R2.1. What problem?

Two commentaries argue that the integration-related issues highlighted in the target article are either unproblematic or do not warrant a shift in practices.

Kellen, Cox, Donkin, Dunn, & Shiffrin (Kellen et al.) adopt an assertive stance, disputing our critique of the one-at-a-time approach on the basis that (1) it seems to be working in some domains (e.g., human memory), where theory and one-at-a-time experiments have accumulated to form a self-consistent and empirically validated body of knowledge; and (2) inconsistent results within a literature do not necessarily indicate a failure of the one-at-a-time approach, as they may have alternative explanations. For example, inconsistent results might arise from hidden preconditions or moderators, or from studying different phenomena not explainable by a common theory.

We acknowledge that an observed lack of integration across several domains of interest does not imply that successful integration cannot occur in principle, or even that it has not occurred in practice. We discussed this in the target article and offered examples of successful instances such as mechanism design applied to auctions. As noted in the target article, the one-at-a-time approach seems to work well in domains characterized by low causal density, but other factors could influence its effectiveness, such as experimenters' knowledge about the range of relevant parameter values, the plausible range of changes in the outcome, and the nature of questions being asked – whether technological (x can do y) or substantively theoretical (x is the mechanism that generates phenomena of interest y). For more discussion on this point, see the related discussion by Meehl (Reference Meehl1990) on why significance testing has worked sufficiently in agronomy, but not psychology.

Kellen et al. point to working memory as “an exemplary case” of a successful cumulative tradition, and indeed it is among the clearest examples of a field being able to better link results across one-at-a-time studies through reliance on shared experimental paradigms (e.g., free recall, the Deese–Roediger–McDermott (DRM) task, and change detection). But even this high-paradigm field has struggled with problems of integration. Consider Oberauer et al. (Reference Oberauer, Lewandowsky, Awh, Brown, Conway, Cowan and Ward2018), a paper cited by Kellen et al. as evidence of the field's wealth of empirical findings, which begins with a premise very much like our own: “Any mature field of research in psychology – such as short-term/working memory – is characterized by a wealth of empirical findings. It is currently unrealistic to expect a theory to explain them all; theorists must satisfice with explaining a subset of findings.” Oberauer et al.'s proposed solution was the curation of benchmark datasets, whereas the integrative approach might be reasonably thought of as the collection of benchmark datasets. A recent attempt to collect such benchmark datasets in the context of working memory by Huang (Reference Huang2023), which was explicitly inspired by the integrative approach we propose, has made considerable progress toward developing unified theories of working memory as a result (Suchow, Reference Suchow2023).

In response to the second point, the inability of the one-at-a-time approach to uncover preconditions and moderators and to delineate between theoretically (and empirically) distinct regions of the space is precisely the failure mode that Newell highlighted in his article, with which we introduced our target article. Therefore, what Kellen et al. see as alternative explanations to the failings of the one-at-a-time approach are what we see as downstream symptoms of the target article's central premises. A primary goal of the proposed integrative approach is to address these specific issues.

Baron contends that the one-at-a-time paradigm is concerned with demonstrating the existence of effects and causal chains, not their generality. However, if one accepts the notion that many of the social and behavioral phenomena are causally dense (“crud factor” by Meehl or “no true zeros” by Gelman), then it follows that almost every plausible hypothesized effect (i.e., X → Y relationship) exists to at least some degree, under some conditions, some of the time. If this is the case, then focusing on a single hypothesis and demonstrating its existence to at least some degree, under some (often unarticulated) conditions, some of the time, demonstrates nothing beyond what we already had good reason to believe. This line of reasoning is often used to criticize null hypothesis testing for theory evaluation: Anything that plausibly could have an effect will not have an effect that is exactly zero because of the high-causal density of our subject matter (Gelman, Reference Gelman2011; Meehl, Reference Meehl1967). In contrast, our argument in the target article is that experimental design should address two key questions: (a) how do the many plausible hypothesized effects contribute to the outcome of interest, both individually and in combination with other plausible hypothesized effects; and (b) how does this contribution vary depending on relevant contextual variables? This line of inquiry forms the core of the integrative approach to experiment design.

R2.2. The solution is already here!

Holleman, Dhami, Hooge, & Hessels (Holleman et al.) contest the lack of a realistic alternative to the one-at-a-time approach that could facilitate the integration of experimental findings. They point to “representative design,” a method introduced by Egon Brunswik about 70 years ago – nearly two decades before Newell's critique of the one-at-a-time approach. Representative design involves generating a sample of stimuli, either directly extracted from the environment or designed to retain its characteristics, to be representative of the population of environments to which the experimenter wishes to generalize. The integrative approach is indeed inspired by and builds upon Brunswik's representative design, which we cite in the target article. We identify at least two connections with his work. First, a frequent criticism of Brunswik's representative design revolves around the challenge of defining the universe of potential environments and formally sampling situations from it. The integrative approach directly addresses these challenges, as we discuss in the definition of the design space and sampling strategies (sects. 3.1 and 3.2 in the target article; sect. R3.2). Second, Brunswik's philosophy emphasizes sampling conditions from the agent's “natural environment.” This ensures that the conditions chosen for experimentation are representative of those to which the agent has adapted and to which generalizations would be applicable (this corresponds with the target article's Fig. 2C; what we call the region of ecological validity in the design space). While this strategy is suitable for certain scientific goals, we describe in section R3.2 other equally legitimate scientific pursuits that would involve sampling conditions that are either infrequently encountered or do not currently exist in the real world. Finally, we note that while representative design indeed bears some resemblance to the integrative approach, the former has not been widely adopted in the ensuing 70 years; thus, the need for an operational solution remains unmet.

R2.3. There is no hope

Mandel objects that many phenomena in social and behavioral sciences may exhibit such extreme causal density as to defeat any attempts to generalize; hence, the target article understates the severity of the problem. We discussed exactly this possibility, noting that when one “point” in the (latent) space fails to provide information about any other point (including, as Mandel posits, the same point over time; similar issues were raised by Olsson & Galesic), any kind of generalization is unwarranted due to extreme sensitivity with respect to contextual factors (including time). As we noted in the target article, such an outcome would be disappointing to many, as it would essentially vitiate the potential for generalizable theory in that domain; however, it would not invalidate the integrative approach. On the contrary, it demonstrates its potential to reveal fundamental limits to prediction and explanation (Hofman, Sharma, & Watts, Reference Hofman, Sharma and Watts2017; Martin, Hofman, Sharma, Anderson, & Watts, Reference Martin, Hofman, Sharma, Anderson and Watts2016; Watts et al., Reference Watts, Beck, Bienenstock, Bowers, Frank, Grubesic and Salganik2018). If true, it is surely preferable to characterize such limits than to indulge in wishful thinking and social science fiction. Moreover, applied research might still have merit, potentially by centering on the exact point (time, context, population) of interest (Manzi, Reference Manzi2012). This could yield reproducible social technologies even if not broad-based scientific theories. As we also note, however, such unforgiving cases are not a foregone conclusion. Rather, the extent to which they arise is itself an empirical question that the integrative approach is positioned to address. By conducting a sufficient number of integrative experiments across various domains, the approach could potentially lead to a “meta-metatheory” that clarifies under which conditions we can or cannot expect to identify generalizable findings.

R3.1. The feasibility of constructing a design space

Several commentaries challenge the first step of the integrative experimentation approach, arguing that constructing the “design space” (or “research cartography”) is practically difficult, if not theoretically impossible. Yet, some commentaries also offer possible solutions and suggestions.

Olsson & Galesic pose the important question: Where do the dimensions of the design space come from? They argue that drawing from past studies might lead to a biased representation of the true design space, influenced by implicit or explicit theories of the original researchers, methodological constraints, or adherence to a particular experimental paradigm. Clark, Isch, Connor, & Tetlock (Clark et al.) add that researchers may overlook certain dimensions that challenge their previous work, contradict their favored theories, fall outside their expertise, or stem from the list of “socially off-limits” – yet plausible – dimensions. Primbs, Dudda, Andresen, Buchanan, Peetz, Silan, & Lakens (Primbs et al.) note that excluding any factor from the design space could lead to the dismissal of integrative experiments' conclusions due to a crucial missing moderator. Such discourse gives rise to the question Shea & Woolley pose – “who decides what variables are included or receive more attention?” – and shares Tsvetkova's concerns that this approach could worsen existing inequalities and hierarchies within academia, which we discuss further in section R3.4.

Shifting focus from the source of the dimensions to the dimensions themselves, Gollwitzer & Prager argue that these dimensions are often theoretical constructs, and the various ways of conceptualizing and operationalizing them may potentially lead to very large (if not infinite) design spaces. Vaynberg, Hoffman, Wallis, & Weisberg underscore the problems posed by a lack of precise operative concepts in the social and behavioral sciences, which could lead different researchers to conceptualize the same dimension differently, thereby creating “conceptual incommensurability” across experiments that ostensibly deal with the same theoretical construct. Higgins, Gillett, Deschrijver, & Ross add yet another layer of complexity by pointing out that even with the same conceptualization of a dimension, researchers might employ different instruments for measurement, leading to “measurement incommensurability” across experiments. They also discuss the implications of the validity and reliability issues of these measurement tools on the integrative approach. Finally, Dubova, Sloman, Andrew, Nassar, & Musslick, as well as Necip Tunç & Tunç, voice concerns that committing to any predetermined list of dimensions could be prematurely restrictive, potentially stifling the exploration of new dimensions beyond that list.

In addition to raising concerns, our commentators also offer some solutions. Clark et al., as well as Amerio, Coucke, & Cleeremans, propose adversarial collaborations, wherein teams would include scholars who have previously published from multiple competing theoretical perspectives, possibly incorporating academics who study similar phenomena from various, even numerous, formerly competing standpoints. Requiring researchers to collaborate with theoretical adversaries would increase the likelihood of the research design space incorporating relevant dimensions. Rather than a winner-takes-all competition between seemingly contradictory hypotheses, this model would encourage exploration for genuine metatheories that clarify contexts in which different claims hold, resolving apparent discrepancies between leading scholars' favored theories. Primbs et al. propose consensus meetings, wherein researchers convene to discuss and commit a priori to the list of dimensions, their operationalization, and the validity and reliability of chosen instruments. Such a consensus would also cover the implications that the results of integrative experiments have for their hypotheses, making it more challenging to dismiss the conclusions drawn from these experiments. Complementing adversarial collaborations and consensus meetings, Katiyar, Bonnefon, Mehr, & Singh suggest a high-throughput natural description approach to tackle the “unknown unknowns” in a specific design space. This approach involves systematically collecting and annotating large, representative corpora of real-world stimuli, leveraging mass collaboration, automation, citizen science, and gamification.

We are sympathetic to the concerns raised and appreciative of the constructive suggestions. As we acknowledge in the target article, building the design space is not a solved problem, nor is it a single problem with a singular solution. In practice, the specific methods are yet to be worked out in detail and are likely to vary from one application to another, but adversarial collaborations, consensus meetings, and high-throughput approaches all seem like promising candidates. Fortunately, as we pointed out in the target article, the integrative approach does not require a design space with fixed, predetermined dimensions. On the contrary, the design space's dimensionality should remain fluid. For example, it can expand when identical points in the design space produce systematically varying results, indicating a need to actively search for an additional dimension to account for these differences. Alternatively, the design space can contract when experiments with systematic variations within the design space yield similar outcomes, suggesting that the dimensions in which they differ are irrelevant to the phenomenon of interest and therefore should be collapsed or omitted. In this way, concerns about misspecification, while reasonable, are not problematic for the integrative approach on their own. As we note in the target article, “the only critical requirement for constructing the design space is to do it explicitly and systematically by identifying potentially relevant dimensions (either from the literature or from experience, including any known experiments that have already been performed) and by assigning coordinates to individual experiments along all identified dimensions.” Beyond that, we are agnostic about the specifics and look forward to seeing how best practices evolve through experience.

We also note that the issues raised in most of these commentaries also apply to the traditional one-at-a-time approach. Employing an integrative approach does not change, for example, the imprecision inherent in the field nor does it make variation across a behavioral dimension any more infinite than it already is. Thus, while we agree that additional advances are needed and care should be taken in how we design and execute our experiments, we do not see the current state of affairs as a weakness of the integrative approach so much as a weakness of all empirical work.

R3.2. The challenge of effective sampling

As mentioned in the target article, efficient and effective sampling of the design space is a practical necessity given the limited resources available for conducting experiments. Vandekerckhove highlights an often-overlooked advantage of sampling from design spaces: Statistical efficiency. Efficiency can be achieved by increasing the number of sampled experimental conditions while decreasing the number of trials per experiment, thereby maximizing estimation accuracy, when the effect is heterogeneous (DeKay, Rubinchik, Li, & De Boeck, Reference DeKay, Rubinchik, Li and De Boeck2022).

The target article outlined different strategies and emphasized that the choice of the best strategy is goal-dependent. Holleman et al. and Tsvetkova note that some sampling strategies could select context and population combinations – or “environments” in Brunswik's terminology – that are not found or are impossible in reality, hence lacking ecological validity. They propose sampling following Brunswikian principles of representative design. Indeed, we agree that if the goal of research is to generalize results to the situations where the participant population functions, we can ensure ecological validity by selecting experimental conditions representative of those situations. It is worth noting, however, that what is considered ecologically valid or relevant can vary across populations, places, and periods, and thus representation of the “natural environment” can change. For instance, Salganik, Dodds, and Watts' (Reference Salganik, Dodds and Watts2006) experimental music market may be more representative of today's environment, with the ubiquity of online audio streaming services like Spotify and SoundCloud, than when the study was initially conducted. Thus, there is merit in sampling beyond what is considered representative of a specific population, place, time, or situation. Conditions change and can be changed; conditions that might not currently exist in the “natural environment” can still be the foundation for valuable technological and platform designs; for example, those that modify the “natural environment” of a digital social network platform to elicit desired behaviors from users.

Gollwitzer & Prager argue against random sampling from the design space, calling for strategies that acknowledge a hierarchy in the potential experiments' informativeness and discriminability. They propose prioritizing experiments that, either logically or theoretically, hold more importance over more peripheral ones. While incorporating such knowledge in the sampling strategy is compatible with the target article's proposed approach, we refer to Dubova, Moskvichev, and Zollman's (Reference Dubova, Moskvichev and Zollman2022) and Musslick et al.'s (Reference Musslick, Hewson, Andrew, Strittmatter, Williams, Dang and Holland2023) work, which examined the epistemic success of theory-driven experimentation strategies such as verification, falsification, novelty, and crucial experimentation, finding that if the objective is to uncover the underlying truth, random sampling proves to be a very robust strategy. We also note that adversarial collaborations and consensus meetings, proposed above, offer potentially useful mechanisms for aligning the sampling strategy with the research goal.

R3.3. Contemplating the nature of “theory”

In the target article, we posit that, much like the traditional one-at-a-time paradigm, the goal of integrative experiment design is to cultivate “a reliable, cohesive, and cumulative theoretical understanding.”

Several commentaries contest this claim about the integrative approach, suggesting it may be blindly empirical or even antitheoretical. In particular, many commentaries expressed discomfort at the suggestion that fitting a machine-learning model (such as a surrogate model within the “active learning” process) can generate or contribute to theory. However, as indicated by Devezer and reflected in those commentaries, there is no consensus on what a theory is or how to differentiate a good theory from a bad one. For instance, Gal, Sternthal, & Calder insist that theory should be expressed in terms of theoretical constructs, not variables. Devezer, as well as Hoffman, Quillien, & Burum (Hoffman et al.) and Smaldino demand theories to be mechanistic, identifying the underlying causal processes. Hoffman et al. stipulate that these mechanisms should be “well-grounded,” meaning they can be explained in terms of well-understood processes. Hullman call for better a definition of what makes a theory interpretable. Smaldino argues that individual theories should align with a broader collection of related theories and share a set of common core assumptions, while Baron advocates for theories with broad scope, reflecting diverse, often ostensibly unrelated phenomena. Vandekerckhove, Smaldino, and Olsson & Galesic call for more computational models and quantitative theories. Vandekerckhove adds that ideally, these would take the form of likelihood functions – functions that describe the probability of data patterns under a theory – over the method space, while Kummerfeld & Andrews argue for using causal-discovery artificial intelligence (AI) to generate multivariate structural causal models.

We empathize with these perspectives on the essential features of a theory. We acknowledge that theories can originate from various sources, including historical records, ethnographic observations, everyday anecdotal experiences, data mining, fitting a black box machine-learning model, constructing analytically tractable mathematical models, or simply thinking hard about why people behave as they do. Nevertheless, a theory's truth is not guaranteed by satisfying any or all of these features, or by the method of its generation. It is also not clear why any specific feature or process of theorizing should always take precedence over others. Indeed, when pressed, researchers who advocate these features for theories will likely assert a connection between the presence of their preferred features and the “success” of the theory in explaining existing observations and predicting unseen data. Hence, we view the following as the most inclusive criteria for what we expect from theories: They should (a) accurately explain observed experiment results and (b) make accurate predictions about unseen experiments. To be clear, we do not object to theories incorporating any other features. However, we argue that a theory's primary evaluation criterion should be its accuracy in predicting unseen experimental outcomes, including out-of-distribution and underintervention scenarios.

More broadly, the commentaries have caused us to reflect more deeply on our use of the word “understanding” when describing the ultimate goal of integrative experimentation. A better word would have been “explanation,” which we view as having two subgoals: (1) Providing an accurate representation of how the world works (emphasizing causality, generalizability, prediction, etc.), and (2) resonating with a human interpreter by evoking a sensation of understanding (emphasizing interpretability and sense making). We sense from some of the commentaries that these two goals are often conflated: Accurate theories are also the ones that make sense to a human interpreter. However, in our view these objectives are distinct in theory and often conflict in practice. This conflict stems from the high-causal density of phenomena under study, leading us to a situation where accurate theories (with robust out-of-distribution performance) may not satisfy our intuitive understanding due to their complexity – the number of factors and scale of their interactions. Conversely, understandable explanations are often incorrect, as simple theories cannot capture the complexity of the phenomenon. Perhaps what our commentators find objectionable about our approach is its preferencing of accuracy over sense making. In other words, the integrative approach is about theory, but it presents a version of theory that places second what many consider theory's primary purpose: Generating a subjective sense of understanding.

Looking ahead, we might have to embrace an era of machine-generated or machine-aided social scientific theories, especially if we prioritize accuracy over sense making in domains of high-causal density, a line of thinking we will explore further in future publications.

R3.4. Diversity and power dynamics

Shea & Woolley, as well as Tsvetkova, raised concerns that the integrative approach might centralize power among a small number of elite researchers and well-funded institutions, exacerbating existing inequalities in research. Shea & Woolley criticize our use of high-energy physics as an exemplar of successful large-group collaborations, noting that that fields requiring significant infrastructure investment tend to be more hierarchical and face significant issues such as sexual harassment and gender-participation gaps.

In response to these concerns, we provide two clarifications. First, while we agree that diversity, equity, and inclusivity must be first-order considerations in any scientific reform, we see them as distinct issues from the intellectual merits of the argument for an integrative approach. Second, there are several mechanisms to ensure that a diversity of perspectives is heard. In the target article (see sects. 5.7 and 5.9) we highlighted the ways in which the integrative approach could allow a broader range of contributors to be involved in the process of designing, conducting, and analyzing experiments. The suggestions raised in the commentaries – such as adversarial collaborations and consensus meetings (see sect. R3.1) – provide further opportunities for participation.

In general, the responsibility of facilitating wide-ranging contributions to science is a burden shared by the entire scientific community. The integrative approach offers a distinctive set of opportunities and challenges in our collective pursuit of this goal: It not only expands the ways in which researchers can contribute to and benefit from research, but also potentially introduces new social dynamics we have to navigate to ensure this potential is achieved.