 40320). Further research has confirmed the anchoring effect's pervasive role in various decision-making processes [27,28]. Studies on anchoring typically examine numerical estimates, beliefs, and stated preferences, revealing the challenge in circumventing anchoring bias [29–32].

The anchoring effect pervades decision-making in multiple settings, affecting value estimation, negotiation, and legal judgments [33,34]. In negotiations, the initial proposal establishes a psychological benchmark, significantly steering the negotiation's trajectory and final outcomes, with later offers often remaining close to this initial figure [35]. The effect extends to economic judgments, where initial pricing can shape perceived value and sway subsequent decisions. Additionally, the anchoring effect influences how individuals assimilate information, evaluate probabilities, and formulate judgments, thus impacting wider psychological and social constructs [36,37]. Awareness of this bias is crucial for the creation of more enlightened and rational decision-making strategies within organizations [24,38] and is valuable for policy formulation to guarantee fair practices and governance.

The availability heuristic is a cognitive shortcut that significantly influences the assessment of the likelihood or frequency of events, based on the ease with which instances can be retrieved from memory [39,40]. This heuristic was initially identified in the context of Simon's behavioral model of rational choice, which introduced the concept of “bounded” rationality [41]. According to Simon, decision-making results from the interaction between external stimuli and internal cognitive mechanisms. Subsequent research has investigated the role of bounded rationality and the utility of heuristics in facilitating accurate judgments under conditions conducive to their use [42]. The availability heuristic expedites judgment by prioritizing information that is easily recalled, potentially leading to an overestimation of its importance or frequency [43]. This bias is prominent in various decision-making scenarios, from routine choices to critical evaluations [44]. Its influence is apparent in the overestimation of the frequency of memorable but rare occurrences, such as aviation disasters or acts of terrorism, due to their prominent media coverage and resultant ease of recall.

The availability heuristic is a mental shortcut that happens when people make decisions based on quick, easily accessible examples rather than careful analysis [45]. This can affect economic choices, such as when investors focus on the latest news instead of looking at long-term market data. It also influences how we think about social issues and risks; for example, people might judge health dangers based on stories they have heard rather than on actual statistics [46]. Understanding this bias is key to making better decisions [47]. By knowing about it, we can take steps like getting information from a variety of sources to counteract its effects [48]. This knowledge can lead to smarter and more informed decision-making.

The decoy effect, also known as the asymmetric dominance effect, constitutes a pivotal aspect of behavioral economics and decision-making research [49,50]. This phenomenon describes the influence of a strategically introduced third alternative, referred to as the “decoy”, on the selection preferences between two other options. The decoy is designed to be less attractive than one of the original choices but more so than the other, making the former seem more appealing in comparison [51]. For clarity, refer to table 1 which compares three electronic devices labeled A, B, and C. In this instance, product C functions as the decoy, ostensibly included to manipulate the consumer's choice towards product A. Here, the decoy (C) is priced slightly higher than the target choice (A) and offers less storage than A but more than the least attractive option (B). The presence of C is intended to make A appear more valuable in terms of both cost and storage capacity, thereby nudging consumers towards choosing A over B. This effect has been empirically demonstrated to significantly alter consumer preferences and is a testament to the non-linearities and imperfections inherent in human decision-making processes [52].

In behavioral evolution studies, the decoy effect provides valuable insights into temporal variations in human choice behavior [53]. Researchers employed the repeated prisoner's dilemma (rPD) game, involving random pairwise encounters, to investigate individual decision-making behavior under the decoy effect [54]. The game included two actions: cooperation (C) and defection (D), with an added decoy action —“reward” (R)— introduced into the game. The game's rules were explicitly explained to the volunteers using the subsequent unilateral and bilateral payoff matrices. Within the confines of the study, cooperation (C) was delineated as the forfeiture of a single unit, facilitating a gain of two units for the opposing player. Conversely, defection (D) was characterized by the participant accruing one unit, concomitant with a one-unit loss for the opponent. The study introduced an additional, decoy action termed “reward” (R). This decoy mimicked the qualitative aspects of cooperation (C) but incorporated an additional feature: the participant would relinquish two units, resulting in a three-unit gain for the opponent. The experimental outcomes underscore the potential of decoys as significant catalysts for fostering voluntary prosocial behavior. These results accentuate the necessity for extended exploration of this effect, as it promises to deepen our comprehension of the intricate dynamics inherent in the decision-making process.

Understanding the intricacies and implications of the decoy effect is critical for the enhancement of decision-making efficacy and rationality [55]. Recognition of this cognitive bias provides a foundation upon which individuals and institutions can construct approaches to attenuate its sway [56]. Concretely, individuals may augment the criticality applied to their decisional processes, whereas organizations might tactically employ the decoy effect to nudge choices in favor of more advantageous outcomes [57]. Consequently, the decoy effect emerges as a formidable cognitive bias with substantial impact on decision-making paradigms in a multitude of scenarios. Acknowledging its presence and comprehending its operational dynamics are imperative in the pursuit of advancing more enlightened and systematic decision-making practices.

In the realm of cognitive science, the concept of collective intelligence is increasingly recognized as a significant contributor to human capability [58]. Yet, individual decision-making is often influenced by social pressures, leading to a phenomenon known as the herding effect, which can result in less than optimal outcomes [59]. This effect can cause uneven distribution of wealth, distort the truth due to a group consensus, and disrupt collective wisdom. When individuals’ assessments of quality are swayed by social factors, the collective decision-making process is vulnerable to manipulation, with far-reaching consequences in economic, political, and health contexts [60].

Herding, or the tendency to conform, significantly affects how individuals make choices [61,62]. This tendency leads people to imitate the majority, often without considering their own information or beliefs [63,64]. Such behavior is rooted in the basic human need to fit in, avoid being excluded, or the belief that the group knows best [65]. The effects of herding are seen in various areas, influencing consumer habits, social behaviors, and voting patterns. For example, in economic scenarios, individuals may follow popular trends or influential leaders, which can lead to significant ups and downs. This behavior can also influence shopping choices and style preferences, with popularity often being mistaken for quality. Social media has intensified these trends by enabling the quick spread of popular behaviors. In social psychology, herding can lead individuals to align their views and actions with what they perceive to be the group norm. Such conformity can even influence political choices, where voters might side with the predominant opinion in their social circles, regardless of their own beliefs or the arguments’ validity. The concept of herding is also applied in public health studies, such as in examining individual decisions to vaccinate during a disease outbreak, using models like game theory [66].

Comprehending the mechanisms and repercussions of the herd effect is vital for achieving greater efficacy in decision-making. This awareness facilitates individuals in resisting the pressure to conform, thereby enabling them to make decisions that are more informed and rational. Concurrently, organizations and societies can construct systems and frameworks to mitigate the risks inherent in herd behavior. In summary, the herd effect, a substantial social influence, significantly shapes decision-making processes across a multitude of contexts. Acknowledging its sway and understanding its operational mechanisms are crucial in the pursuit of more informed and rational decision-making.

When we look at how people make decisions with limited information and under certain constraints, we see that rewards and punishments play a big role. Studies using games as an example have helped us understand why people cooperate and help each other, even when it costs them something [67–72]. These studies show that people often keep others in check by punishing those who do not play fair, like those who take advantage of the group without contributing. However, recent research tells us that giving rewards can also encourage people to work together, and it might lead to better results than punishment [73]. Rewards can prevent negative effects like damage to someone's reputation or the chance of them hitting back [74]. They may also help stop harmful punishments that can make the situation worse. In the past, people thought punishment was the best way to get cooperation, but now we see that rewards can work just as well [73]. This is shaking up the old belief that strict punishment is the best policy. Some theories even suggest that sticking to either rewards or punishments, not both, could be better in the long run.

The contrast between punishment and reward is a fundamental aspect of decision-making, as demonstrated by the extensive research in operant conditioning [75–77]. Decisions range from mundane daily choices to complex organizational policies and are invariably driven by the dual forces of seeking rewards and avoiding punishments. This dynamic is evident across various fields [78], with workers striving for incentives while steering clear of misconduct penalties, and students adjusting their efforts based on the rewards of academic achievement and the avoidance of failure. In economic behavior, consumer purchasing decisions are motivated by the interplay between the perceived benefits of goods and the risks of financial detriment [79], while businesses balance the prospects of profit against the risks of adverse outcomes in their strategic considerations. Social conduct, too, is moderated by the potential for community endorsement or social exclusion [80,81]. In conclusion, a comprehensive understanding of the roles that both rewards and punishments play is essential to improving decision-making mechanisms. Delving into the principles that govern these motivational forces is crucial for developing sophisticated strategies that capitalize on these dynamics to enhance outcomes in a multitude of contexts.

Decision-making behavioral patterns bear considerable consequences on the performance, safety, and resilience of systems predicated on network structures, particularly those encapsulated by prospect theory [82,83]. The prospect theory, an innovative decision-making framework proposed by psychologist and economics Nobel laureate Daniel Kahneman along with Amos Tversky, is rooted in empirical findings [26]. The theory elucidates the decision-making process when individuals face probabilistic alternatives, each with varying degrees of risk and uncertainty in outcomes [84]. To encapsulate the transformation from actual to perceived probabilities, Kahneman and his colleagues astutely devised the inverse S-shaped probability weighting function $W{:}~[0, 1] \rightarrow [0, 1]$ (fig. 1). In this function, a true probability denoted by x is perceived $\text{as} W(x)$ [26,85]. The expression for the Prelec weighting function is then subsequently presented as follows:

$$\begin{equation} W(x) = \exp(-(-\ln x)^{\gamma}),\quad x \in [0,1]. \end{equation} \tag{ 1 }$$

The gradient of the function can be interpreted as a gauge for the sensitivity of preferences in response to alterations in probability. The rationality coefficient, denoted as $\gamma \in (0,1]$, dictates the disparity between objective and subjective probabilities. The specific value of γ is contingent upon the precise circumstances of the decision-making scenario and exhibits variability amongst individuals [86,87]. A lower γ is indicative of reduced rationality in an individual. Specifically, a scenario where γ = 1 and $W(x)=x$ signifies a fully rational individual.

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Prospect theory is a way of understanding how people make choices, particularly when they are dealing with the possibility of winning or losing something. It suggests that people think about potential gains and losses rather than the final outcome, and they usually care more about avoiding losses than making gains [88]. This idea can be seen in many areas, from personal finance to government policy [89]. For example, investors might hold onto a losing stock for too long because they fear the loss more than they value the chance to invest the money elsewhere [90]. Similarly, shoppers might feel more upset about a price increase than they are happy about a discount of the same amount, which can affect what they buy [91]. Businesses and governments use this knowledge to shape their strategies and policies. Companies might frame price changes as discounts rather than hikes to keep customers happy. Policymakers might emphasize the negative effects of not acting on issues like climate change to get support for their initiatives [92]. Understanding prospect theory can help people, companies, and governments make better decisions by acknowledging the sometimes irrational way we all perceive wins and losses [93].

The framing effect stands as a notable phenomenon influencing choice architecture, wherein individuals’ perceptions of the desirability of a prospect are contingent upon whether it is framed as a gain or a loss relative to a reference point [94]. This subjective valuation underscores that perceived payoffs are intrinsically comparative rather than absolute measures [95]. Typically, the reference point is derived from an individual's historical experiences and their anticipated outcomes. Moreover, empirical evidence suggests a heightened sensitivity to losses in comparison to gains, a phenomenon recognized as loss aversion [96]. As delineated in fig. 2, the value function's gradient is more pronounced in the domain of losses than in that of gains, indicating a steeper descent in utility with losses. This function exhibits concavity with respect to gains, signifying a risk-averse disposition, while it displays convexity in the context of losses, revealing a propensity for risk-seeking behavior. Additionally, the function exhibits diminishing sensitivity, where the incremental perceived value diminishes as the magnitude of gains or losses increases. The prospect value function [94], representing the perceived payoff, is defined accordingly as follows:

$$\begin{equation} V(\Delta u = u-R_n)= \left\{\begin{array}{l@{\quad}l} (u-R_n)^\alpha, & \mbox{if }~u > R_n,\\ -\lambda(R_n-u)^\alpha, & \mbox{if }~u < R_n, \end{array} \right. \end{equation} \tag{ 2 }$$

where R_n is the reference point, and u is the actual payoff of a possible prospect. Parameter $\lambda \geq1$ is the loss multiplier. The sensitivity coefficient $\alpha \in (0, 1]$ represents the bump degree of the value function.

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The framing effect originates from an inherent cognitive bias where individuals exhibit a proclivity towards risk-aversion when options are positively framed and risk-seeking when options are negatively framed [97]. Although an integral aspect of human cognition, the framing effect can precipitate decisions that are not necessarily optimal [98]. The deepening of our comprehension of its underlying mechanisms holds promise for enhancing decision-making processes within both individual and institutional contexts. Future research trajectories may include the development of personalized interventions tailored to mitigate the framing effect, the exploration of its influence across various cultural milieus, and the harnessing of technological advancements to neutralize cognitive biases.

Unlike the assumptions of complete rationality or complete irrationality, bounded rationality recognizes that decision-makers are influenced by factors such as resource constraints, time limitations, and cognitive limitations when processing information and choosing options. This prospective study summarizes some key factors that substantially influence decision-making within the framework of bounded rationality, including cognitive biases such as anchoring, availability heuristics, and the decoy effect, as well as herd behavior and the dichotomy of rewards and punishments. Anyway, we recognize that in real-world scenarios, these factors often do not operate in isolation. Instead, they interact in complex ways to shape the decision-making process. The current scope of this prospective has been to introduce and explain each of these factors on their own merit, primarily due to the intricate nature of their interplay, which could warrant a dedicated study in its own right.

While there is a wealth of studies on how one make decisions, our understanding still has significant gaps. The existing problems include but are not limited to: i) Few studies have looked at how outside changes, like shifts in the environment, and internal factors, such as how individuals think, work together to influence decision-making within the limits of what we can process. ii) Most research has only looked at pieces of this puzzle, leaving us without a full picture that brings together different psychological aspects for a better understanding of how we behave. iii) The integration of bounded rationality into AI research remains a relatively underexplored field. However, this domain can present substantial potential for enhancing the decision-making capabilities of AI systems by aligning them more closely with human cognitive processes.

Based on the above discussion, future research on behavioral decision-making may focus on: i) Clarifying the influence of interpersonal connections and social networks on departures from rational thought processes. ii) Presently, many models utilize non-linear equations to depict particular psychological tendencies. Expanding these models to incorporate a wider array of bounded rationality traits remains an open and promising field of investigation. iii) Current research primarily focuses on the impact of single factors of bounded rationality on individual behavior, yet comprehensive analysis of how multiple factors interact to influence behavioral change remains inadequate. Given that these factors are often interwoven and collectively shape individual behavior in real life, delving into the interrelationships among these factors and how they jointly influence decision-making patterns is a crucial direction for future research. iv) In complex and uncertain environments, it is challenging to build excellent models that integrate the bounded rationality of machines with environmental factors, and to optimize the decision-making process of AI.

This work was supported by the National Natural Science Foundation of China (Nos. U23A20331, 62173095).

Data availability statement: No new data were created or analysed in this study.