Invisible Hands and Fine Calipers: A Call to Use Formal Theory as a Toolkit for Theory Construction

Theories, target systems, and phenomena

Scientific theories have two characteristic functions: They explain and they represent. Theories explain phenomena: the robust, generalizable features of the world that we as scientists seek to understand (Bogen & Woodward, 1988; Haig, 2014), such as the Flynn Effect (Trahan et al., 2014), the matching phenomenon (Feingold, 1988), or the simple observation that some individuals experience recurrent panic attacks (Kessler et al., 2006). Much of psychological science is focused on establishing these phenomena, and many of the recent efforts to improve psychological science have focused on bolstering our ability to confidently conclude that genuine phenomena have been observed (Munafò et al., 2017; Shrout & Rodgers, 2018). These efforts are critically important to the progress of theory in psychology, as carefully established phenomena are a prerequisite for the development of theories to explain them.

Theories aim to explain phenomena by representing the components of the real world that give rise to the phenomena of interest. We refer to these components of the real world and the relationships among them as the target system (Elliott-Graves, 2014). We refer to the components of the theory and the relationships among those components as the theory’s structure. Among philosophers of science, there has been a growing consensus that representation is crucial to the practice of science (Bailer-Jones, 2009; Suárez, 2010). Theories can be understood as models that represent the target system (Suárez & Pero, 2019). As representations of the target system, theories allow us to engage in surrogative reasoning (Swoyer, 1991), using the theory to make predictions about the target system. Just as we can learn to navigate the streets of Paris by consulting a map that represents the city, we can learn about, predict, and even control what will happen in the real world by reasoning from our theory. Theories thus equip us to achieve our most fundamental aims in psychological science: the explanation, prediction, and control of psychological phenomena. To achieve these aims, we must develop theories that are sufficiently good representations of the target system that they allow for surrogative reasoning.

The “immense deductive fertility” of formal theories

The ability to engage in surrogative reasoning hinges on our ability to deduce from a theory how the target system will behave (e.g., how the components of the target system will evolve over time). Unfortunately, for most theories in soft psychology, it is difficult to make precise predictions about the target system’s behavior. The reason for this shortcoming is that most psychological theories are verbal theories: They express the structure of the theory in words and are thus limited by the imprecision of natural language (Smaldino, 2017). In contrast, formal theories express the structure of the theory in a more precise language, such as the language of mathematics (i.e., a mathematical model), formal logic, or a computational programming language (i.e., a computational model). By doing so, formal theories allow researchers to precisely deduce the behavior implied by the theory.

Example 1: a theory of panic attacks

Consider the vicious-cycle theory of panic attacks. Panic attacks are a robust phenomenon characterized by sudden and spontaneous surges of arousal and perceived threat that often seem to arise “out of the blue” (American Psychiatric Association, 2013). In a highly influential verbal theory, Clark (1986) posited that if some initial arousal-related bodily sensations (e.g., increased heart rate) are perceived as threatening (e.g., indicating a heart attack), that perceived threat will elicit more arousal, which, in turn, will exacerbate the sense of perceived threat, resulting in a vicious cycle that culminates in a panic attack. This verbal theory uses words to express the theory’s structure: positing two core components (arousal and perceived threat) with positive (amplifying) effects on one another. It asserts that the target system represented by this theory can give rise to spontaneous surges of arousal and perceived threat, thereby offering an explanation of panic attacks.

We can create a formal vicious-cycle theory by expressing this same structure using the language of mathematics. For example, we could use a difference equation to define how the state of arousal (A) evolves over time as a function of itself and perceived threat (T ): A_τ+1 = A_τ + α(νT_τ – A_τ), where α constrains the rate at which arousal can change and ν specifies the strength of a linear effect of perceived threat on arousal. Difference and differential equations are often used to model target systems in this way because they allow us to determine how the theory components will evolve over time (in discrete time for difference equations and continuous time for differential equations). For this model, if the product of ν and T is greater than the current level of A, A will increase at the next time step; if it is less than the current level of A, A will decrease at the next time step. If we define a similar equation specifying how perceived threat evolves as a function of arousal, these coupled difference equations provide us with a formal theory of the target system (see Appendix A for further details). We can then use this formal theory to deduce what we refer to as the target system’s theory-implied behavior: the theory’s prediction about how the components of the target system will evolve together over time.

In Figure 1, we present four possible formalizations of the verbal theory of panic attacks. ¹ In each, we define the two key effects in the system as being either linear or sigmoidal (note that these are only two of many possible forms this relationship could take). Alongside these effects, we also incorporated a regulating effect of homeostatic feedback on arousal that returns arousal to its baseline in the event that arousal becomes substantially elevated. The effect of homeostatic feedback was the same across each of the four implementations of the verbal vicious-cycle theory. We specified each of these effects as difference equations and implemented those equations as computational models using the R software environment (Version 4.0.2; R Core Team, 2020), thereby providing us with four distinct formal theories (see Appendix A). Using these formal theories, we are now able to precisely deduce the theory-implied behavior of the target system. That is, we can determine precisely how arousal and perceived threat will behave over time within an individual according to each formal theory.

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Fig. 1.

The verbal theory of panic attacks expresses the theory’s structure in words, positing a positive feedback loop between arousal and perceived threat. This structure can be expressed as a causal diagram, where solid arrows represent amplifying effects and dashed arrows represent dampening effects. The dampening self-loop on arousal represents the effect of homeostatic feedback on elevated arousal (see Appendix A). Because of its imprecision, the verbal theory can be interpreted in many ways. We present four possible formalizations, defining the effects of perceived threat on arousal as being either linear (a and b) or sigmoidal (c and d) and the effects of arousal on perceived threat as being either linear (a and c) or sigmoidal (b and d). We then simulated how an individual’s target system would evolve over time according to each formalization of this theory. We did so in two conditions. In Condition 1, we perturbed the system by inducing a specified level of arousal (0.50) at Minute 10 and evaluating how the system responded. In Condition 2, we did not perturb the system; rather, we incorporated stochastic variation in arousal to represent natural fluctuations in arousal arising from internal or external stimuli.

As seen in Figure 1, despite being an implementation of the same verbal theory, each of the four formal theories predicts different system behavior (for a similar illustration of this point from cognitive psychology, see Lewandowsky & Farrell, 2010, pp. 39–56). For example, consider the formal theory depicted in Figure 1a. In Condition 1, we induced a specified level of arousal (0.50 at Minute 10), with no direct manipulation of perceived threat. The system responded to this perturbation with a sustained moderate level of both arousal and perceived threat for the duration of the simulation. In Condition 2, we induced stochastic variation around a low mean level of arousal, representing natural fluctuations in arousal experienced throughout the day. The system responds to this stochastic variation with persistent and fairly severe oscillations in both arousal and perceived threat.

The formal theory depicted in Figure 1b predicts qualitatively distinct behavior. In response to perturbation (Condition 1), the system quickly enters a state of runaway positive feedback, leading to a surge of both arousal and perceived threat that subsequently subsides. In Condition 2, arousal fluctuates around a relatively low mean, and perceived threat remains largely absent for much of the simulation, interrupted by two sudden surges of arousal and perceived threat. Accordingly, despite being a faithful implementation of the same verbal theory, these two formal theories predict qualitatively distinct target system behavior, and only that presented in Figure 1b predicts behavior resembling that of a panic attack. It is thus impossible to deduce precisely what the verbal theory predicts because what it predicts depends upon information not specified in the verbal theory.

Notably, even if the verbal theory were expressed with greater precision, it would still be limited because it does not provide a means of deduction. For example, we can specify in words that there is a perfect linear effect of arousal on perceived threat and of perceived threat on arousal, thereby approaching the specificity of the formal theory depicted in Figure 1a. However, to deduce the behavior implied by this verbal theory, we are limited to performing some unspecified mental derivation or simulation. Typically, the accuracy of such mental simulations is unknown. However, in this case, we can compare the theory-implied behavior derived from our mental simulations with that derived from our computational-model simulations (see Fig. 1a). We encourage the reader to give it a try. In our opinion, it is prohibitively difficult to mentally simulate something resembling the actual theory-implied behavior, even in this very simple system. In a more complex system, mentally simulating the theory-implied behavior would be all but impossible.

A tool for thinking

Formal theories require an intimidating level of specificity. In the early stages of theory generation, psychologists may be reluctant to posit relationships with a level of precision that goes beyond what is known from empirical research. However, avoiding inaccuracies by remaining imprecise is detrimental to progress. Theories that are imprecise give an illusion of understanding and agreement by masking assumptions, omissions, contradictions, and other theory shortcomings (Smaldino, 2016). Formalizing a theory uncovers these shortcomings and, in doing so, clarifies how the theory can be improved. Further, formalizing theory instills a “scientific habit of mind,” forcing the theorist to think critically and carefully about all aspects of the theory and committing them to uncovering what remains unknown (Epstein, 2008; Muthukrishna & Henrich, 2019). Formalization thus acts both as a thinking tool and as a guide for future empirical research.

For example, we recently endeavored to formalize the vicious-cycle theory of panic attacks (Robinaugh et al., 2019). This effort revealed that there is little empirical guidance for specifying the precise form of these effects, emphasizing the need for further descriptive research on the relationship between arousal and perceived threat (Robinaugh et al., 2019). In the absence of clear empirical guidance, we were required to think carefully about the form of these relationships. For example, we posited that individuals can experience low-level fluctuations in arousal without elicitation of perceived threat, and we embodied this theoretical position by specifying a sigmoidal rather than linear effect of arousal on perceived threat (for an illustration, see Fig. 1b). Formalizing each causal effect posited by the theory in this way required us to think deeply about the nature of each of these relationships and made us realize the considerable amount of information about this target system that remains unknown (for further detail, see Robinaugh et al., 2019).

The value of formal theory as a thinking tool can similarly be seen in the agent-based model presented in the previous section (Conroy-Beam et al., 2019). Even in our cursory overview of this work, one is immediately struck by the rigorous thought that must be invested to specify each aspect of this model. By forcing theorists to think carefully and critically about each aspect of their theory, formalization can uncover questions previously unrecognized (e.g., how do we integrate information across traits when determining the attractiveness of a potential mate?). Further, by making each aspect of the theory explicit, formalization can reveal areas where theorists hold differing views, even when working from seemingly straightforward and well-understood verbal theories. In doing so, formalization provides opportunity for constructive disagreement among theorists on issues that may have been masked when working from verbal theories alone (for an example of such a disagreement from the matching-phenomenon literature, see Aron, 1988; Kalick & Hamilton, 1986, 1988). The act of formalizing the theory thus provides a vehicle for rigorous theory generation and sets the stage for subsequent theory development.

A tool for evaluating explanation

Formalization is not an end unto itself. It is the beginning of an ongoing process of theory evaluation and development. We believe the primary way a theory should be evaluated is by its ability to explain phenomena (Borsboom et al., 2021; van Rooij & Baggio, 2020). Typically, a verbal theory’s ability to explain a phenomenon is simply asserted. This is problematic because to demonstrate that the theory explains the phenomenon, we must first show that the phenomenon does indeed follow as a matter of course from the theory. In other words, explanation presumes accurate deduction (Hempel & Oppenheim, 1948). The deductive infertility of verbal theories thus substantially constrains their ability to provide clear explanations.

Consider again the vicious-cycle theory of panic attacks. Of the four possible formalizations of the verbal theory presented in Figure 1, only one shows that panic attacks follow from the theory. It is thus unclear whether the verbal theory explains panic attacks because the answer to that question depends on how one interprets and implements the verbal theory. In contrast, formal theories allow us to precisely deduce what the theory predicts, thereby strengthening our ability to evaluate what the theory can and cannot explain. For example, the formal theory presented in Figure 1a is a plausible interpretation of the verbal vicious-cycle theory, yet it fails to produce the characteristic surge of arousal and perceived threat from low-level variations in arousal. From this failure, we learn that the formal theory does not explain panic attacks. Where the verbal theory is imprecise and inconclusive, the formal theory is precise and wrong. Here again, we would argue that it is better to be precise and wrong than to be imprecise. Theories that are wrong move us forward, clarifying the direction we should (and should not) go in further developing the theory. When we arrive at a formal theory that does produce the phenomenon of interest (e.g., Fig. 1b), our confidence in that explanation is increased because the theory showed us, rather than merely told us, that it can account for that phenomenon. Formal theories thus provide a tool for evaluating what is perhaps the most important function of a theory: its ability to explain phenomena. Given this strength, we believe that theorists should operate under a simple guiding principle: “Don’t trust an explanation that you can’t simulate” (Westermann, 2020).

In the early stages of theory construction, we suspect that theorists will be best served by focusing on one or a narrow set of robust and likely qualitative phenomena to explain, such as the matching phenomenon (Borsboom et al., 2021; Haslbeck et al., 2019). However, it is critical that theory evaluation does not end there. Researchers should continue to evaluate the theory, investigating its explanatory breadth (i.e., the number of phenomena for which the theory can account) and explanatory precision (i.e., the specificity with which the theory can explain the phenomena of interest). This expansion in scope and precision is needed to guard against the possibility that the initial explanatory successes achieved by a formal theory are the result of “overfitting” the theory to a specific phenomenon. As the breadth and precision of explanation increases, the more confident we can be that the theory’s explanatory successes are attributable to its adequacy as a representation of the target system.

Evaluating a theory’s explanatory breadth can simply entail examining its ability to account for additional qualitative phenomena expected to arise from the target system beyond those the theorist initially set out to explain. However, to evaluate a theory’s explanatory precision requires that we move beyond visual inspection of qualitative theory-implied behavior (e.g., as depicted in Fig. 1) and focus instead on a comparison between two types of models. Empirical data models are any representation of data collected from the real world, such as a mean, correlation coefficient, latent factor structure, or any other summary of the data. Empirical data models are used in the appraisal of theories because data themselves are idiosyncratic, error prone, and subject to many causal influences beyond those that are of core interest (Bogen & Woodward, 1988). Theory-implied data models are these same representations of data (e.g., mean, correlation, and many other commonly performed statistical analyses) but use data that are deduced by the combination of our theory and our auxiliary hypotheses (for an extended discussion, see Haslbeck et al., 2019).

To illustrate this process, consider again the example of the matching phenomenon. The model of mating behavior developed by Conroy-Beam and colleagues adopted the maximize-attraction theory: Agents seek the available partner to whom they are most attracted (Conroy-Beam et al., 2019). To create a formal maximize-similarity theory, we adapted this model so that agents instead seek the partner whose level of attraction to the agent is most similar to the agent’s level of attraction to the partner. All other aspects of the original model were retained. To evaluate this formal maximize-similarity theory, we used the model to simulate the theory-implied target system behavior (see Fig. 2). We then used a set of formalized assumptions regarding measurement to produce theory-implied data and examined the correlation between an agent’s mate value (i.e., how attractive the agent is to members of the opposite sex in general) and the mate value of the agent’s partner, the same statistical analysis that Conroy-Beam et al. (2019) performed on their empirical data when examining the matching phenomenon. As seen in Figure 2, the maximize-similarity theory produces a strong positive association between an agent’s mate value and the mate value of the agent’s partner, thus demonstrating that it can indeed account for the matching phenomenon. However, there is some cause for concern. In empirical data collected by Conroy-Beam et al. from 45 different countries, the mean correlation between an agent’s mate value and the mate value of the agent’s partner across samples was r = .38 (see also Feingold, 1988). In contrast, the mean correlation across the simulations performed with the formal theory was notably higher (r = .64). Thus, although the theory can explain the matching phenomenon, it does not provide an especially precise account of the phenomenon.

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Fig. 2.

Formal theories can be used to precisely deduce the data models we should expect from our theory. First, the deductive fertility of formal theory is leveraged to deduce the theory-implied target-system behavior (e.g., how attraction and mate-selection choices play out across generations). Second, using a formalized set of assumptions about how the components of that system are measured, we can produce theory-implied data (e.g., calculating an overall mate value [MV] for each agent on the basis of their traits and the preferences of potential partners). Finally, we can analyze the data to produce a theory-implied data model using the same statistical analyses used in our empirical data. Here, we examined the correlation between an agent’s mate value (calculated as the euclidean distance from the agent’s traits to the average preferences of members of the opposite sex) and that of the selected partner; correlations were examined within a series of individual samples (each of 45 countries in which data were collected for the empirical data and each of 225 simulation iterations for the formal theory). By comparing the theory-implied data model with a data model derived from empirical data, we can gain insight into the adequacy of the theory as an explanation of a given phenomena and as a representation of the target system. Just as importantly, we can use any discrepancies between these data models to improve the theory, inferring the best explanation for the observed discrepancy and thereby identifying potential avenues for further theory development. Here, the theory-implied data model produced by the formal maximize-similarity theory demonstrates that the theory can account for the matching phenomenon: Agents with higher mate value tended to partner with other high-mate-value agents.

We next examined whether the maximize-similarity theory could explain additional phenomena related to mate selection. In their empirical data, Conroy-Beam et al. (2019) found that (a) individuals generally fulfill their mate preferences, (b) fulfillment is highest among those with high mate value, and (c) those with higher mate value tend to set their sights on partners with higher mate value (i.e., compared with people with lower mate values, people with higher mate values report that their ideal partner has higher mate value). As seen in Figure 3, the maximize-similarity theory fails to account for each of these additional phenomena, thus exhibiting limited explanatory breadth.

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Fig. 3.

A comparison between data models based on empirical data and the data models implied by two theories of mate selection for the maximize-similarity theory and maximize-attraction theory (for further information about the empirical data, see Conroy-Beam et al. (2019)). We compared theory-implied-data and empirical data models relating to four phenomena: (a) the association between an individual’s mate value and their partner’s mate value (i.e., the matching phenomenon); (b) the distribution of mate-preference fulfillment (0 = no fulfillment to 10 = complete fulfillment); (c) the association between an individual’s (or agent’s) mate value and their mate-preference fulfillment; and (d) the association between an individual’s mate value and their ideal-partner value. For all associations, the data were standardized within samples (i.e., individual countries in the empirical data; distinct iterations of the model simulations in the formal theories). The maximize-similarity theory accounts for the matching phenomenon (a) but fails to produce each of the other phenomena observed in the empirical data (b–d). In contrast, the maximize-attraction theory accounts well for each of the phenomena, although it does appear to overestimate the level of mate-preference fulfillment we should expect to see in the empirical data.

The maximize-attraction theory embedded in the original model by Conroy-Beam et al. (2019) fares much better (see Fig. 3). As expected, the theory produces a positive association between an agent’s mate value and the mate value of the agent’s partner, thereby demonstrating that the theory can explain the matching phenomenon (see also Conroy-Beam et al., 2019; Kalick & Hamilton, 1986, 1988). In contrast to the maximize-similarity theory, the maximize-attraction theory suggests a moderate association between these variables (mean correlation of r = .45), accounting reasonably well for the strength of this phenomenon. Furthermore, the maximize-attraction theory can provide an account for each of the additional phenomena we examined (see Fig. 3; see also Figs. 1 and 2 in Conroy-Beam et al., 2019). The maximize-attraction theory thus exhibits both greater explanatory precision and greater explanatory breadth, giving us more confidence that its explanatory successes are due to its adequacy as a representation of the target system. These relative merits of the maximize-attraction theory would have been missed had we focused our evaluation only on the matching phenomenon, especially if we had limited our evaluation to a null-hypothesis significance test. To better evaluate our theories, we must rigorously assess their explanatory breadth and precision, efforts that all but require formal theories.

A tool for measurement

A close examination of the simulation results presented in the previous subsection reveals that the explanatory shortcomings of the maximize-similarity theory arise, at least in part, because of how this formalized mate-selection strategy interacts with auxiliary hypotheses embedded in the model regarding reproduction. Because agents do not necessarily choose the most attractive mate available to them, mate preferences in future generations do not converge on the traits that are optimal for reproduction; thus, there is little relationship between an agent’s mate value and the mate value of their ideal partner. As Meehl would have noted (Meehl, 1978, 1990a), the discrepancy between our theory-implied data models and our empirical data models does not necessarily mean that our theory of mate selection has failed, only that the conjunction of the theory and our auxiliary hypotheses has failed. The fault may not lie in the formal theory, but in the auxiliary hypotheses. Formalization does not eliminate this fundamental difficulty in drawing inferences from explanatory failures (or failed hypothesis tests). However, formal theories do confer advantages in addressing this difficulty. By forcing us to explicate both the theory and our auxiliary hypotheses, formalization allows us to interrogate both and consider both as potential explanations for the inability to produce a phenomenon of interest. If we deem the auxiliary hypotheses implausible, we can revise them and investigate them. If we deem the auxiliary hypotheses well supported, we may conclude that the theory is indeed the most likely explanation for our observed explanatory shortcomings. It is thus critical that we formalize and critically examine not only our theory but also our auxiliary hypotheses.

Among these formalized auxiliary hypotheses, we believe formalized measurement warrants particular attention. In recent years, measurement in psychology has been critically appraised, leading some to call for more precise and transparent measurement practices (Flake & Fried, 2019; Fried & Flake, 2018). Formalizing measurement addresses these needs. Formalization requires that we specify precisely and transparently not only what variables are being assessed but also our assumptions about how those variables relate to components of the real world. In other words, researchers must specify the measurement function that links the component of the target system to the measured variable in the data (for an extended discussion, see Kellen et al., 2021).

Consider again the example of panic attacks presented in Figure 1. To determine what we should expect to see in an empirical study of perceived threat and physiological arousal, we must specify our assumptions about how people reflect on their thoughts and emotions when responding to our assessments (van der Maas et al., 2011). Do they report the average level of perceived threat over the specified time period? A weighted average that favors the moments immediately before the assessment? Or, as some research suggests, will their responses reflect the most intense perceived threat they experienced over the time window (Schuler et al., 2021)? Similar questions arise in our examination of mate-selection strategies. In our adapted computational model, we assumed that individuals can and do accurately self-report their traits. There is good reason to question this auxiliary hypothesis (Kenealy et al., 1991). To better derive theory-implied data would require us to consider the function that relates objective trait values with self-report trait values. The measurement assumptions we make will affect the data models we expect from our theories, and any misspecification of measurement functions has the potential to both reveal and mask differences between theory-implied data and empirical data models. For example, it is well known that in 2 × 2 factorial designs, not all interaction effects are robust against monotonic transformations (Loftus, 1978; Wagenmakers et al., 2012). This means that an interaction effect may be observed when adopting one measurement function, but not when adopting a monotonic transformation of that function. Our expectations regarding measurement will thus determine what we can learn from empirical data, not only in the approach proposed here but also in any effort to use empirical data to evaluate predictions made by a theory.

It is thus critical to make our assumptions about measurement transparent. Just as formalizing a theory reveals hidden assumptions and unknowns in the theory, we suspect that formalizing measurement will similarly reveal many hidden measurement assumptions and raise important questions about precisely what our data have captured. Formalizing measurement will thus strengthen what Meehl identified as the second pillar of good science: the “fine calipers” of precise experiments and accurate measuring instruments. Indeed, we believe that the comparison of theory-implied data models and empirical data models laid out in Figure 2 achieves what Meehl saw as the key to good science: joining together rich formal theories with precise measurement.

A tool for informing theory development

The process of comparing theory-implied data models and empirical data models closely resembles what Meehl referred to as a consistency test: a comparison between a theory-derived parameter value and the actual value of that parameter derived from empirical data (Meehl, 1978). However, there is a critical distinction between Meehl’s approach and the approach we wish to advocate here. Rather than using this consistency test with an eye toward refutation or corroboration of the theory, we propose that the consistency test be used as a tool for theory development, informing how the theory can be revised and refined (Haslbeck et al., 2019). That is, we propose that if a discrepancy between the theory-implied-data and empirical data models is observed, researchers should not necessarily abandon the theory; rather, they should consider the best explanation for the discrepancy and use this information to consider revisions to the theory that would bring it more in line with robust findings from empirical research.

For example, the maximize-attraction theory accounted reasonably well for a range of phenomena related to mating behavior (see Fig. 3), but there were limits to the theory’s explanatory success. The model overestimated the extent to which mates achieve their partner preference. In the empirical data, even high-mate-value individuals have limits in their ability to realize their ideal-mate preferences, whereas in the theory-implied data model, high mate-value individuals achieve near complete fulfillment (see Fig. 3). These limits suggest areas in which the theory or its auxiliary hypotheses could be further developed. One plausible explanation for the discrepancy is that the ability to fulfill one’s preferences may be constrained by the structure of one’s social network. In the theory we evaluated here, we assumed a fully connected network. That is, each agent had the potential to partner with every agent of the opposite sex. In computational models adopting more realistic assumptions about the structure of one’s social network, the strength of the matching phenomenon becomes attenuated as that network becomes more sparse, a decline driven by high-mate-value agents who are unable to partner with other high-value agents because of the constraints on their social network (Jia et al., 2015). Accordingly, incorporating more realistic assumptions about social network structure may allow the theory examined here to more precisely explain the empirically observed rates of preference fulfilment. We suspect that nearly all theories will benefit from an extended period of revisions and refinements such as this before being subjected to the kinds of “risky tests” advocated by Meehl. Accordingly, we regard the ability to inform theory development to be among the most valuable tools in the formal theory toolkit.

It is important to note, however, that there are unique challenges and unanswered questions about precisely how best to use data models to inform formal theories in this way. For example, it remains unclear how best to balance parsimony and explanatory breadth when revising a theory. For an extended discussion of how data models can best inform theory development, see Haslbeck et al., 2019. Here, one point is of particular importance. Theorists must be careful to ensure that the data models they are using to inform theory development are robust. Just as the hardest findings to explain are those that are not true (Lykken, 1991), the most misguided revisions to a theory will be those made to accommodate a data model that cannot be reproduced or replicated. The need for robust empirical findings to inform theory generation and development underscores that our call to strengthen theory construction is not in lieu of or at odds with calls to strengthen the empirical rigor of psychological science (e.g., Munafò et al., 2017; Shrout & Rodgers, 2018); rather, it complements these efforts by calling for similar rigor in the construction of psychological theories.

A tool for collaboration and integration

Finally, formal theories provide a tool for open and collaborative theory construction. The social psychologist Walter Mischel once quipped that theories are like toothbrushes: “No self-respecting person wants to use anyone else’s” (Mischel, 2008). We suspect this siloed development of theories “owned” by a specific theorist arises at least in part because verbal theories do not lend themselves to collaborative development. To know what a theory asserts, it is often necessary to consult with the theorist who, as noted, may themselves be uncertain about the specifics of his or her verbal theory. This slows development, failing to marshal the efforts of a wide range of theorists and limiting the domains of expertise brought to bear in developing a theory. This is especially problematic in psychology, where most phenomena straddle biological, psychological, and social realms. Further, it leads to a fractured theoretical landscape in which the theories within one domain play a limited role in the theories within another. Formal theories remedy these limitations by making the theory explicit, transparent, and expressed in languages used across domains of science. Formal theories are available to any theorists to advance, revise, or refute as they see fit and can be collaboratively developed by researchers across domains of expertise. Indeed, our ability to access, adapt, and evaluate the computational model of mating behavior developed by Conroy-Beam and colleagues is a clear illustration of the way in which formal theories support open and collaborative theory development. Furthermore, because formal theories are specified in a common language, they can be more readily integrated with other formal theories, and commonalities across theories may be more readily identified. Formal theories thus have the potential to support the integration of theories across domains and the development of theories that cut across multiple target systems (Muthukrishna & Henrich, 2019). In other words, formal theories set the stage for precisely the type of cumulative and integrative growth that Meehl wanted to see in psychology.