Recurring Suboptimal Choices Result in Superior Decision Making

doi:10.21203/rs.3.rs-1724502/v2

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Recurring Suboptimal Choices Result in Superior Decision Making

https://doi.org/10.21203/rs.3.rs-1724502/v2

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In real-life situations involving risk and uncertainty, optimal policy hinges on selecting a course of action characterized by the highest expected value (i.e., future outcomes weighted by their probabilities). Nevertheless, a vast body of findings from economic and psychological studies indicate that people rarely follow this principle and make suboptimal choices. In the current research, we tested a hypothesis that recurring suboptimal choices result in superior decision making. In one simulation study and three well-powered (N = 1,046) fully-incentivized empirical studies, we demonstrated that people who traded off their decision accuracy for the number of possible choices performed better (i.e., they earned more money) than those who made optimal decisions in terms of maximizing the expected value. Our results demonstrate that decision makers can adapt to the requirements of a decision task. They are inclined to make more suboptimal decisions, resulting in better overall performance than normatively better choices.

decision making

numeracy

optimal decisions

adaptive decision making

expected value

Optimal decisions under risk and uncertainty are often attributed to complex and effortful calculations aimed at establishing the expected value of a particular course of action (i.e., the sum of possible outcomes weighted by the likelihood that the outcome will occur). By definition of the expected value, selecting options with the highest expected value should always lead to the best possible outcomes in the long run. In the present research, we provided evidence that recurring suboptimal decisions in separate individual choice problems resulted in superior overall performance in the compound decision task. This indicates that skilled decision makers are likely to adapt their behavior according to task constraints and make suboptimal choices to maximize their final payoff.

Historical correspondence between Blaise Pascal and Pierre de Fermat debating a fair division of the stakes in a game of chance set the foundations of modern probability theory and introduced the use of expected value (EV) as a benchmark for optimal decision making (Hacking, 1975). Nowadays, the concept of expectations calculated as a sum of future outcomes multiplied by the probability of their occurrence has been widely used in various areas to optimize long-run decision making. For instance, national lotteries and casino games such as roulette incorporate EVs to maximize the profits of their owners and diminish the total reward of the players (Thaler & Ziemba, 1988). Insurance companies use EVs to make their health insurance policies profitable, and companies recruit consultants to optimize their profit margin by analyzing EVs for their future investments (Machina & Viscusi, 2014). Last but not least, optimal decision rules in complex systems such as production may be reached by taking into account EV (Simon, 1956). From a purely formal perspective, optimal reward-oriented decision making under risk and uncertainty requires following the principle of EV maximization (Schoemaker, 1982). Although the EV model is being completely discounted as a positive theory of human behavior, its normative credentials remain intact.

In the present research, we challenge this thesis. In particular, the results of our simulation study and three well-powered fully-incentivized empirical studies indicated that recurring suboptimal choices result in superior decision making.

Making Good Decisions

Since the St. Petersburg paradox described by Bernoulli (Bernoulli, 1954), the EV maximization principle has been challenged as a valid model of decision making under risk and uncertainty. Alternative explanations of human decision making have instead considered maximization of expected utility (von Neumann & Morgenstern, 1944), maximization of subjective value (Tversky & Kahneman, 1992), satisficing (Simon, 1990), aspirations (Lopes, 1987), or feelings (Loewenstein et al., 2001) as pivotal factors that motivate choices and shape the decision-making process. Despite the irrefutable advantage of these descriptive models for theorizing about human decision making, from a formal perspective, the expected value model is a benchmark for making optimal choices under risk (assuming that a decision maker aims to maximize their reward). Nevertheless, the complexity of a task and the computational capabilities of decision makers restrict brute-force optimization and rational decision making (Simon, 1990).

In response to these constraints, people employ an adaptive toolbox of heuristics that is likely to approximate optimal strategies (Gigerenzer, 2008) to a satisfactory level or sometimes even outperform them. For example, DeMiguel and colleagues (2009) demonstrated that a simple yet frugal strategy to allocate money equally among each investment fund led to higher financial profits in a shorter time frame than optimal asset allocation proposed by the Nobel Prize laureate Harry Markowitz (Markowitz, 1952). However, this solitary example of non-optimal behavior resulting in superior decision making is overpowered by empirical findings and predictions of theoretical models suggesting that optimal decisions are determined by rationality. In dual-process theories of reasoning, judgment, and decision making (positing that people process information via the two information-processing systems: analytical-rational and intuitive-experiential), Pacini and Epstein (1999) argue that “the safest prediction that can be made when optimality is at issue is that non-optimal responses will be inversely related to rationality, directly related to experientiality, or both (p. 981)“. How, then, should rational people make good decisions—those leading to the greater total reward they aim to achieve?

Skilled Decision Makers

A vast body of evidence suggests that skilled and numerate decision makers who understand the concepts of probability and statistics and can use them efficiently in everyday situations are more likely to make superior choices than people who are less statistically numerate (Cokely et al., 2018; Garcia-Retamero et al., 2019; Peters, 2012; Reyna & Brust-Renck, 2020). Numerate individuals make more choices maximizing EV (Cokely & Kelley, 2009; Millroth & Juslin, 2015; Sobkow et al., 2020) and are more sensitive to variations in EVs (Jasper et al., 2013; Peters & Bjalkebring, 2015). Interestingly, they can also adapt to the structure of the task and its requirements. For example, it has been demonstrated that more numerate individuals (in comparison to people with lower numeracy) tend to maximize EVs in meaningful choice problems (i.e., when they can earn substantially more because of an evident difference in the EVs of the options), However, at the same time they employ less effortful heuristic decision strategies when faced with trivial problems (i.e., when it does not matter which option to select because the difference in EVs is negligible). Under such conditions, they make more random choices to save time and cognitive resources. As a consequence, numerate individuals create an opportunity to make more choices. Even if they do not follow the EV maximization principle, making more suboptimal decisions may enable them to obtain a higher total reward.

Recent behavioral and neuroscience findings appear to support this general prediction (Glimcher, 2022; Ho et al., 2022; Mastrogiuseppe & Moreno-Bote, 2022). For instance, people adapt their behavior in a complex problem-solving task and use heuristic planning strategies to behave in an optimal manner when resources are constrained (Callaway et al., 2022). A reanalysis of eye-tracking data has revealed that attentional bias to a low-EV option was related to a higher reward rate—the reward that could be obtained per unit of time invested in a choice problem (Zilker, 2022). Furthermore, it was demonstrated that high-value decisions were being made faster and with greater accuracy than low-value decisions (Shevlin et al., 2022), which undermines the predictions of normative decision models.

The Overview of the Present Study

The present research aims to test the normative credentials of expected value theory by providing evidence that recurring suboptimal choices will result in superior decision making. In other words, we hypothesize that even if individual choices considered in isolation may be regarded as suboptimal in light of the EV maximization principle, some people (especially those with higher numeracy) can adapt their decision strategy to the task structure and requirements, making faster suboptimal (or random in terms of EV maximization) decisions that result in overall superior performance (e.g., earning more money).

In the current study, we used the EV maximization model as a benchmark for accurate behavior under risk that maximizes reward. That is, compared to various models describing actual decision making (e.g., prospect theory), maximization of EV is the normatively superior strategy when there are no resource constraints available. However, as Anderson’s (1990) seminal work dictates, rational analysis of behavior should include a step where resource constraints are considered when defining a rational model. Following this line of argument, we attempt to demonstrate how a constrained rational model (i.e., algorithmic level description of human behavior) could achieve a better result than an unconstrained rational model of human behavior in a constrained task scenario. Importantly, in contrast to prominent frameworks describing adaptive decision making, such as bounded rationality (Gigerenzer et al., 1999) or accuracy-effort tradeoff (Payne et al., 1993), we predict that decision makers will use fast and effortless strategies to maximize their total reward—making recurring suboptimal choices will not only approximate rational strategy based on the EV maximization principle but also outperform it. We tackled this problem using a simulation study and three empirical studies.

Sample

A diverse sample of N = 1,046 volunteers (52% females, M_age = 31.82, SD_age = 13.11) recruited via the Prolific platform took part in the three online studies (N_{Study 1} = 350, N_{Study 2} = 345, N_{Study 3} = 351; see Table 1 for a detailed description of the samples). Participants were paid £1.88 for a study lasting approximately 15 minutes. Additionally, they were informed that they would be compensated based on their performance on a decision task. In particular, participants collected points they could win with a given probability in a series of choice problems. Each participant received an additional one pound on top of the flat payment for completing the study for every 200 points. Participants gave informed consent before the study. The study protocol was approved by the Ethics Committee at the Author-identifying information.

Table 1

Demographic characteristics of the samples in the three studies

	Study 1 (N = 350)		Study 1 (N = 345)		Study 1 (N = 351)
	N	Percent	N	Percent	N	Percent
Age
18-33	286	81.7%	303	87.8%	130	37.0%
34-49	52	14.9%	31	9.0%	102	29.1%
50-65	11	3.1%	10	2.9%	101	28.8%
66-81	1	0.3%	0	0.0%	18	5.1%
NA	0	0.0%	1	0.3%	0	0.0%
Gender
Male	176	50.3%	173	50.1%	154	43.9%
Female	174	49.7%	172	49.9%	196	55.8%
NA	0	0.0%	0	0.0%	1	0.3%
Employment
Full-Time	96	27.4%	111	32.2%	110	31.3%
Part-Time	71	20.3%	64	18.6%	56	16.0%
Unemployed	65	18.6%	61	17.7%	18	5.1%
Due to start work	10	2.9%	6	1.7%	3	0.9%
Unpaid work	7	2.0%	11	3.2%	49	14.0%
Other	55	15.7%	50	14.5%	19	5.4%
NA	46	13.1%	42	12.2%	96	27.4%
Student
Yes	178	50.9%	192	55.7%	49	14.0%
No	139	39.7%	121	35.1%	228	65.0%
NA	33	9.4%	32	9.3%	74	21.1%

To detect the smallest effect size (i.e., the correlation between the proportion of EV choices and total gain of r = .2 at α < .05 and the power of the test of β = .95), we needed to collect data from 314 participants. Nevertheless, we decided to recruit substantially more participants to account for the possible drop-out rate and quality of the data collected in an online study. The final number of participants in each study was constrained by our budget (i.e., constant flat fee and varying bonus payments).

We applied exclusion criteria following the preregistration at https://osf.io/k7tfx. Specifically, we analyzed data only from the participants who completed all the tasks. We also excluded repeated submissions from participants with the same ID, those who did not make any choice to maximize EV, and those whose total gain on the whole task was 0 points. Based on these criteria, we excluded 10 participants in Study 1, 12 participants in Study 2, and 28 participants in Study 3. The majority of excluded participants accepted an invitation to the study but withdrew after starting the procedure, which was the main reason for exclusions.

Tasks

Examples of the experimental task, data sets, codes, and scripts of the present project can be found at https://osf.io/56xfa/

Decisions-from-experience Task

In all studies, we used a decisions-from-experience task (DfE) to investigate information search and choices (Wulff et al., 2018). Contrary to common lottery choice problems in which outcomes and probabilities are presented explicitly in a descriptive format, the DfE task participants have no access to such information. Instead, they can freely explore outcomes and frequencies by drawing random samples from each distribution. In each decision problem, participants were presented with two boxes symbolizing binary two-outcome gambles with an unknown payoff distribution. Participants were informed that they could sample information from each gamble without limitations. For each selection of a gamble, an outcome drawn randomly from a given distribution was displayed for 400 ms.

Participants were able to decide by themselves which distribution they wanted to sample from, when to switch between the gambles, and when to terminate exploration. When participants were ready to make a choice, they finished sampling and indicated which gamble they preferred by clicking the “Done” button below the boxes and then selected a chosen gamble by clicking on the corresponding box. Feedback on their choice was provided immediately. In addition, information on their total current gain was presented in the screen’s bottom-left corner. Choice problems consisting of two-outcome gambles in the gain domain were randomly selected with replacement from a set of ten choice problems (see Table S1 in Supplementary Online Materials for parameters describing the choice problems used in all studies, choice probabilities, and metrics regarding exploration behavior) and presented in random order. Furthermore, recording the number of decisions, preferences for gambles, and time spent on exploration, we also measured the number of samples drawn from both payoff distributions (gambles) and the switching ratio (i.e., the ratio between the number of actual switches between gambles and the possible number of all switches given a total number of drawn samples). Fig. 1 illustrates the mechanism of the DfE task.

Statistical Numeracy

We measured statistical numeracy using the Berlin Numeracy Test (BNT; Cokely et al., 2012). The BNT is a standardized psychometric instrument that efficiently measures objective numerical abilities, including statistical numeracy, risk literacy, and comprehension of probability. The BNT consists of mathematical tasks of varying difficulty (e.g., “Imagine we are throwing a five-sided die 50 times. On average, out of these 50 throws, how many times would this five-sided die show an odd number (1, 3 or 5)?”. In the three experiments, we used the computerized 4-item BNT version. Items were presented sequentially in a fixed order. We took the sum of the correct answers on the BNT to calculate the measure of numeracy (from 0 to 4).

Procedure

The order of tasks (BNT and DfE) was counterbalanced across participants. Prior to the DfE task, each participant was familiarized with the mechanics of the DfE task. First, participants were taught how to explore information hidden in the box. Then, the lottery concept and the bonus payment mechanism were explained, and participants were asked to explore the two gambles and select the one they preferred.

Finally, each participant had to provide correct answers on two training trials involving decisions from experience according to specific instructions. In particular, in the two consecutive choice problems, participants had to select a gamble that returned 0 points less frequently and a gamble that offered the highest possible profit, respectively. Tips concerning the mechanism of the DfE task were displayed on a computer screen during the training session. To proceed to the main DfE task, participants had to provide correct answers on the training task. They received feedback on the accuracy of their decisions and had to repeat the training task until they provided two correct responses.

The critical difference between the three studies concerned the time constraints and information provided about the decision task. In Study 1 (preregistered), participants were explicitly informed that their task was to make exactly 30 decisions in 30 choice problems without any time constraints. In addition, reminders about the total gain (updated depending on their choices) and the choice problem’s number sequence were displayed at the bottom of the screen during the DfE task. In Study 2, participants were informed that the task would last exactly 5 minutes, and they received only a reminder about the total gain on the DfE task (updated depending on their choices). In comparison to Study 2, in Study 3, we additionally displayed a timer that indicated the elapsed time during the DfE task (counting down from 5 minutes). All other conditions were the same as in Study 2 (see Table 2 for a summary of differences between studies).

In all studies, participants were informed that they would be additionally compensated based on their performance on the tasks. This bonus payment mechanism was explained before the task. There were no manipulated variables and no blinding involved in any of the studies.

Statistical Approach

We used Pearson’s correlation coefficients and fitted linear regression models to test our hypotheses. Although our data have a multilevel nested structure (i.e., samples and choices nested in participants), for the sake of brevity, we decided to conduct all analyses on aggregated data (one raw score representing one participant) because we were mainly interested in the total gain and the overall number of choice problems solved. In regression modeling, we predicted total gain on the DfE task with the proportion of choices maximizing EV (i.e., EV sensitivity) and BNT score, controlling the sampling behavior (i.e., the number of samples drawn and switching ratio). All predictors were mean-centered. Analyses were conducted using the R statistical environment (R Core Team, 2020) and JASP statistical program (JASP Team, 2022).

Simulation study

In the simulation study, we tested the hypothesis that more suboptimal choices might lead to a better overall performance in a decision task (as measured by a higher total gain). We generated responses (i.e., dichotomous choices between two gambles) to 10 choice problems (see Table S1 in Supplementary Online Materials). The simulation was based on a sample of N = 300 subjects varying in their EV sensitivity (i.e., the probability of selecting a gamble with a higher EV; 0, .25, .5, .75, 1) in making 40 choices (drawn from a set of 10 choice problems with replacement). The simulation resulted in 60,000 observations.

First, we selected the first 30 choice problems for each subject to predict total gain. Fig. 2 (panels A and B) displays the total gain as a function of EV sensitivity (i.e., the probability of selecting a gamble with a higher EV) as well as EV sensitivity and the number of decisions, respectively. Clearly, with a fixed number of 30 choice problems to solve, higher EV sensitivity was positively related to a higher total gain (b = 63.15, p < .001, R² = .32). Second, we predicted total gain as a function of a varying number of decisions and EV sensitivity. Panel C in Fig. 2 clearly shows that a higher total gain is related to greater EV sensitivity (b = 62.61, p < .001) and more decisions made (b = 4.13, p < .001). The model explains R² = .55 of variance. Our main prediction is illustrated in Panel D (Fig. 2). We posit that when decision makers are informed about the total time available to make as many choices in the gain domain as they want, they can trade off the accuracy of their individual choices for the number of choices within a given time frame and make more suboptimal decisions, resulting in a higher total gain. To illustrate, “blue” decision makers (Fig. 2, Panel D) select a gamble with a higher EV in 75% of choice problems, leading to a higher total gain in 30 choice problems in comparison with “orange” decision makers. However, the “orange” decision makers make faster random choices with an EV sensitivity of .5 that allows them to make 40 decisions within the same fixed time frame, resulting in a higher total outcome. Such recurring irrational behavior can be adaptive in terms of maximizing the total aggregated payoff.

Empirical studies

We tested the predictions from the simulation in three empirical studies. All descriptive statistics and Pearson’s r correlation coefficients are presented in Table S2 in Supplementary Online Materials. A clear picture of the relationship between suboptimal choices and performance emerges across these studies.

In line with our preregistered hypothesis in Study 1, we found that when participants were presented with a fixed number of choice problems, better performance on the decision task (measured by a total gain) was related to their EV sensitivity (r = .266, p < .001, 95% CI [.166, .361]). Participants who maximized EV collected more points on the decision task. They also spent more time exploring choice problems (r = .106, p = .048, 95% CI [.001, .208]) and sampled more information (r = .125, p = .019, 95% CI [.020 .227]) on average. We found no evidence to suggest that people with higher numeracy earned more points on the task than those with lower numeracy (r = .014, p = .789, 95% CI [-.091, .119]). Nevertheless, we confirmed our other preregistered hypotheses suggesting that people with higher numeracy sample more information about a decision problem than their less numerate counterparts (r = .249, p < .001, 95% CI [.080, .283]) and are more likely to make choices maximizing the expected value (r = .176, p < .001, 95% CI [.072, .276]). These results corroborate previous findings and the predictions of our simulation study, indicating that a decision strategy based on extensive processing of a choice problem by investing time and effort results in more choices that maximize EV and, consequently, the final reward.

Studies 2 and 3 confirmed our prediction that recurring suboptimal choices result in superior decision making. In particular, we found negative relationships between total gain and the proportion of choices maximizing EV in Study 2 (r = -.236, p < .001, 95% CI [-.333, -.134] and Study 3 (r = -.355, p < .001, 95% CI [-.442, .260]), respectively. In other words, people who did not maximize EV and tended to make more random, suboptimal choices earned more money than those who followed the EV maximization principle. This effect can be explained by the fact that a higher total gain was determined by a greater number of decisions made (r = -.940, p < .001, , 95% CI [.926, .951] in Study 2 and 3), shorter mean time spent on solving choice problems (r = -.885, p < .001, 95% CI [-.906, -.860] in Study 2 and r = -.855, p < .001, 95% CI [-.881, -.825] in Study 3), and less effort dedicated to making a choice (as measured by the number of samples, r = -.630, p < .001, 95% CI [-.690, -.562] in Study 2 and r = -.285, p < .001 in Study 3, as well as a more chaotic exploration of gambles, r = .403, p < .001, 95% CI [.311, .488] in Study 2 and r = .368, p < .001, 95% CI [.274, .455] in Study 3). The results are plotted in Fig. 3.

In Study 2, numeracy was not associated with total gain (r = -.009, p = .875, 95% CI [-.114, .097]) or the number of decisions made (r = -.013, p = .807, 95% CI [-.119, .093]). However, more numerate participants were more likely to maximize EV (r = .151, p = .005, 95% CI [.046, .256]). When more numerate participants were provided with an additional contextual cue to highlight the time that has elapsed during the task in Study 3, the correlation between numeracy and the proportion of EV choices became nonsignificant (r = .006, p = .913, 95% CI [-.099, .110]), suggesting that the more numerate participants adapted to the new task conditions and switched to making fewer choices, maximizing EV. This observation is partially reflected in the correlations reported in Study 3. In particular, we found marginally significant correlations between numeracy and total gain (r = .100, p = .062, 95% CI [-.005, .202]; two-tailed) and the number of decisions made (r = .095, p = .0.74, 95% CI [-.009, .198]; two-tailed). These effects become significant when only extreme scores in the BNT (i.e., 0 vs. 4) are considered (r = .220, p = .020, 95% CI [.036, .389] and r = .188, p = .047, 95% CI [.002, .361], respectively).

We further investigated the predictors of superior decision making by fitting multiple linear regression models (Table 3).

Table 3

Results of linear regression modeling predicting total gain in the three studies

	Coefficient	B	SE	t	p		95% CI
Study 1	(Intercept)	135.76	1.64	82.59	<.001	***	[132.52, 138.99]
R² = .07	EV sensitivity	65.25	14.16	4.61	<.001	***	[37.4, 93.09]
	Numeracy	-0.93	1.40	-0.67	.506		[-3.7, 1.83]
	Number of samples	0.29	0.24	1.20	.233		[-0.19, 0.77]
	Switching ratio	6.03	7.34	0.82	.412		[-8.41, 20.47]

Study 2	(Intercept)	156.45	4.45	35.19	<.001	***	[147.7, 165.19]
R² = .42	EV sensitivity	-74.72	35.05	-2.13	.034	*	[-143.65, -5.78]
	Numeracy	2.49	3.64	0.68	.495		[-4.68, 9.66]
	Number of samples	-5.27	0.46	-11.58	<.001	***	[-6.17, -4.38]
	Switching ratio	57.83	18.71	3.09	.002	**	[21.02, 94.63]

Study 3	(Intercept)	173.90	4.88	35.67	<.001	***	[164.31, 183.49]
R² = .27	EV sensitivity	-248.84	42.06	-5.92	<.001	***	[-331.57, -166.12]
	Numeracy	12.49	3.94	3.17	.002	**	[4.74, 20.23]
	Number of samples	-0.35	0.14	-2.56	.011	*	[-0.62, -0.08]
	Switching ratio	133.99	19.41	6.90	<.001	***	[95.8, 172.17]

Note: EV sensitivity is the probability of selecting a gamble with a higher expected value.

In Study 1 (with a fixed number of choice problems), a higher proportion of EV choices predicted total gain (b = 65.25, p < .001). Crucially, when participants were allowed to trade off their decision accuracy for the number of decisions they could make in Study 2, EV sensitivity predicted total gain in the opposite direction (b = -74.72, p = .334). In other words, participants who were less likely to make choices maximizing EV earned more money on the decision task. Further, and contrary to the results of prior research and predictions of theoretical models (e.g., cumulative prospect theory; Tversky & Kahneman, 1992), people who put less effort into processing choice problems ended the study with a higher reward. Study 3 replicated the effect of suboptimal choices on superior decision making (b = -248.84, p < .001). Interestingly, by highlighting the temporal context of the task, this study revealed that numeracy was not related to EV sensitivity, and non-optimal choices made by numerate decision makers resulted in better overall performance (b = 12.49, p = .002).

Our results demonstrate that decision makers can adapt to the requirements of complex and ambiguous decision tasks. In contrast to predictions of normative/rational decision theory and findings from behavioral decision-making research, skilled decision makers were inclined to make more suboptimal choices (not those that maximize EV or expected utility), resulting in better overall performance than normatively better choices. Importantly, in contrast to the accuracy-effort tradeoff framework (Payne et al., 1993), we showed that adaptive decision makers employed less effortful strategies and not only approximated the accuracy of normative procedure (i.e., maximization of EV) but outperformed it.

These results are intriguing. Rational expectations based on probability rules, rational decision theory, and even common sense would suggest that optimal decision making results from selecting an option for which the sum of the outcomes weighted by the probability of their occurrence is the highest. In contrast, we found the opposite effect—individuals who made more suboptimal choices objectively outperformed those more likely to make choices that maximize EV. In light of contemporary psychological models, such behavior cannot be regarded as rational (Stanovich, 1999). However, philosophical considerations of truth may shed light on this issue and prompt a rethink of the criteria of good decisions (Hammond, 2000). For example, the decision-making process may be coherent with standards of rationality (e.g., people make consistent choices maximizing EV), decisions may correspond to facts (e.g., people select alternatives that appear to be the most beneficial based on experienced outcomes), and decisions may be pragmatic (e.g., they increase the likelihood of achieving personal goals (Dunwoody, 2009)). We believe that integrating these criteria to understand human decision making will contribute to theory development (e.g., it may help to explain discrepant conclusions between heuristic-and-biases (Gigerenzer et al., 1999) and ecological (Tversky & Kahneman, 1974) approaches in the field of judgment and decision making). Skilled decision makers who often perform better on the decision task should increase the chance of achieving their personal goals based on consistent and logical processing of available information about the decision problem while being aware of the constraints related to cognitive resources, temporal dynamics, task complexity, and the structure of the decision environment.

Superior or optimal decision making cannot be fully realized without considering the constraints associated with task characteristics (e.g., time pressure, uncertainty, opportunity cost) and human reasoning (e.g., resource limitation, cognitive thresholds). Unlike most prominent economic and psychological models in decision making, the concept of resource constraints (such as time) has gained sufficient attention in the field of applied sciences such as operations research, computer science, engineering, and health care. The framework that tries to find the best solution in light of the available constraints is known as constrained optimization. Similar to most decision-making models, constrained optimization entails maximizing an object function. However, the function is not just informed by decision variable(s) but also by constraint(s) (Sarimveis & Nikolakopoulos, 2005). For example, in a hospital, the main goal is to provide each patient with the best possible treatment. However, the severity of each patient’s condition is different, the hospital’s available resources are limited, and the benefits of the treatment vary across patients (Crown et al., 2017). Therefore, a hospital needs to prioritize and find a strategy to deal with the influx of mild and severe clinical cases to provide treatment while working under time, personnel, and budget constraints. Similarly, in the current study, participants could have chosen the normative solution (i.e., choose the option with a higher expected value), but each choice takes a significant amount of time. Therefore, when there is a time constraint, current normative models (maximization of expected value) cannot provide the optimal strategy to maximize overall reward. Similarly, theoretical models in behavioral ecology also incorporate constraints such as time or energy when predicting the optimal behavior of animals (Parker & Smith, 1990).

Since the studies of the current project employed only a limited set of choice problems in the gain domain (due to ethical issues), our findings cannot be directly generalized to the loss domain or other, non-lottery-based tasks. Monetary lotteries are to decision sciences what fruit flies are to biology (Bateman et al., 2007), that is, they allow testing the foundations of decision making in controlled laboratory settings. We believe that our chosen approach provides a promising starting point to test whether recurring suboptimal choices lead to superior decision making in real-life problems or in scenarios involving losses where skilled decision makers should be less likely to make more inferior choices.

Finally, we believe that our findings will prompt scholars interested in decision making to rethink the criteria of good decisions as well as provide the impetus for redesigning boosting or nudging interventions aimed at supporting good choices (Hertwig & Grüne-Yanoff, 2017). Individuals and policymakers should be aware that, at least under some conditions, recurring suboptimal choices can result in superior decision making.

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Data availability

Data and materials for all studies are available at https://osf.io/56xfa/

Code availability

Code for all studies is available at https://osf.io/56xfa/

Contributions

These authors contributed equally: Jakub Traczyk (JT), Dominik Lenda (DL).

J.T. and D.L. developed the concept of the research, programmed procedure, J.T., D.L., and S.M. analyzed the data wrote, reviewed and accepted the final version of the manuscript.

Acknowledgements

The current research was funded by the Ministry of Higher Education in Poland under Diamond Grant project No. DI2017011147 and the National Science Centre, Poland (Grant No. 2019/35/O/HS6/04026).

Competing interests’ statement

We have no competing interests to declare.

Table 2 is in the supplementary files section.

There is NO Competing Interest.

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Recurring Suboptimal Choices Result in Superior Decision Making

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