Setting the space for deliberation in decision-making

Abstract

Decision-making models in the behavioral, cognitive, and neural sciences typically consist of forced-choice paradigms with two alternatives. While theoretically it is feasible to translate any decision situation to a sequence of binary choices, real-life decision-making is typically more complex and nonlinear, involving choices among multiple items, graded judgments, and deferments of decision-making. Here, we discuss how the complexity of real-life decision-making can be addressed using conventional decision-making models by focusing on the interactive dynamics between criteria settings and the collection of evidence. Decision-makers can engage in multi-stage, parallel decision-making by exploiting the space for deliberation, with non-binary readings of evidence available at any point in time. The interactive dynamics principally adhere to the speed-accuracy tradeoff, such that increasing the space for deliberation enables extended data collection. The setting of space for deliberation reflects a form of meta-decision-making that can, and should be, studied empirically as a value-based exercise that weighs the prior propensities, the economics of information seeking, and the potential outcomes. Importantly, the control of the space for deliberation raises a question of agency. Decision-makers may actively and explicitly set their own decision parameters, but these parameters may also be set by environmental pressures. Thus, decision-makers may be influenced—or nudged in a particular direction—by how decision problems are framed, with a sense of urgency or a binary definition of choice options. We argue that a proper understanding of these mechanisms has important practical implications toward the optimal usage of space for deliberation.

Introduction

Arguably the most important thing human beings do throughout their lives is make decisions. From William Shakespeare’s Hamlet, pondering whether to be or not to be, to Albert Camus’s famous “first problem” in philosophy, whether to commit suicide or not, writers and philosophers have pitched the essence of being human as a matter of making life-changing choices (see Lauwereyns 2010, for a comprehensive introduction). In a much more mundane fashion, we can note that our lives are filled with decision-making, from simple to complex, from trivial to important. To study decision-making scientifically, we need a principled approach that applies to all types of decisions—a theoretical framework that allows us to capture how humans make decisions, which is with inherent fallibility. We often make errors in ways that do not make sense from a strictly rational point of view. So, we need a unifying platform to investigate how we make our choices, and our errors, basically as a dealing with uncertainties.

One of the first and most influential of such frameworks was Blaise Pascal’s famous wager, positing that humans bet with their lives on the existence of God (included in Pascal’s Pensées of 1670; cf. Connor 2006). Draw a 2 × 2 table, with two alternative bets (your actions) and two mutually exclusive possibilities. You can bet that God exists, and live accordingly, or you can bet that He does not exist, and ignore any religious teachings. Meanwhile, logic dictates that only one of these two statements can be true: Either God exists, or He does not. Considering the four potential outcomes, and the values you might expect from them, Pascal argued in favor of betting on the existence of God. In uncertainty, rather than tossing up a coin or guessing, the seventeenth-century polymath pleaded for avoiding the worst error (landing in Hell for all eternity) and therefore accepting the proposal that God exists.

Regardless of whether Pascal was right, his train of thought and use of logic turned out to be a great inspiration, more in the fields of statistics and economics than in theology. Later, Bernoulli (1738|1954) refined the ideas, pointing out that the definition of expected value (as the product of gain and probability) is flawed, requiring a more subjective metric of utility (ultimately relating to pleasure or satisfaction)—ideas that take us to the twentieth-century notions of loss functions, risk functions, Bayesian procedures, expected utility maximization, et cetera (Wald 1939; von Neumann and Morgenstern 1944|1953). Ultimately, the logic remains rooted in Pascal’s, but the betting is done with more sophistication in the estimation of probabilities and what they mean for the decision-maker. An important addition to the framework is the notion of decision rules, that is, the introduction of criteria or thresholds.

Even today, most decision-making models in the behavioral, cognitive, and neural sciences typically consist of forced-choice paradigms like the one introduced by Pascal. Yet, our day-to-day experience with decision-making tends to be more complex and nonlinear. We usually make choices among multiple items, often with graded judgments, and without clear or absolute deadlines. In the present review, we explore how the complexity of decision-making in the real world can be addressed using conventional decision-making models by focusing on the interactive dynamics between criteria settings and the collection of evidence.

Threshold theory

The contemporary approach to modeling human decision-making took off in earnest with efforts in the field of experimental psychology (psychophysics or behavioral science), particularly Signal Detection Theory (Green and Swets 1966|1988) and its cognates (cf. Green 1964; Luce 1963, 1986; Luce and Green 1972). In essence, this work applied the logic of inferential or Bayesian statistics to human decision-making by imposing straightforward decision rules on probability distributions in the shape of thresholds that mark the boundary between two alternative responses. Figure 1a gives an example in which the boundary is placed exactly at the intersection point of the distributions. Faced with exactly two mutually exclusive possibilities, namely, either signal present or signal absent, Signal Detection Theory posits two respective probability distributions: the signal distribution (drawn in green in Fig. 1a) and the noise distribution (drawn in red in Fig. 1a). Here, placing the boundary at the intersection point can be interpreted as a form of rational decision-making, aimed at minimizing the likelihood of any kind of error. Accordingly, the decision to accept that “a signal is present” is made only if the likelihood that the signal is in fact present given the evidence reading E_x exceeds the likelihood that there is actually only noise given the same evidence reading E_x. Thus:

$$\begin{array}{cc}& \text{If}[\text{P}\left(\text{S}|{\text{E}}_{\text{x}}\right)>\text{P}\left(\text{N}|{\text{E}}_{\text{x}}\right)]\Rightarrow \text{''S''}\hfill \\ \hfill & \text{If}[\text{P}\left(\text{S}|{\text{E}}_{\text{x}}\right)\le \text{P}\left(\text{N}|{\text{E}}_{\text{x}}\right)]\Rightarrow \text{''N''}\hfill \\ \hfill \end{array}$$

Fig. 1.

Conceptual graphs of Signal Detection Theory. a Basic framework. As a function of the amount of evidence in a detector mechanism (e.g., a neural mechanism for visual processing), we can distinguish a probability distribution for cases when the signal is present (green distribution) versus when the signal is absent (red distribution). Decisions are made by introducing a threshold or criterion for the acceptance that a signal is present (indicated by the dotted line). If the amount of evidence exceeds the threshold, the decision-maker reports that the signal is present. If the amount of evidence remains below the threshold, the decision-maker concludes that there is no signal (i.e., the level of activity in the detector mechanism is attributed to noise). b As in A, with a different threshold. c Introducing a space for indecision in Signal Detection Theory. Rather than using a single threshold for decision-making as a function of the amount of evidence in the detector mechanism, we may introduce two thresholds with an intermediate zone of indecision in order to move beyond forced choice between two alternatives. d Follow-up on indecision by gathering more evidence. The introduction of an explicit zone of indecision invites sequential processing (turning Signal Detection Theory into a sequential sampling model). (Color figure online)

Decision-making, then, simply comes down to comparing the evidence reading against a threshold. Importantly, decision-makers may use different strategies, requiring either more or less evidence—setting a higher or lower threshold—before concluding that a signal is present. Figure 1b gives an example of a lowered threshold, requiring less evidence. Such a strategy may be reasonable when false negatives (calling “Noise” when there was in fact a signal) are costlier than false positives (calling “Signal” when there was in fact only noise; see more detailed explanation below).

The threshold theory of decision-making received surprisingly detailed corroboration through neurophysiological investigation. In a visual discrimination task, macaque monkeys were required to make saccadic eye movements in response to targets presented on the screen while the activity of frontal eye field neurons were being recorded (Hanes and Schall 1996). It was found that the initiation of a saccadic eye movement consistently occurred when the activity of the frontal eye field neurons reached a fixed threshold (around 100 spikes per second) even though the reaction time showed a considerable amount of variation. The variation in the reaction time was attributable to the growth rate in the frontal neuronal activation toward the fixed threshold. Applying the concepts of Fig. 1 to this finding, it means that the frontal neuronal activation reflects the detector mechanism that gives the amount of evidence, while the threshold was situated at 100 spikes per second.

The great merit of Signal Detection Theory is that it perfectly translates a 2 × 2 matrix of possible responses and possible stimuli (much like Blaise Pascal’s 2 × 2 matrix) into a set of characteristics of probability distributions relative to a threshold. Accordingly, we can now identify the origin of human errors. In Fig. 1a, an erroneous decision that a signal is present (or a false positive) occurs when, for a given evidence reading E_x higher than the threshold, the data point actually belonged to the probability distribution with the lesser likelihood (i.e., the noise distribution). Thus, the area of the noise distribution to the right of the threshold indicates the likelihood of a false positive. Conversely, an erroneous decision that there is only noise (or a false negative) occurs when, for a given evidence reading E_x lower than the threshold, the data point actually belonged to the signal distribution. Thus, the area of the signal distribution to the left of the threshold indicates the likelihood of a false negative.

With this framework it also becomes clear that we can consider two important influences on the process of decision-making (Lauwereyns 2010, 2018). The quality and the likelihood of responses are determined by where we set the threshold (see Fig. 1b). We can manipulate our responses to different levels of evidence, and so create response biases (Lauwereyns and Wisnewski 2006; Lauwereyns et al. 2002a,b; O’Doherty et al. 2017; Summerfield and Koechlin 2008). Note that there may be a variety of causes for response bias, not only preferences in terms of reward or reinforcement, but also prior propensities with respect to the choice options’ probability, accessibility, proximity, familiarity, et cetera (Lauwereyns 2010).

In Fig. 1b, by shifting the threshold to the left, that is, by requiring lower levels of evidence before we accept that a signal is present, we can create a response bias toward saying “signal present.” This reduces the likelihood of a false negative but increases the likelihood of a false positive. Such decision-making could be preferable if false negatives are considered particularly damaging (e.g., a medical doctor missing a case of cancer, which could lead to the death of a patient). Conversely, decision-makers might shift the threshold to the right, requiring more evidence before accepting that a signal is present, thus creating a response bias against concluding “signal present.” This may be a preferable strategy when false positives are considered particularly costly (e.g., in the case of false convictions in murder trials leading to capital punishment).

On the other hand, rather than manipulating the response biases, we can aim to change the signal-to-noise ratio. We can try to improve signal processing by making the signal more salient or easier to discriminate (Shadlen et al. 1996). Practical examples would include such actions as turning up the sound volume or wearing eyeglasses to see more sharply. Improved signal processing, or heightened sensitivity, may also be achieved by covert mechanisms of mental effort, selective attention or concentration (Bogacz et al. 2006; Carrasco et al. 2009; Martinez-Trujillo and Treue 2004; Maunsell and Treue 2006; Zhang et al. 2019). In terms of the signal and noise distributions, an improved ratio implies reducing the amount of overlap between the distributions, with means that are further apart (i.e., the distributions shift to the left or right on the horizontal dimension) and/or smaller standard deviations (i.e., narrower distributions). With less overlap, it is possible to set the decision threshold so that there will be fewer errors, both fewer false negatives and fewer false positives. Notably, however, improving the signal-to-noise ratio in the real world typically involves efforts at signal reception—efforts toward better sampling, or collecting more evidence. The longer the sampling, the better the signal-to-noise ratio. Time comes into it. Yet, in its original formulation, Signal Detection Theory does not incorporate the temporal domain. For any computational model to be relevant for human decision-making, the temporal dynamics must somehow be addressed.

Information seeking and the speed-accuracy tradeoff

In reality decision-making takes time. Even though decision-making is usually studied with forced-choice paradigms between two alternative options, in real time there must be a zone of indecision between the moment when a choice problem appears and the moment when the choice is made. As a corollary to this proposition, we note that, even in a forced-choice paradigm between two alternatives, the process of decision-making itself logically implies a third state, one in which there is (as yet) no selection between the two alternatives. Rather than glossing over this in the conventional atemporal scheme of Signal Detection Theory, in Fig. 1c we make explicit room for it by introducing a zone of indecision between two thresholds that each mark the required level of evidence for a particular choice option. The decision for “signal” is reached if the amount of evidence exceeds the green threshold, whereas the decision for “noise” is activated if the evidence reading falls below the red threshold. For evidence readings in between the two thresholds, the decision-maker remains undecided.

Effectively, the zone of indecision covers the evidence readings where there is a considerable amount of overlap between the signal and noise distributions. By introducing the non-committal option, the decision-maker can reduce the number of false positives as well as false negatives, albeit at a cost, with fewer correct signal and noise decisions. Furthermore, the introduction of the non-committal option invites a temporal perspective, connecting Signal Detection Theory to sequential sampling models. We can envision a stepwise protocol, in which, upon obtaining an evidence reading that falls in the zone of indecision, the decision-maker proceeds to seek more information (Dieterich et al. 2016). Then, with the extra information and the consequent revisions in the evidence readings, the signal and noise distributions might change, possibly leading to less overlap, or a reduction of uncertainty (see Fig. 1d).

Such a protocol would basically implement a speed-accuracy tradeoff (Heitz 2014). Seeking more information would tend to produce higher accuracy in decision-making at the cost of an increase in response time. This relationship between speed and accuracy is typically studied as a function of environmental pressures (or instructions by the experimenter), comparing decision-making under various levels of urgency (Kozma et al. 2007; Miletic and Van Maanen 2019; Reddi and Carpenter 2000). However, even when the decision-making is entirely self-paced, the notion of extended sequential sampling would only seem reasonable if the inherent cost of time is offset by a return in terms of increased accuracy. Thus, the investment of time will be one of the core aspects we can aim to control strategically toward optimal decision-making, that is, in meta-decision-making or deciding how to decide (Gluth et al. 2012, 2013). Before exploring the topic of meta-decision-making in more detail, it is already clear that the proper consideration of sequential sampling must move on from Signal Detection Theory to models that explicitly incorporate the factor of time. Signal Detection Theory, with its measures of bias and sensitivity, remains a useful framework to study behavioral response likelihoods in a relatively atemporal fashion, but to study response times, and to incorporate neural or behavioral correlates over time that reflect the decision process, we turn to more dynamic threshold theories.

A good place to start is the LATER model, or the Linear Approach to Threshold with Ergodic Rate, which offers the simplest possible linear model that incorporates time in the decision-making (Carpenter 1981; Carpenter et al. 2009; Noorani 2014; Noorani and Carpenter 2016). The LATER model makes abstraction of within-trial variation in the decision-making process, assuming that any variation in response times is due to random fluctuation between trials in the gradient of the linear approach. Figure 2 implements the linear approach concept in a diffusion or random walk framework with a lower and an upper bound (see Smith and Ratcliff 2004 for a comprehensive taxonomy of sequential sampling models). Figure 2a shows the basic framework with a horizontal dimension for time, and a vertical dimension for the approach to thresholds, here bounded by two alternative options (“Blue” or “Green”) as polar opposites of a single dimension of evidence readings. Figure 2b shows the detector mechanism in action, with a linear approach from the time of stimulus onset to the time when the threshold for “Green” is reached.

Fig. 2.

Sequential sampling in decision-making. a Basic framework. With continuous sequential sampling, we can turn the concept of evidence-based decision-making into a framework that incorporates the temporal dynamics and explains not only response likelihood but also response times. In this scheme, the horizontal axis represents time and the vertical axis represents the relative strength of evidence in favor of two alternative options (“Blue” or “Green”). The horizontal dotted lines represent the respective thresholds for the acceptance that a blue or a green signal is present. The vertical dotted line represents the onset of a stimulus. b Response time as an approach to a threshold. Assuming a linear model, the evidence accumulation by a detector mechanism would start at the moment of stimulus onset and finish at the time when a signal threshold is reached (in the illustrated example, the green signal), which is when the decision is completed, and the response activated. The time between stimulus onset and decision is the reaction time (RT). In the simplest version, RT depends on an intercept (or starting point) plus a rate of accumulation of the amount of evidence required to reach the threshold. In the illustrated example, the starting point for the accumulation is at zero, or equidistant from the two alternative thresholds, with equal values for both options (V_blue = V_green). c A change in the rate of evidence accumulation. Here, “Green” has a higher value than “Blue” (V_blue < V_green). One possibility in this case is that the detector mechanism gives higher weight to evidence for “Green,” leading to a higher rate of evidence accumulation in favor of “Green.” In the simple linear model of RT, this is reflected by a steeper gradient. d A change in the initial distance to threshold. It is also possible that the unequal value of options leads to a change in the starting point for the detector mechanism relative to the two alternative thresholds. The shortened distance between the starting point and the threshold for “Green” is shown as a shift of the threshold, while the starting point remains at zero; conceptually, however, this is equivalent to keeping a fixed threshold and shifting the starting point away from zero, toward the threshold for “Green.” It should also be noted that changes in the initial distances to the thresholds can co-occur with changes in the rates of evidence accumulation. (Color figure online)

In this framework, improved signal processing, or heightened sensitivity, is achieved through a steeper gradient of the linear approach, such that, without changing the threshold, responses can be made faster following improved signal processing (Reddi et al. 2003; Carpenter 2004). Figure 2c illustrates a change in sensitivity, as compared to Fig. 2b, particularly for a case when the green option has a higher value than the blue option. Conversely, in such a case of unequal values between the two choice options, there may be a response bias at work, favoring one choice option over the other even before stimulus onset (Lauwereyns and Wisnewski 2006; Summerfield and Koechlin 2008). Figure 2d illustrates how response times may be faster for the high-value option due to a change in the threshold level, with a shorter distance between the starting point and the required amount of evidence to initiate a response for “Green.”

In a linear model, however, any gradient for the approach mechanism that is not exactly zero should eventually lead to reaching a threshold, and even the slightest nonzero gradient immediately after stimulus onset necessarily determines the choice, with no possibility of a change of mind along the way (Resulaj et al. 2009). Yet, behavioral and neural correlates of decision processes show clear evidence of deliberation within trials, more akin to a random walk that can occasionally change direction (Krajbich et al. 2010; Lauwereyns 2012; Ratcliff et al. 1999, 2007; Redish 2016; Sen et al. 2020; Shimojo et al. 2003; Tejo et al. 2019; Zommara et al. 2018). Figure 3a shows such a random walk, or drift diffusion, in action, with an otherwise unchanged framework (Smith and Ratcliff 2004). Here, there is no guarantee that the random walk will ever reach either of the thresholds for “Blue” or “Green.” To deal with the risk of never being able to reach a conclusion, the model will have to include another mechanism that bounds the random walks.

Fig. 3.

A drift diffusion model with varying evidence accumulation. a Accounting for within-trial variability. Here, the evidence accumulation of the detector mechanism is seen to fluctuate, without actually reaching either threshold within the given time window. Thus, the decision-maker remains undecided. b Imposing a deadline on the drift diffusion. In the example, the deadline occurs at a time when the detector mechanism’s evidence reading is closer to the threshold for “Green” than to the threshold for “Blue.” Once the deadline is reached, the evidence accumulation is aborted. c Setting an earlier deadline on the drift diffusion. Depending on the definition of the choice options, the decision-maker’s action in response to the given evidence reading will change. In a two-choice definition (“Blue” or “Green”), the decision-maker will decide “Blue,” whereas in a three-choice definition (“Blue,” “Green,” or “Undecided”), the decision-maker will decide to remain “Undecided.” With a graded definition of the choice options, the decision-maker will give a more nuanced judgment, reflecting the relative strength of the evidence for “Blue” (depending on the precision of the answer scale; e.g., “73% in favor of Blue”). Finally, even when the decision-maker decides to remain undecided, it would be possible to either erase the evidence reading at the time of the deadline, or to encode the evidence in memory for later usage. d Collapsing boundaries. Conceptually, it is also feasible to represent the narrowing of the space for deliberation by dynamic shifts in the thresholds rather than by imposing a deadline. (Color figure online)

Meta-decision-making with a value-based equation

The process of decision-making itself will inevitably be shaped by boundaries, set by environmental conditions such as the competition for limited resources, the availability of multiple alternatives, and the inherent costs involved in terms of time and effort. This shaping of the process of decision-making can be addressed strategically by the decision-maker, in what may be termed “meta-decision-making” (Boureau et al. 2015; Dror and Langenburg 2019; Shenhav et al. 2017). Analogous to the concept of meta-cognition, meta-decision-making refers to making decisions about how to make decisions, principally with respect to the time and effort the decision-maker is willing to spend for information seeking (Bhui 2019; Gluth et al. 2012, 2013), the allocation of weights to different information sources (Afacan-Seref et al. 2018), the definition of the number and types of alternative options (Churchland et al. 2008; Gluth et al. 2018, 2020), and the weighting of these alternative options (Rigoli et al. 2017; Schultz 2013, 2015; Schultz et al. 1997).

Critically, we propose that such meta-decision-making can be regarded as a predictive, value-based exercise to constrain the process of decision-making toward minimizing adverse impacts from uncertainty (Clark 2013, 2016; Friston 2010; Friston et al. 2013, 2016; Hohwy 2013, 2017). Although at first sight the meta-decision-making might seem overly complex for computational modeling, we propose that the entire value-based equation ultimately comes down to setting the space for deliberation. This space for deliberation, in the framework presented in Figs. 2 and 3, reflects the closed space bounded by the vertical line for the onset of a stimulus, the upper and lower boundaries (the threshold for “Green” versus “Blue”) and second vertical boundary, that is, a deadline (see Fig. 3b, c)—either a self-imposed deadline, or a deadline imposed by environmental pressures. Closing the space for deliberation can also be achieved by allowing for dynamic changes in the thresholds (see Fig. 3d), a notion that is discussed in the literature in terms of “collapsing boundaries” (e.g., Hawkins et al. 2015; Tajima et al. 2016).

While we have already considered how the process of decision-making may be influenced by shifting the horizontal thresholds (creating response biases), here we note that the diffusion can be prevented from drifting interminably through the application of a deadline. The deadline would abort the information seeking and evidence accumulation.

More to the point, the way in which we apply a deadline will have a vast impact on the outcome of decision-making. For instance, as compared to Fig. 3b, the deadline is placed closer to the time of stimulus onset in Fig. 3c. With the drift diffusion moving as it does in the example, the decisions can vary markedly depending on when the deadline is set. If the set of potential answers is defined as a forced choice between “Green” and “Blue,” by computing the closest threshold given the evidence reading, then the decision should be “Green” in Fig. 3b, but “Blue” in 3c.

It should be noted that, conceptually, with respect to forced choices between two options, the function of a deadline is similar to that of “collapsing boundaries” (e.g., Hawkins et al. 2015; Tajima et al. 2016), as illustrated in Fig. 3d. In the given example, the collapse of the boundaries made it possible for the drift diffusion to reach the threshold for “Green.” Here, the urgency is not imposed by a separate mechanism but implied in the dynamics of the boundaries themselves. The discussion on collapsing boundaries proceeded from observations of time-variant decision-making in monkeys performing a random dot motion discrimination task (Ditterich 2006). Reanalyzing data obtained by Roitman and Shadlen (2002), Ditterich (2006) suggested that the monkeys optimized their reward intake by gradually increasing the gain of sensory signals over time. Thura et al. (2012), however, proposed an urgency-gating model to explain the growth of neural activity (see also Cisek et al. 2009). They suggested that, in naturally changing environments, the optimal policy for reward intake would be to estimate evidence by accumulating only novel information and to compare this to gradually decreasing thresholds.

Formally, one might consider a deadline to be a special case of collapsing boundaries, with abrupt total collapse of both the upper and lower boundaries. However, conceptually the two approaches may differ in one critical aspect. The notion of collapsing boundaries implies that decisions are made when the drift diffusion reaches a threshold. Instead, the notion of a deadline implies that the drift diffusion may be terminated without reaching a threshold. As such, the termination of the decision process by a deadline is compatible with alternative decision policies, beyond the forced choice between two options. For instance, the set of potential answers could be defined as [“Green”; “Blue”; “Undecided”]; if so, the same decision—to remain undecided—will be reached upon the moment of the deadlines in both Fig. 3b, c. With an option to remain undecided (an “opt-out option”), there may be no incentive to let the boundaries collapse. One interesting avenue for future research, then, is the prediction that time-variant decision-making with collapsing boundaries is likely to occur when the set of potential answers is strictly defined (or reinforced) as a choice between two options but not when the set explicitly leaves open a third option, to remain undecided.

In addition to the alternative decision policy with an opt-out option, the termination of the drift diffusion at a deadline also enables non-categorical decisions. For instance, the evidence readings could be translated to non-binary output, giving a relative or graded judgment. Finally, even if the decision is to remain undecided, the aborted evidence accumulation does not necessarily mean that the evidence is wiped or lost. Although Fig. 3b, c reflect the aborted processing by having the drift diffusion terminate at the deadline, it would be possible to encode the evidence reading in memory for later usage. This way, it would be possible to pause the decision process, and return to it later—potentially much later, as long as the evidence reading remains accessible in long-term memory.

The encoding of evidence readings in memory would make the decision-making more flexible and non-linear, such that the decision-maker could engage and disengage in the process of evidence accumulation over discontinuous periods of time (over days or months or even longer) while tending to other tasks in the meantime, or even while engaging in other decision-making processes. Conceptually, we can envision multiple decision processes occurring in parallel (i.e., multiple random walks of evidence accumulation toward thresholds in different dimensions or categories; Daw et al. 2005). Such parallel processes could be either interactive or independent, that is, they could impact on one another, or not. For instance, as an example of interaction, if the choice between “Green” and “Blue” (e.g., a green versus a blue sweater while shopping) is paused in a state of indecision at a self-imposed deadline, the decision-maker might end up making a decision in a different category (e.g., buying a book at the bookshop next to the clothes store) that impacts on the choice for a green versus blue sweater: With a depleted budget, the decision-maker might decide to move on from a paused state of indecision to a final rejection of both the “Green” and “Blue” options.

Clearly, along with the setting of evidence thresholds (the horizontal thresholds in Figs. 2, 3) and the definition of decision rules (2-choice; 3-choice with an explicit indecision option; graded; etc.), the setting of an internal deadline should be one of the main ways in which a decision-maker can influence the process of decision-making. To our knowledge there has been no empirical work yet to systematically explore how decision-makers set their internal deadlines under different decision policies—indeed, the present critique is primarily a call for such empirical research. Although there is a wealth of research on the speed-accuracy tradeoff and the investment of deliberation time under a fixed decision rule (typically a forced binary choice), researchers have not systematically compared how the deliberation time changes as a function of meta-decision factors with respect to how decisions are made—categorical or continuous, with or without an opt-out function, with different levels of advance commitment (“prejudice”), et cetera.

Here, we propose that the setting of internal deadlines, that is, the setting of deliberation time (Delib_time), involves at least four major factors: the decision execution time (Exec_time), the prior propensities (PriorProp), the economics of information seeking (InfoSeek), and the potential outcomes (PotentOut). Exec_time would be a non-weighted positive variable, reflecting the minimal time needed to simply execute the relevant response; the other variables would be weighted, and, together, would determine a compound that can be set strategically, but cannot be negative. The higher the values of InfoSeek and PotentOut, the longer Delib_time. In contrast, the stronger the PriorProp, the shorter Delib_time. Thus, as a preliminary hypothesis:

$${\text{Delib}}_{\mathit{time}}={\text{Exec}}_{\mathit{time}}+\left(x\text{InfoSeek}+y\text{PotentOut}\right)/z\text{PriorProp}.$$

We are fully aware that this hypothesis is just a first stab—but not entirely in the dark. First of all, the deliberation time cannot be shorter than the execution time. Also, evidence suggests that deliberation can continue while the motor processes of execution are going on; indeed, sometimes decision-makers change their mind during motor processes, suggesting that drift diffusion continues after response initiation and can lead to reaching the alternative threshold (Resulaj et al. 2009). Such changes of mind are more likely for lengthy or effortful motor executions (e.g., operating a manual switch) than during fast, near-ballistic motor executions (e.g., making an eye movement to a green dot). Thus, we include the factor of Exec_time.

Since Delib_time must be equal to or bigger than Exec_time the remaining factors are added as a compound. Below, we provide a brief rationale why we think the factors of prior propensities, the economics of information seeking, and the potential outcomes would co-determine the setting of deliberation time. For now, we note that, in the compound of these three factors, xInfoSeek and yPotentOut should contribute positively, whereas zPriorProp should contribute negatively. However, the compound as a whole should not be negative (it cannot lead to reduction of Exec_time). For this reason, we opt to place zPriorProp as a non-zero positive denominator in the compound. Finally, we suggest that xInfoSeek and yPotentOut are non-zero positive factors that operate independently. For this reason, we opt to define the numerator of the compound as an addition of xInfoSeek and yPotentOut.

Prior propensities

Response biases have already been identified as a major source of systematic variability in decision-making (Lauwereyns 2010). Typically, the cognitive and neural mechanisms of response biases are considered to alter the distance to the threshold for decision-making, either by lowering the required level of evidence for the favored option, or by pre-activating the neural representation of the favored option (Lauwereyns et al. 2002a,b). However, the existence of a prior propensity may also impact on the setting of the deliberation time. From the perspective of reinforcement learning and delay discounting, it seems reasonable to posit that, with an outspoken bias toward a particular option, the decision-maker would also be set to resolve the decision process as soon as possible in order to obtain the favored outcome (Scherbaum et al. 2018). The implication here is that, in addition to a biased starting point, the decision-maker will lean toward urgency, and so reduce the time for the collection of evidence that might run counter to the preferred outcome.

In line with the theory of predictive dissonance (Kaaronen 2018), as derived from the well-known concept of cognitive dissonance (Festinger 1957), the stronger the prior propensity, the more likely the decision-maker engages in methods of evidence collection that rig the process in favor of agreeing with the prediction. Such rigging of the decision process essentially comes down to the creation of a confirmation bias, which influences the subsequent information processing (Clark 2016; Ounjai et al. 2018, 2020). This might be done either by cherry-picking data that corroborates, or by preventing data from being considered. A self-imposed early deadline, in conjunction with a pronounced response bias, would be the most effective strategy toward ensuring that the preferred option ends up being chosen even if there is no new evidence to support it—even if, upon the arrival of the stimulus, the detector mechanism registers nothing but noise.

Indeed, as a thought experiment, we can consider an extreme case in which the decision-maker is predisposed in favor of one option to the point that the strategic compound in the deliberation time, that is, (xInfoSeek + yPotentOut)/zPriorProp, approaches the limit of zero. Thus, the decision-maker sets the deliberation time so that the deadline comes immediately after stimulus onset. In this case, without any collection of new information, and deciding on the basis of the relative strength of the (entirely pre-stimulus) evidence, the decision necessarily matches the response bias. More generally, we note that decision-making under urgency exacerbates the influence of prior propensities (Xu et al. 2020).

Experimental manipulations of prior propensities include likelihood (whether a type of stimulus is more or less likely to appear than another) and reward value. Also, factors such as familiarity, culture, and political preferences may determine prior propensities in value-based decision tasks. Such prior propensities can be assessed independently (e.g., via questionnaires) and then correlated with the setting of deliberation time in different decision tasks.

The economics of information seeking

Any confirmation bias operating through urgency will play off against the drive to seek information. As opposed to efforts toward translating prior propensities into decisions, we can see the economics of information seeking at work in the setting of deliberation time when decision-makers place value on new information (Howard 1966; Lawrence 2012). The economics of information seeking, in our formula reflected by the single term InfoSeek, exhibits a complexity that we are only beginning to understand. Classic, normative approaches to decision-making connected the value of information to its instrumental utility, as a means toward obtaining rewards or avoiding punishments. Obviously, valid, predictive information will be valued higher than invalid, unpredictive information, and so will invite more information seeking. However, in the last decade several lines of research have also shown that humans and other animals engage in information seeking that has no instrumental value, suggesting that information sometimes has intrinsic value, activating brain regions usually associated with reward processing (Bromberg-Martin and Hikosaka 2009; Brydevall et al. 2018; Iigaya et al. 2020). This non-instrumental information seeking, driven by curiosity, fluctuates in ways that have yet to be fully understood—the desire for knowledge can be highly selective and idiosyncratic (Gruber et al. 2014; Kidd and Hayden 2015).

A proper characterization of the economics of information seeking must incorporate both the instrumental and intrinsic gains offered by information, but that is only part of the equation. InfoSeek must also factor in any non-temporal costs of information seeking (Wittek et al. 2016). The temporal costs may be regulated directly in the setting of deliberation time (given that InfoSeek is positively correlated with Delib_time), but other costs such as money, effort, and risk incurred during the information seeking must also be integrated into the value of InfoSeek. Experimental manipulations of InfoSeek could include for instance the quality of information—whether it provides a signal that can be reliably extracted from noise, or whether it provides useful information (e.g., other people’s opinions about choice options; the opinions might be manipulated to be good or poor predictors of value). For poor-quality information, decision-makers would invest less time than for high-quality information.

Potential outcomes

The third major component in the setting of deliberation time would be the weight of the potential outcomes. On the one hand, the deliberation time itself should be regarded as a cost that, from a delay discounting perspective, should be minimized (Bogacz et al. 2006; Simen et al. 2009). Over time, the reward intake depends, among other factors, on the number of decisions that can be made (Khodadadi et al. 2014). As a baseline, reason tells us that it should be preferable to avoid procrastination in decision-making. As for the time that is being spent anyway, rational decision-making should tend toward investing more time on high-value (important) decisions than on low-value (trivial) decisions. By this account, given the same-level of volatility or noise in the evidence accumulation toward choice options, decision-makers would spend more time deliberating high-value choice options (e.g., when choosing one of two expensive cars) than low-value choice options (e.g., when choosing one of two pieces of cake). This also applies when the stakes are high in a differential sense, as when, under a given level of uncertainty, a correct choice leads to a big reward, but an incorrect choice leads to a big punishment. Such high-stakes decision-making would be given priority, with a longer deliberation time than low-stakes decision-making where a correct choice leads to a small reward, but an incorrect choice leads to a small punishment.

One way or another, the values of the potential outcomes must be integrated and included in the value-based exercise that sets the deliberation time (we gave this component the label “PotentOut” in the above equation). At present, the literature has yet to resolve how the potential outcomes of multiple options are valued in the decision-making process, either through divisive normalization (where each option is valued comparatively, taking the set of alternative options as a baseline; see Louie et al. 2011, 2013) or through a value-based attention mechanism (Gluth et al. 2020). Given that both very positive and very negative potential outcomes can raise the stakes, we suggest that PotentOut should track the salience of the choice options (i.e., the level of polarization relative to neutral; see Matsumoto and Hikosaka 2009, for a salience-tracking dopamine mechanism). Empirical research will be required to define the number of choice options that should be integrated: All the available options, or only the two most salient ones, or only the ones that are salient enough to attract attention.

The locus of control

In the discussion on the meta-decision-making with a value-based equation, we have proposed that the decision-maker sets the deliberation time as a function of prior propensities, the economics of information seeking and potential outcomes. In doing so, we have left open whether this process of meta-decision-making itself should be regarded as an explicit exercise, a matter of conscious, strategic control, or instead as an implicit exercise, a matter of unconscious, automatic control. As with the basic or primary level of decision-making, it may well be that both approaches coexist, as in model-based versus model-free reinforcement learning (Daw et al. 2005). To our knowledge, the question of the locus of control in meta-decision-making remains largely unaddressed. On the one hand, most research either imposes deadlines in decision-making tasks, preventing decision-makers from setting their own deliberation times, or the research limits the decision-making tasks to a single paradigm with fixed numbers of choice options and procedures. To the extent that researchers have discussed the tradeoffs between time and information processing, the focus has been less on the locus of control of how to set the tradeoff than on the computational characteristics of the tradeoff.

We propose that the question of the locus of control in meta-decision-making deserves to be investigated systematically. As one example, in a recent series of studies in our lab, on the evaluative processing of food images, we found that subjects changed their decision processes as a function of how the set of choice options was defined (Wolf et al. 2018, 2019). The choice paradigm consisted of a serial decision-making task, in which subjects were presented with food images from a database of 80 images. Each image was presented one by one until the subject had chosen 15 items. When the decision in each trial was defined as a binary choice (“Accept” or “Reject”), the subjects invested less time and considered fewer food items than when the paradigm was presented as a non-binary choice (“Accept,” “Reject,” or “Defer judgment”). Thus, the framing modulated the effort and level of processing during decision-making. In these studies, the framing as binary versus non-binary choices was kept constant in blocks of 80 trials. Possibly, the change in the subjects’ approach to decision-making happened not as a result of strategic control, but as an implicit, unconscious response to external influences—effectively, a type of nudging (Noggle 2018; Thaler and Sunstein 2008). We are currently investigating how more salient changes in framing affect the subjects’ approach to decision-making.

Along with the question of the locus of control in meta-decision-making, at present there has been little or no work on the question when meta-decision-making takes place—whether it occurs before or during the decision processes. Although the parameters for deliberation time should likely have initial settings before the decision processes, these might be adjusted during the decision. Particularly, the economics of information seeking may be monitored on the go, and so the weight of InfoSeek might change mid-deliberation, as a function of an evaluation of the process of information extraction. For relatively efficient information extraction, InfoSeek might be upregulated, whereas the investment in seeking information may be reduced if it turns out difficult to gain useful evidence.

In general, framing, nudging, any manipulation of the decision-making may have an enormous impact in real life when applied to policymaking, public discourse, and all aspects of health and wellbeing in society. Understanding exactly how and when decision-makers set the deliberation space and time for their decision-making is therefore not only a relevant question for basic research and theory. It has urgent, important practical implications because of its dual-use potential. Knowledge of how meta-decision-making works might be exploited unethically. Conversely, such knowledge in the right hands could be used to prevent exploitation and to optimize how people make their decisions.

Authors’ contributions

The two authors wrote the paper together and approved the final version.

Funding

This research was supported by KAKENHI project grant JP16H03751 from the Japan Society for the Promotion of Science to J.L.

Declarations

Conflict of interest

The authors declare that there are no conflicts of interest and no competing interests.