The Aggregation–Learning Trade-off
Organizational decision making that leverages the collective wisdom and knowledge of multiple individuals is ubiquitous in management practice, occurring in settings such as top management teams, corporate boards, and the teams and groups that pervade modern organizations. Decision-making structures employed by organizations shape the effectiveness of knowledge aggregation. We argue that decision-making structures play a second crucial role in that they shape the learning of individuals that participate in organizational decision making. In organizational decision making, individuals do not engage in learning by doing but, rather, in what we call learning by participating, which is distinct in that individuals learn by receiving feedback not on their own choices but, rather, on the choice made by the organization. We examine how learning by participating influences the efficacy of aggregation and learning across alternative decision-making structures and group sizes. Our central insight is that learning by participating leads to an aggregation–learning trade-off in which structures that are effective in aggregating information can be ineffective in fostering individual learning. We discuss implications for research on organizations in the areas of learning, microfoundations, teams, and crowds.
Organizational decision making that leverages the collective wisdom and knowledge of multiple individuals is ubiquitous in management practice, occurring in settings such as top management teams, corporate boards, and the teams and groups that pervade modern organizations. Numerous threads of the organization science literature have consequently sought to study how individual knowledge aggregates to the level of the organization. This work spans a range of topics, including organization design (e.g., Knudsen and Levinthal 2007, Christensen and Knudsen 2010, Csaszar and Eggers 2013), information processing (e.g., Turco 2016, Mack and Szulanski 2017, Joseph and Gaba 2020), crowds (Mannes et al. 2014, Mollick and Nanda 2016, Becker 2017, Felin et al. 2017, Keuschnigg and Ganser 2017), and collective intelligence (e.g., Page 2007, Woolley et al. 2010, Bernstein et al. 2018). Uniting much of this work is the recognition that the decision-making structures organizations employ, such as plurality voting or delegation, shape the effectiveness of knowledge aggregation.
In this paper, we argue that decision-making structures play a critical role beyond just shaping knowledge aggregation—they also shape the learning of individuals that participate in organizational decision making. If decision-making structures that better aggregate individuals’ knowledge are also better at facilitating individual learning, distinguishing between these dual outcomes of knowledge aggregation and individual learning would be unnecessary. There is, however, no ex ante reason to believe that these two outcomes operate in concert. Indeed, it may well be the case that decision-making structures that more effectively aggregate individuals’ knowledge may ultimately be less effective at facilitating the learning trajectory of individuals within the organization. Were this the case, it could give rise to the possibility of an aggregation–learning trade-off.
To explore this potential trade-off, we start with the observation that learning by individuals in the context of an organization differs from the traditional learning by doing. This is because, in a traditional learning-by-doing situation, an individual makes a decision alone by selecting from a menu of alternatives and garnering performance feedback on that alternative (e.g., Cyert and March 1963, Denrell and March 2001). By contrast, in an organizational context, an individual participates in the organization’s decision making by voicing a preferred alternative to the group, which then chooses an alternative based on the particular decision-making structure employed by the organization. We refer to this process of individual decision making in an organizational context as learning by participating. When individuals learn by participating, the alternative chosen by the organization does not necessarily correspond to the alternative favored by the individual, and, as a consequence, the individual receives performance feedback on the organization’s choice (and not necessarily on the individual’s own).
Learning by participating forces us to grapple with the recognition that decision-making structures may vary not just with respect to how effectively they tap into and aggregate individual knowledge (e.g., Sah and Stiglitz 1986), but also that they may vary with respect to how effectively they shape individuals’ learning. In order to understand the implications of learning by participating for the link between decision-making structures, aggregation, and learning, we proceed in two stages. First, we develop a theoretically grounded conceptual framework to characterize the organizational decision-making structures used to aggregate individuals’ knowledge to organizational decisions. Second, we employ a computational model of organizational decision making under uncertainty to compare organizations that vary with respect to different decision-making structures. In our analyses, we consider not only the structure of decision making itself, but also the role of organizational size (number of organizational members). Our model extends the canonical single-agent model of learning under uncertainty, the multiarmed bandit (e.g., Posen and Levinthal 2012, Puranam and Swamy 2016, Stieglitz et al. 2016, Laureiro‐Martinez et al. 2019), to a multiagent setting (e.g., Aggarwal et al. 2017).
The central insight of this paper is that learning by participating leads to an aggregation–learning trade-off: the efficacy of information aggregation and the extent of individual learning are inversely related. In other words, organizations that are more effective in aggregating information are less effective in fostering individuals’ learning. We find that this trade-off between information aggregation and individual learning exists across different decision-making structures as well as different organizational sizes (i.e., number of individuals participating in decision making). Because organizational performance over the longer term depends in part on how much its individual members learn, the trade-off between effective aggregation and individual learning translates into a short- versus long-term trade-off with respect to organizational performance. Organizations need to decide whether to adopt a decision-making structure and size that is effective in aggregating and performance in the short term or one that is effective in fostering the learning of its members and performance in the long term.
We find that at the core of this trade-off is the role of organizational contrarians: individuals who prefer alternatives other than those chosen by the organization. Different organizational decision-making structures draw on and shape the knowledge of contrarians in different ways. Decision-making structures that are most effective in aggregating individuals’ knowledge tend to marginalize contrarians. This marginalization process is akin to how, in the wisdom of crowds, incorrect estimates cancel each other out (e.g., in Galton’s (1907) famous ox experiment). By contrast, decision-making structures that are most effective in fostering individual learning leverage contrarians rather than marginalizing them: they allow contrarians to learn and allow other organizational members to learn from contrarians.
2. Theoretical Background
2.1. Learning by Participating: Bridging Experiential Learning and Information Aggregation
Our research bridges two research streams in the Carnegie School tradition that have developed mostly independently of one another: experiential learning and information aggregation.
The first stream, experiential learning, focuses on how performance feedback shapes beliefs about the merits of an agent’s choice alternatives and subsequent actions (e.g., Levinthal and March 1981, Miner and Mezias 1996, Greve 2003, Reagans et al. 2005, Denrell and Le Mens 2007, Argote and Miron-Spektor 2011, KC et al. 2013, Jaspersen and Peter 2017, Sengul and Obloj 2017, Clough and Piezunka 2020). An individual learns by doing as the individual makes a choice, receives feedback on that choice, and updates beliefs about the merits of the alternatives based on feedback. A basic assumption, which we relax in this paper, is that the agent receives feedback on the alternative the agent has chosen.
In parallel with this work on experiential learning, a second pillar focuses on the topic of information aggregation in organizations. This work has its intellectual roots in Simon’s (1947) view of the organization as an information-processing system. Scholars in this stream have built on Sah and Stiglitz (1986) to examine the link between structures of decision making and organizational outcomes (Knudsen and Levinthal 2007, Christensen and Knudsen 2010, Csaszar 2013) as well as the ways in which structure shapes how individual-level knowledge aggregates to shape organization-level outcomes (e.g., March 1991; Argote et al. 2003; Reitzig and Sorenson 2013; Piezunka and Dahlander 2015, 2019; Reitzig and Maciejovsky 2015; Criscuolo et al. 2017; Keum and See 2017; Aggarwal et al. 2020; Davis and Aggarwal 2020).
These two pillars—experiential learning and information aggregation—have evolved somewhat independently. The information aggregation literature has had as its primary focus the question of how organizations can tap into and aggregate the knowledge of individuals with the (often implicit) assumption that individuals’ capacity to learn is limited.1 With a few exceptions in which scholars have studied learning among interdependent individuals (Knudsen and Srikanth 2014, Puranam and Swamy 2016, Aggarwal et al. 2017), the literature on experiential learning has generally tended to abstract away from organizations’ decision-making structures, instead conceptualizing organizations as unitary actors (e.g., Levinthal 1997, Posen and Levinthal 2012).
Taken together, these two streams of literature collectively point to the theoretical merit of studying how organizational decision-making structures shape the trajectory of experiential learning by individuals and whether this then leads to an aggregation-learning trade-off.2 By examining this issue, we complement prior work at the intersection of individual and experiential learning in the context of issues such as social learning (e.g., March 1991, Denrell and Le Mens 2007, Fang et al. 2010) and learning with task decomposition (e.g., Knudsen and Srikanth 2014, Puranam and Swamy 2016, Aggarwal et al. 2017). Our point of departure is the recognition that, even in the absence of social learning and task decomposition, there is a fundamental but as yet unexplored dynamic relation between the design of organizational decision-making structures, the efficacy of information aggregation, and the extent of individual learning.
2.2. Conceptualizing Different Decision-Making Structures in Organizations
We consider four organizational decision-making structures that reflect the broad spectrum of structures discussed in prior work and used in practice. In considering the behavioral plausibility of these decision-making structures, we note Csaszar and Eggers’ (2013, p. 2262) observation that although “there are an unlimited number of potential decision-making structures to study,” the ultimate choice is driven by prevalence in real-world organizations.
We consider four decision-making structures that are well known in practice—in boards, committees, teams, and political democracies. Plurality voting is the structure in which the alternative that gathers the largest number of participants’ votes becomes the organizational choice. It is used in many social and organizational situations (e.g., most U.S. elections and voting by boards of directors). Two-stage voting is the structure in which, in the first stage, the two alternatives gathering the most votes are selected, and then in a second stage, participants vote only on these two, with the alternative garnering the most votes in the second stage becoming the organizational choice. This structure is common in organizational settings in which a large set of alternatives is whittled down by first-stage voting to create a short list, and a subsequent vote is made to select from that list. It is also common in electoral systems (see, e.g., Fishburn and Gehrlein 1976). Average beliefs is the structure in which the beliefs of all participants regarding the value of each alternative are averaged. This creates a notional individual who makes decisions on the basis of the average beliefs across alternatives (Hastie and Kameda 2005, Csaszar and Eggers 2013). Each member of the team rates each alternative, averages for each alternative across individuals are calculated, and the alternative with the highest average is then the organizational choice. Finally, rotating dictatorship is a form of hierarchical delegation of authority to a single individual (Bodily 1979) in which decisions are delegated to randomly selected individuals over time (Gibbard 1977, Barberà et al. 1991, Chatterji et al. 2014). Although delegation is common, randomness in delegation is less common although it was used in ancient Athenian democracy (Ober 2009) and recently used in the Belgian political system.3 It has also been observed in the context of interfirm collaborations (Davis and Eisenhardt 2011).4,5
To understand the implications of learning by participating, we require a theoretically grounded conceptual framework to characterize these structures. We use the literature on social choice as an anchoring point to develop this framework. We think of decision-making structures as a mapping from individual-level beliefs to an organizational-level choice. The basic structure articulated by Arrow (1951), which continues to be the basis of much research, is that “inputs are messages of judges or voters and [the] outputs are the jury or electoral decisions” (Balinski and Laraki 2007, p. 8720, emphasis added). Our conceptual framework distinguishes among the input side of the decision making with decision-making structures differing along two dimensions as depicted in Figure 1.
The first dimension of the input side of our conceptual framework is that each individual’s beliefs are transformed into “messages” that are transmitted to the organization (Balinski and Laraki 2007) as depicted on the x-axis in Figure 1. In our setting, a message is the information of individuals’ beliefs (i.e., utilities, preferences, etc.) about the merits of the alternatives. For example, a message can take the form of a ballot in a group decision-making setting. Depending on the structure, it may include the name of the alternative for which the individual votes or the full list of the individual’s beliefs across the alternatives. We consider only monotonic (i.e., rank preserving) transformations. The transformation can be minimal (indeed, none) as in the case of the transmission of individuals’ raw (untransformed) beliefs, which is the basis of the average beliefs decision-making structure. A major transformation, as in the plurality voting decision-making structure, is one in which an individual’s highest belief across alternatives is coded as one and all others as zero. This transformation is lossy in an information-theory sense. In between these two extremes are different forms of rank ordering transformations (Fishburn 1974). For instance, the two-stage voting decision-making structure (sometimes called “majority runoff” or “double plurality”) uses a binary transformation of beliefs in the first round and another binary transformation in the second round on the two alternatives not eliminated (Fishburn and Gehrlein 1976).
The second dimension of the input side of our conceptual framework is that each individual’s message may or may not be included as an input into the organizational decision. We depict this on the y-axis in Figure 1. Individuals’ messages transmitted to the organization may be assigned different weights. When each individual is weighted the same, we describe this as balanced weighting. When the weights differ across individuals, inclusion is unbalanced. Although there is, of course, a large set of potential weighting systems, we consider only decision-making structures in which weights are binary. One can think of individual inclusion in organizational decision making as delegation of the decision to a subcommittee of individuals that includes or excludes certain individuals from the organizational decision (Csaszar and Eggers 2013).6
The output side of decision-making structures is the aggregation of the messages of individuals included in decision making. We consider an output function that is common to all four decision-making structures we study. We assume the organization sums each individual’s message on each alternative, adjusted by each individual’s weight, and then chooses the alternative that has the maximum score.7
3.1. Model Overview
We envision a setting in which an organization chooses among a fixed set of independent alternatives over time. The challenge faced by the organization is that the alternatives are of uncertain merit.8 Performance feedback from selecting an alternative is imperfect and noisy, and as such, one learns from experience with a particular alternative only slowly and imperfectly. Each individual in the organization has beliefs about the merits of the alternatives that evolve over time and voices those beliefs as an input to organizational decision making across time.
Our model builds on the single agent (unitary actor) multiarm bandit model, the canonical representation of learning under uncertainty (Sutton and Barto 1998, Denrell and March 2001, March 2010, Posen and Levinthal 2012, Baumann 2015, Puranam and Swamy 2016, Stieglitz et al. 2016, Laureiro‐Martinez et al. 2019). There are two key individual behavioral assumptions in the model: reinforcement learning from performance feedback and the opportunity to explore across the set of choice alternatives. The literature suggests that the bandit model provides a good representation of the psychological processes underlying individual learning under uncertainty. As Puranam et al. (2015, p. 342) note, the bandit is appropriate in settings in which choices involve “discrete alternatives with uncertain and unknown outcomes” together with subjective beliefs about these alternatives that evolve over time through reinforcement learning. In the management literature, the bandit is employed to model responses to environmental turbulence (Posen and Levinthal 2012), the formation of organizational routines (Aggarwal et al. 2017), risk taking (Denrell and March 2001), and agency considerations (Lee and Puranam 2016). Not all decision-making contexts are characterized by this model. For example, work on learning via adaptive aspiration reflects a different decision-making context (Levinthal and March 1981) as does work on learning under complexity, particularly characterized by the NK model (Levinthal 1997, Rivkin and Siggelkow 2003, Adner et al. 2014, Rahmandad 2019).
The single-agent model is an analogy to a slot machine with multiple “arms.” Each arm reflects a choice alternative that has a fixed probability of yielding a reward (success) in a given period. The reward probabilities associated with the arms are, ex ante, unknown to individuals. Individuals have beliefs (priors) about the merits of each of the arms. They seek to enhance their decision making by learning about the merits of the arms: sampling arms and receiving performance feedback in the form of success or fail outcomes. The goal for an individual is to identify a high-performing arm, just as a gambler may seek to learn about the various slot machines in a casino in order to find a high-payoff machine.
We extend the standard single-individual bandit model to consider an organization consisting of multiple individuals. In the organizational setting, individuals’ beliefs about the merits of the choice alternatives are the inputs to organizational decisions. Individuals’ beliefs are aggregated into organizational decisions based on the specifics of the decision-making structure in use (per the details outlined in Section 2.2 and Figure 1). Individuals learn by participating. That is, all individuals in the organization get feedback on the organization’s choice, and they each update their beliefs on that basis.9
3.2. Individual Beliefs, Organizational Choices, and Individual Learning
The task environment faced by the individuals in an organization consists of N choice alternatives. Each alternative is Bernoulli in that the reward to choosing an alternative is either success (reward = 1) or failure (reward = 0) with probability . These probabilities, which are ex ante unknown to the individuals, remain fixed over time.
An organization consists of M individuals. Each individual holds a vector of beliefs about the payoffs from the alternatives with indices for individual i, time period t, and alternative n. Individuals are endowed with initial beliefs (priors) when they join the organization. These initial priors are developed in a prejoin learning phase of g periods. Each individual starts the prejoin phase with uninformed beliefs in the sense that each alternative is believed to have a payoff probability of 0.5. They then engage in individual learning about the alternatives for the duration of the prejoin phase by sampling alternatives in a highly exploratory manner and receiving feedback on their choices. If the prejoin period is of length g = 0, then individuals’ initial beliefs at the start of organizational decision making are identical and uninformed. As g increases, individuals’ initial beliefs become more accurate with respect to the true payoff probabilities . At low to intermediate levels of g, individuals’ priors when they join the organization are informative about the true payoff probabilities, but they hold a diversity of beliefs with, for example, some individuals overestimating the value of low-performing alternatives and others underestimating the value of high-performing alternatives.
In the usual bandit model setup, the extent of exploration is controlled by the temperature parameter τ. Higher τ leads to greater exploration. The Softmax function maps an individual’s beliefs of payoff probabilities for each alternative, , which are each in the range (0, 1) to choice probabilities such that (Luce 1959).
The organization aggregates individuals’ beliefs to an organizational decision based on a decision-making structure. The M individuals’ beliefs in a given period, , are the basic inputs to organizational decision making. The beliefs are transformed into messages. In the plurality voting decision-making structure, each individual transforms these beliefs in a binary manner such that the alternative with the highest belief is one and the others are set to zero. In this decision-making structure, individual inclusion is balanced, so each individual has equal weight in the organizational decision. The output of decision making results when the organization sums the individuals’ messages on each alternative and chooses the alternative with the highest value. Two-stage voting is similar to plurality voting, but the input and output of decision making occurs twice: the full set of alternatives is considered in the first round, and the top two alternatives are considered in the second round. The average beliefs decision-making structure functions as plurality voting does but without any message transformation. Finally, rotating dictatorship is like plurality voting but with highly unbalanced individual inclusion; in each period, one randomly selected individual is assigned a weight of one and all other individuals are weighted zero.
Individual learning occurs when an alternative chosen by the organization is implemented, the outcome is observed by all individuals in the organization, and individuals update their beliefs based on performance feedback. An individual’s belief about the payoff probability of an alternative at a given point in time is the average, including the initial prior, of the observed rewards for a given alternative (March 1996). When individual learning is absent, individuals do not update their beliefs; thus, their initial priors are stable across time.
We focus on two key metrics of performance. Organizational performance in a given period is the payoff to the alternative the organization selects in that period. Individual learning is based on the change in individual efficacy over time. Individual efficacy in any given period is the performance an individual would realize if, based purely on the individual’s own beliefs at that time, the individual were to choose the alternative the individual believed to be best. Individual learning over a time window is the difference in an individual’s efficacy from the start to the end of the window.
3.3. Model Parameter Settings
In our analysis, we consider organizations of M = 1, 3, 5, 7, and 9 individuals. The task environment consists of five alternatives that vary in their performance. Specifically, these five alternatives have expected payoffs with probabilities 0.3, 0.4, 0.5, 0.6, and 0.7. The prejoin period, in which initial prior beliefs are formed, is five periods. Exploration is set to a level of τ = 0.01. In later analysis, we examine robustness to a wide range of alternative parameter settings. Each simulation runs for 200 periods, and we run each simulation 10,000 times.10
In this section, we exercise the model. We demonstrate the trade-off between the efficacy of information aggregation and the extent of individual learning. In particular, we start by examining the implications of individual learning for the efficacy of different decision-making structures and how these decision-making structures impact the extent to which individuals learn. We then turn to an analysis of the mechanisms underlying these results.
4.1. Organizational Performance and Individual Learning Across Decision-Making Structures
4.1.1. Organizational Performance Across Decision-Making Structures.
We first examine how organizational performance varies across decision-making structures of different types and organizations of different sizes. In doing so, we show that decision-making structures that are relatively effective in the absence of learning are relatively ineffective in the presence of individual learning. The results are reported in Figure 2, (A) and (B). Figure 2(A) reports results as an average across organizations of different organizational sizes; Figure 2(B) decomposes results by size. Organizational performance is defined as the payoff to the choice made by the organization. The results show two cases: a first in which there is no individual learning, and a second in which individuals learn by participating.11 In both cases, we compare organizational outcomes to the unitary actor baseline (all in period 200). The error bars around the points are 95% confidence intervals (although these intervals are quite small, so they are hard to distinguish).
Turning first to the case of no-learning in Figure 2(A), we see that plurality, two-stage voting, and average beliefs each result in higher organizational performance than does the unitary actor. This reflects the effect of information aggregation. There is no organizational performance benefit, however, to the rotating dictatorship structure in the no-learning case because, in a no-learning case, this decision-making structure is functionally equivalent to the unitary actor.
There are notable differences among the plurality, two-stage voting, and average beliefs decision-making structures in the no-learning case in Figure 2(A). Organizational performance varies as a function of the degree of message transformation. Specifically, plurality voting, which embodies the greatest information loss because of its binary message transformation, produces the lowest organizational performance among the three decision-making structures. By contrast, the average beliefs decision-making structure, which employs no transformation and, thus, engenders no information loss, has the highest organizational performance.
In considering the learning case, we observe a key finding: decision-making structures that are relatively effective in the absence of learning are relatively ineffective in the presence of learning. That is, there is a reversal in the rank ordering of decision-making structures in terms of organizational performance. Our results, thus, illustrate that taking into account learning (by participating) requires a reassessment of the effectiveness of organizational decision-making structures.
Among the decision-making structures, rotating dictatorship stands out as it exhibits the highest performance among all decision-making structures we examine when individuals learn even though it exhibits the lowest performance in the absence of individual learning. Among the three decision-making structures that vary along the message transformation dimension (plurality voting, two-stage voting, and average beliefs), plurality voting exhibits the highest organizational performance. This result is somewhat counterintuitive as the messages communicated by individuals in the plurality voting case are those that are most highly transformed such that they are the lossiest (least information communicated).
In Figure 2(B), we disaggregate the results by the organizational size. Consider the no-learning case first. Greater organizational size increases organizational performance in the case of plurality, two-stage voting, and average beliefs. This result underscores the well-known idea that, in a setting in which individual beliefs remain static, there is value to the organization in aggregating information across a higher number of individuals, that is, the wisdom of organizational crowds.
By contrast, when individuals learn by participating, the effect of organizational size disappears for plurality voting, two-stage voting, and average beliefs. Organizational performance achieved by each of these decision-making structures is equivalent regardless of organizational size. Only in the case of rotating dictatorship is there an increase in organizational performance from increased organizational size.
4.1.2. Individual Learning Across Decision-Making Structures.
We next examine how individual learning varies across different decision-making structures. Individual learning is defined as the change in individual performance over 200 periods, in which individual performance is that which individuals could achieve if they were to act alone, selecting the alternatives they believed to be best. Results are in Figure 2, (C) and (D).
The most central result—which constitutes our headline finding—is that decision-making structures that lead to the best organizational performance in the absence of learning (because they effectively aggregate information) are the least effective at facilitating individual learning. Rotating dictatorship engenders the most individual learning, followed by plurality voting, two-stage voting, and then average beliefs.
These differences in individual learning across decision-making structures explain the reversal of organizational performance rank order once learning is taken into consideration (Figure 2(A)). Long-term organizational performance depends in part on how effective decision-making structures are in fostering individual learning. Simply put, organizations that foster individual learning perform better in the long term because they aggregate knowledge from smarter individuals who have learned more.
A comparison of learning by doing by the unitary actors to learning by participating by organizational members reveals that, in most cases, the unitary actor learns more. This can be seen by comparing plurality voting, two-stage voting, and average beliefs to the unitary actor in Figure 2(C). We return to this question and examine whether individuals in organizations simply learn more or whether there is also a difference in the type of knowledge they acquire.
We note further that organizational size affects individual learning in counterintuitive ways. Larger organizational size reduces individual learning in the case of plurality voting, two-stage voting, and average beliefs. Although size is traditionally associated with more wisdom, individuals in larger organizations actually learn less. The only decision-making structure for which size is positively associated with learning is rotating dictatorship. Not only do individuals generally learn the most in rotating dictatorship, their learning increases with the size of the organization.
In sum, our core insight is that the efficacy of information aggregation and the extent of individual learning are inversely related, a relationship we refer to as the aggregation–learning trade-off. In the subsequent sections, we focus on settings in which individuals learn by participating to unpack the mechanisms underlying this result.
4.2. Alignment of Individual and Organizational Choices in Learning by Participating
The aggregation–learning trade-off is anchored in the concept of learning by participating. Individuals’ preferred alternatives are voiced to the organization, which then selects the organizational choice via its decision-making structure. A key consequence is that the alternative an individual selects may deviate from the organizational choice.
We illustrate the frequency and type of deviations in the context of learning by participating by a plurality voting decision-making structure using the heat map in Figure 3.12 The figure illustrates the frequency of the different types of deviations. The cells above the diagonal illustrate cases in which organizations choose a higher-performing alternative than a randomly sampled member would choose alone. We refer to individuals whose opinion deviates from the organization and favor a worse alternative as incorrect contrarians. The cells below the diagonal illustrate cases in which organizations choose a lower-performing alternative than a randomly sampled member. Corresponding to our definition, we refer to these individuals as correct contrarians. The heat map illustrates that incorrect contrarians (below the diagonal) are more common than correct contrarians (above the diagonal). This result, although demonstrated in the case of plurality voting, is generalizable across all decision-making structures.
4.3. Individual Beliefs and Organizational Performance
We now turn to what individuals learn and how it affects individuals’ selections and organizations’ choices. Our prior analysis shows that decision-making structures differ in terms of how much individuals learn and that contrarians are common in the types of organizational decision making we model with incorrect contrarians outnumbering correct contrarians. Yet decision-making structures impact not only how much individuals learn but which individuals learn and what they learn.
4.3.1. Individual Beliefs on Low- and High-Performing Alternatives.
The hallmark of decision making and learning is individuals’ tendency to become subject to false positives and negatives when they overestimate or underestimate the value of some alternatives. Learning by doing by a unitary actor and learning by participating by an organization differ markedly in this respect. In Figure 4, we show the distribution of beliefs under learning by participating for the worst and best alternatives, alternatives 1 and 5, respectively, across the various decision-making structures in the final period (for organizations of size five).
Beliefs on the lowest performing alternative 1 display enormous variation across decision-making structures in individuals’ tendency to overestimate this alternative. Unitary actors and individuals in rotating dictatorship are least likely to substantially overestimate the low-performing alternative (i.e., are less likely to hold strongly false positive beliefs on bad alternatives). The reason is simple; if a unitary actor or an individual in a rotating dictatorship overestimates the low-performing alternative substantially, the individual selects the alternative, receives performance feedback, and corrects the overestimation. By contrast, in the other decision-making structures, an individual who overestimates the lowest-performing alternative is likely to be an incorrect contrarian. Thus, the individual does not learn about that alternative (because the organization is unlikely to choose it), and the individual’s overestimation is preserved.
A different picture emerges with respect to underestimating the value of highest performing alternative 5. Unitary actors frequently underestimate it, often holding strong false negative beliefs. The underlying reason is illustrated by Denrell and March (2001) in work on the hot stove effect: individuals choose a high-performing alternative and receive incidental negative feedback that does not represent the alternative’s true value, which leads to an underestimation that is then preserved as they do not return to the underestimated alternative. Our analysis shows that learning by participating offers a remedy against the hot stove effect. Even if an individual accidentally underestimates the alternative and, thus, does not favor it, the individual is likely to receive more performance feedback on the alternative because other members of the organization are likely to favor it (given its high performance), making it the organization’s choice and resulting in more feedback, which then allows the individual to correct the underestimation.
The analysis illustrates how learning by doing by a unitary actor and learning by participating by an organization differ, in particular, with respect to what individuals learn. Individual learning by doing provides a relatively nuanced and accurate understanding of low-performing alternatives in the sense that poor alternatives are quickly ruled out. Organizational learning by participating provides a relatively nuanced and accurate understanding of high-performing alternatives in the sense that, for instance, the organization can more effectively distinguish between the top two alternatives.
4.3.2. Disconnect Between Individual Beliefs and Organizational Choices.
The learning-by-participating process can engender a rather stark disconnect between the extent of false beliefs (false positives/negatives on poor/good alternatives) and organizational choices as the outcome of the decision-making structure. Figure 5 contrasts the alternatives individuals believe to be best (Figure 5(A)) and the alternatives organizations choose (Figure 5(B)).
Figure 5(A) shows that unitary actors and members of rotating dictatorships are almost never subject to false positives, although members of the other decision-making structures are, which echoes our findings in Figure 4. The process of information aggregation leads to the persistence of these false positive beliefs in the plurality voting, two-stage voting, and average beliefs decision-making structures. Among all three of these structures, as organizational size increases, the fraction of false positive individuals also increases, a contrast with what happens in rotating dictatorship decision making.
Consider how individuals’ beliefs translate to organizational choices. In Figure 5(B), we show the distribution of alternatives selected by the organization when individuals learn by participating in decision making (in period 200). Comparing Figure 5(B) with Figure 5(A) produces a somewhat surprising observation. In decision-making structures in which many individuals remain subject to false positive beliefs, organizations rarely choose the worst alternative. They marginalize contrarians and are, thus, able to choose high-performing alternatives. The contrast between Figure 5(A) and Figure 5(B) illustrates an important facet of the aggregation–learning trade-off: decision-making structures such as plurality, two-stage voting, and average beliefs are effective in aggregation as they marginalize contrarians and, thus, forgo picking low-performing alternatives, but it is that very marginalization that also keeps individuals from learning, as they cannot influence the organization to implement their preferred alternative and, thus, cannot correct their false positives.
Figure 5(B) also reveals the answer to why organizational decision-making structures that are effective in aggregation nevertheless perform relatively poorly when learning is allowed (as observed in Figure 2, (C) and (D)). Although such structures are very effective in avoiding the lowest performing alternative, they are challenged in distinguishing among the high performing alternatives.
4.3.3. Leveraging Contrarians to Enhance Organizational Performance.
There is merit in leveraging the wisdom of contrarians—evidently when they are correct but even when they are incorrect, and decision-making structures vary in their ability to do so. Often organizations fail to leverage individuals who are contrarians in period t in their decisions in period t + 1, and thus, contrarians in one period may remain marginalized as contrarians in subsequent periods. We plot the fraction of individuals who are correct versus incorrect contrarians in their organizations in period 200 in Figure 6. A number of results stand out. First, rotating dictatorship produces far fewer contrarians than do the other decision-making structures. Second, the probability of an individual being a contrarian is increasing in size. Third, contrarians are much more likely to be incorrect than correct by period 200. Finally, among plurality voting, two-stage voting, and average beliefs, increasing the extent of message transformation (i.e., to binary in plurality voting) leads to a decrease in the number of contrarians in the long run.
The capacity to leverage the wisdom of contrarians is an important feature of decision-making structures when individuals learn by participating, and decision-making structures vary in their ability to do so. It is evident that the presence of contrarians is positively correlated with the long-term performance of a decision-making structure. Contrarians play an important role in the efficacy of different decision-making structures when individuals learn. Clearly, if a contrarian is correct in recognizing the best alternative, marginalizing the individual by excluding the individual’s knowledge is problematic. Less obvious is that there are unexpected long-term costs to marginalizing some incorrect contrarians. This is because incorrect contrarians may still hold valuable knowledge regarding the merits of the other alternatives.
To illustrate the efficacy of decision-making structures in leveraging contrarians, consider two types of individuals. One type is what we call a genius. This is an individual who, in period 1, correctly believes that alternative 5 is the highest payoff. By contrast, another type of individual is what we call an antigenius. This is an individual who, in period 1, incorrectly believes that alternative 1 is the highest payoff. Either a genius or an antigenius can be a contrarian if the person is, within the organization, small in number. For instance, one antigenius in an organization of size five is likely to be an incorrect contrarian, but if there are three antigeniuses, they would no longer be contrarians.
We start by examining the implications of geniuses. We illustrate that performance differences across decision-making structures stem in part from the ability to leverage small numbers of geniuses. In Figure 7, across decision-making structures and size, we show organizational performance after 200 periods of learning by participating as a function of the number of individuals who are geniuses. The y-axis shows organizational performance, and the lines plot the average performance of organizations with a specific number of geniuses (0, 1, 2, or 3).
It is somewhat self-evident that, regardless of decision-making structure, performance should increase with the number of geniuses. Decision-making structures that are balanced with respect to individual inclusion in decision making (plurality voting, two-stage voting, average beliefs) function relatively poorly when geniuses are few in number as these are likely to get marginalized. For instance, one genius in a plurality voting decision-making structure is likely to be a contrarian and has little influence on the organization’s choice; in this sense, the plurality decision-making structure bears the cost of not being able to make effective use of this knowledge. When a genius does not influence the organizational decision, others in the organization are not exposed to the genius’ knowledge regarding the highest payoff alternative. By contrast, in the rotating dictatorship decision-making structure, a single genius is sufficient for the organization to reach a high level of performance. In this structure, a genius, when the genius gets a turn to make the organizational decision, chooses the highest performing alternative, and the other members of the organization can then learn about the true value of that alternative.13
Organizations of different sizes are differentially sensitive to the number of geniuses they contain. For instance, one genius in a plurality decision-making structure of size three has a substantially greater positive impact on organizational performance than will that individual in a larger organization. There is a sharp downward slope in performance as organizational size increases among the decision-making structures that involve balanced individual inclusion. By contrast, rotating dictatorship is somewhat less sensitive to organizational size because even a single genius eventually gets a turn to make the organizational decision in a large organization. This also explains why rotating dictatorship is the only decision-making structure for which an increase in size has a clearly positive effect in the learning-by-participating case (Figure 2(B)). The larger the organization, the higher the chance that it harbors at least one genius from whom the organization can learn.
Taken together, the extent of message transformation across these decision-making structures has a substantial impact on whether a genius, when the genius is a contrarian (the genius would be a correct contrarian), is able to influence the organizational choice. The mechanism described by which organizations vary in their capacity to tap into the useful knowledge of geniuses is a close cousin of the mechanism by which organizations leverage the knowledge of correct contrarians and explains, in part, the difference in the distribution of beliefs regarding the high-performing alternative 5 (per Figure 4 discussed earlier).
We now turn to antigeniuses: individuals who believe, in period 1, that the worst alternative is best. Such individuals are highly likely to be contrarians in the early periods. Differences across decision-making structures in the capacity to make effective use of individual knowledge stem from the ability to leverage the knowledge of antigeniuses. It might seem, on the surface, that this is an absurd idea. But antigeniuses may not be devoid of useful knowledge. Although they may well believe, incorrectly, that alternative 1, the lowest payoff alternative, is the highest payoff alternative, they may also believe that alternative 5 is better than alternative 4 and, indeed, that alternatives 2 and 3 are mediocre. In our model, for the set of antigeniuses, 54.3% correctly believe at the outset that alternative 5 is superior to alternative 4 even though they incorrectly believe that alternative 1 is best. In this sense, even antigeniuses may hold knowledge that is valuable to the organization.
This insight helps explain why rotating dictatorship performs so well; it can make more effective use of the knowledge of antigeniuses, who tend to be incorrect contrarians, than do the other decision-making structures. In plurality voting, if the antigenius votes time and time again for the worst alternative, alternative 1, the antigenius does not contribute to the organization’s efforts to distinguish alternative 4 from the superior alternative 5. Yet the rotating dictatorship decision-making structure eventually gives the antigenius a turn at making the organizational decision. The antigenius then chooses alternative 1, which the antigenius erroneously favors, and is likely to observe negative feedback that then helps the antigenius recognize that it is a low-payoff alternative and to, thus, correct the false positive belief. The next time the antigenius gets a say in the organization, the antigenius is more likely to select alternative 5, the best alternative, and in doing so help the organization distinguish between the best and second best alternatives.
Interestingly, it can be the case that it is not strictly better to have fewer antigeniuses. One would expect that, in choice problems, the addition of an incremental antigenius is detrimental to performance. However, an additional antigenius in the organization can actually increase long-run performance in the plurality voting, two-stage voting, and average beliefs decision-making structures. In these decision-making structures, a lone antigenius is an incorrect contrarian and is unlikely to receive feedback on the alternative the antigenius thinks is (erroneously) best. By contrast, if there are two or three such antigeniuses, the antigenius may not be a contrarian. This, in turn, allows feedback on that poor alternative, which subsequently unlocks their knowledge on the other alternatives.
4.4. Robustness Analysis and Model Extensions
The results presented highlight mechanisms by which the performance of decision-making structures vary when individuals learn by participating in decision making. We conduct additional analyses to establish the robustness of our insights and illustrate some contingencies. All references to figures that follow refer to those in the online appendix.
First, we examine short-run learning-by-participating results. In the main models, we considered the no-learning case and the case of individual learning over 200 periods. In Figure A1, we add a learning result at the 25th period. The results are interesting for rotating dictatorship. After 200 periods of learning, this decision-making structure is clearly the best performer, both organizationally and in terms of individual learning. Yet we see that, at period 25, this decision-making structure underperforms the plurality voting, two-stage voting, and average beliefs decision-making structures in terms of organizational performance. Rotating dictatorship is quite exploratory, and it facilitates individual learning, which comes at a substantial short-run cost to organizational performance.
Second, we examine how individuals’ initial knowledge diversity impacts the performance of different decision-making structures. In our model, individuals are endowed with initial beliefs (priors) when they join the organization. These initial priors are developed in a prejoin learning phase of g periods in which individuals independently sample alternatives in a highly exploratory manner and receive feedback on their choices. After this prejoin phase, individuals join the organization. In the main models, g = 5. Reducing the length of this prejoin phase reduces initial diversity in beliefs, and increasing it does the opposite. In Figure A2, we set the prejoin period to g = 1 and observe that the pattern of results is quite similar to our main results in Figure 2. In Figure A3, we set the prejoin period to g = 50. In this situation, there is substantially less initial knowledge diversity as individuals have nearly reached steady-state knowledge, converging on good alternatives even before they join the organization. The results differ slightly from our main findings. It is obvious that individual learning is much reduced in this setting. More interesting is that we observe a positive impact of organizational size on performance when individuals learn for the plurality voting, two-stage voting, and average beliefs structures, which is not observed in our main results. Size has a positive effect because individuals hold fewer false positives when they join the organization with the extended prejoin phase. Thus, the downside of size, that individuals are less able to correct false positives, is greatly reduced.
Third, we examine the implications of increasing the organizational size. In our main analysis, we consider sizes three through nine as these reflect a reasonable range for decision-making groups. Of course, one can imagine larger decision-making groups. To assess the implications of larger size, we examine settings with 31, 51, and 101 individuals. The results are in Figure A4. As one would expect, in the no-learning case, increasing organizational size has a large positive impact on organizational performance. This is no surprise as it is purely the case of information aggregation (as in the wisdom of crowds). Indeed, as the size gets arbitrarily large, organizational performance approaches 0.7 (the maximum possible in this setting). In the learning case, increasing size offers no additional performance benefits over smaller sizes, and long-run performance is below that of the no-learning case. This is because if the initial information aggregation leads to the choice of the best alternative in the absence of learning, then learning can offer no benefits, and learning’s myopias come to dominate. In particular, because even the best alternative (with a payoff of 0.7 in our model) produces negative results 30% of the time, hot stove effects (Denrell and March 2001) may lead the learning organization to abandon the good alternative and, quite possibly, never return to it. This is exacerbated because larger organizations employing the plurality, two-stage, and average beliefs decision-making structures are very unlikely to explore even if the individuals are quite exploratory. The exception is rotating dictatorship, in which the no-learning case (which lacks information aggregation) is far inferior to the learning case as the latter is able to resolve hot stove issues by randomly allocating decision making.
Fourth, we examine the implications of varying the task environment characteristics. In our main models, we consider five alternatives with payoffs of In Figures A5–A8, we examine environments that have (A5) more choice alternatives, (A6) choice alternatives that are more munificent, (A7) choice alternatives that are less munificent, and (A8) choice alternatives that are more similar. Although the results vary quantitatively, they are qualitatively robust in that the rank ordering of decision-making structures with respect to performance and learning remains unchanged.
Fifth, we consider two forms of variation along the exploitation–exploration continuum. In our main models, we set τ = 0.01, which is a very mild level of exploration. We tested the implications of making individuals greedy with τ approaching zero. The results, which are in Figure A9, are largely unchanged. It is worth noting that, even in the absence of individual exploration, organizations can explore because of individuals’ heterogeneous beliefs. In addition, we relax the assumption that, in the context of plurality voting, votes are counted accurately. We configured the model with a probability of 0, 0.1, or 0.2 that any participant’s vote is counted twice or not at all. We find that an increase in the level of noise decreases the benefits of organizational aggregation given that the weighting of votes is random and results in the marginalization (or even exclusion) of valuable knowledge.
Finally, we considered alternative characterizations of organizational contrarians and geniuses. In our main analysis, we defined a contrarian as an individual who favors a choice alternative (i.e., the alternative that the individual believes is best) that differs from that chosen by the organization. We examine a different formulation based on the Spearman correlation between individuals’ beliefs in an organization. The results are in Figure A10, which is quite similar to Figure 6 in the paper. Likewise, we can use Spearman correlations to define geniuses. The results are in Figure A11, which is quite similar to Figure 7 in the paper. Taken together, these results suggest that different measures of contrarians and geniuses do not change our interpretation of the mechanism by which they act.
We examine the dual role of structure in aggregating individuals’ beliefs and shaping individuals’ learning. Our central argument is that, when individual learning within organizations is possible (learning by participating), alternative decision-making structures give rise to an aggregation–learning trade-off wherein decision-making structures that more effectively aggregate individuals’ knowledge can be less effective at facilitating individuals’ learning. An implication of this insight is for work comparing the effectiveness of organizational structures. This work often does not consider the role of learning. We show that, when learning is taken into account, the rank order of structures’ effectiveness may change markedly. Beyond this insight, our paper has theoretical implications for a host of issues in the domain of organizations, including learning, microfoundations, teams, and crowds.
5.1. Implications for Theory
5.1.1. Learning Processes in Organizations.
This paper has implications for the vast body of work on social learning. A central focus of this work has been on the network ties that connect individuals, with network structure seen as a key factor shaping how and what individuals learn (e.g., Granovetter 1973, March 1991, Hansen 1999, Burt 2004, Fang et al. 2010, Aral and Van Alstyne 2011, Tortoriello et al. 2011, Padgett and Powell 2012, Clough and Piezunka 2020). We show that there is an important channel for learning that operates orthogonally to informal network structure—namely the formal decision-making structure employed by the organization. Because decision-making structures shape the trajectory of individual knowledge over time, they can operate in tandem with the effects of social networks. These structures are, of course, particularly salient to decision making in organizational settings, in which repeated interactions among individuals engender individual-level learning alongside the effects of social influence (e.g., Denrell and Le Mens 2007, Le Mens and Denrell 2011).
In addition to demonstrating that alternate decision-making structures can lead to variation in individual-level learning outcomes, our research also points to challenges for individual learning that stem from individuals being surrounded by knowledgeable others in an organization (Ingram and Simons 2002, Waldinger 2012, KC et al. 2013, Hwang et al. 2015, Myers 2018). Prior research points to the difficulties inherent in social learning from well-performing peers (Posen et al. 2020). Our work, on the other hand, suggests that there may be equally important challenges to learning with well-performing peers. The upside of being in an organization with knowledgeable peers, of course, is that individuals can learn about high-performing alternatives. The downside, however, is that individuals may not have the opportunity to learn about low-performing alternatives. As a consequence, if and when an individual acts alone, the individual may have little knowledge of the implications of low-performing alternatives, making the individual more likely to select alternatives from this low-performing set.
Our work also demonstrates the consequences of enabling or avoiding “mistakes” in organizational decisions. Although individuals learn from mistakes, organizations often strive to keep employees from making mistakes. We find that decision-making structures that make the fewest mistakes are also the ones that are least effective in fostering individuals’ learning as well as the ones that perform the worst over the long term. This insight, though based on a different mechanism, relates to work by Stan and Vermeulen (2013), who show that hospitals that want to avoid failure (and, thus, reject certain challenging patients) are the ones that learn the least. Our study illustrates the need for organizations to create opportunities for employees to fail and moreover to learn from that failure.
5.1.2. Microfoundations and Individual Agency.
We also advance our understanding of the microfoundational approach to organizations. The central question in the domain of organizational microfoundations is how individual-level factors interact and aggregate to shape macro, organizational-level phenomena (Barney and Felin 2013, Felin et al. 2015, Aggarwal et al. 2017, Schilke 2018, Davis and Aggarwal 2020, Piezunka and Schilke 2021). We show that there is an ongoing recursive interaction between the organization and the individual (e.g., Coleman 1990) wherein the structures used to aggregate individual decisions in an organization shape what and how individuals learn and, as a consequence, inform the subsequent actions of individuals over time. This demonstrates not only that the mapping from individual beliefs to individual and organizational actions is difficult to cleanly disentangle from the structure that governs organizational decision making, but more importantly, it enables us to gain insight into the learning-by-participating process, which operates as a fundamental mechanism of aggregation linking together the individual and organizational levels of analysis.
The cross-level interactions engendered by this aggregation process, furthermore, lead to interesting trade-offs across organizational levels. Although individuals benefit (themselves) from learning, organizations benefit (at least in the short term) from effective aggregation. This trade-off points to the possibility of agency conflict in which individuals may favor decision-making structures that differ from those that are in the best interests of the organization. Although, over the long term, maximizing individual learning may also maximize organizational performance, this form of agency conflict can persist.
Agency conflict within organizations arising from aggregation processes (and their inherent trade-offs) further relates to individual-level career considerations. Research on individual careers has examined how factors such as peers (Waldinger 2012), employers (Sutton and Callahan 1987, Burton et al. 2002, Bidwell et al. 2015), entrepreneurship (Sorenson et al. 2021), and education (Lazear 2004, Eesley et al. 2016, Eesley and Lee 2020) affect various features of the individuals’ careers, such as income and employability. We add another important feature to this debate, the structure of the learning process, and show that it can make a significant difference whether an actor learns by doing or by participating and, for the latter, in which kind of decision-making structure.
5.1.3. Teams and Structure.
Our work speaks to the importance for groups, committees, top management teams, and boards to consider the decision-making structure under which they operate. A large literature on top management teams examines the characteristics, education, and experience of top managers for firms’ decisions and outcomes (e.g., Hambrick and Mason 1984, Haleblian and Finkelstein 1993, Chen et al. 2016). Likewise, there is a growing literature on entrepreneurial teams (e.g., Tarakci et al. 2016, Garg et al. 2018, Clough et al. 2019, Ganco et al. 2019, Hoppmann et al. 2019). Much of this work points to factors that help explain success, such as hierarchy (Lee 2021, Lee and Csaszar 2021), fault lines (Vissa 2010), and knowledge distribution (Aggarwal et al. 2020). With the recent exception of Chen et al. (2021), however, the question of the effective design of decision making in entrepreneurial teams has received little attention. Although team design is clearly a multifaceted topic, our research suggests that there may be merits to a renewed focus on information processing and decision making in the Simon (1947) tradition, which may be extended to not only consider the role of information aggregation across team members, but also the extent of individual learning and how these two functions interact.
In considering the issue of team design, one of our most interesting results is the effectiveness of the rotating dictatorship decision-making structure. By allowing individuals to revisit and thereby correct their beliefs, rotating dictatorship may provide a remedy against the hot stove effect (Denrell and March 2001), and as such, it may be a useful tool for organization designers considering the ways in which teams should be structured. Yet, if this structure is so effective, why is it not more commonly used in organizations? One answer is that it is ineffective in the absence of learning or when only short periods of learning are available. Rotating dictatorship, for example, involves making early mistakes that then allow for the correction of individuals’ erroneous (false positive) beliefs about the merits of the alternatives. To the degree that the organization operates in an environment that is less forgiving of early mistakes, the relative value of rotating dictatorship as a team decision-making structure may be diminished.
5.1.4. Crowd-Based Decisions.
We contribute to research on organizational design that intersects with work on the wisdom of crowds (Le Mens et al. 2018, Becker et al. 2019). The “crowds” in organizations differ from traditional crowds in a manner that has important implications for organizational design. First, crowds in organizations include a relatively small number of individuals. Second, individuals in organizations often engage in repeated decision making through which they have the opportunity to learn from feedback on prior decisions (Christensen and Knudsen 2009). Scholars have increasingly sought to apply the underlying ideas of the wisdom of crowds to organizational decisions (Page 2007), implying that the wisdom-of-crowds idea (Surowiecki 2005, Atanasov et al. 2016) is directly applicable. Our study suggests, however, that a naive application of the wisdom-of-crowds logic may lead to decision-making structures with inferior long-run performance outcomes.
Our study also informs the linkage between the size of crowds and decision effectiveness. Although prior work suggests larger crowds are more effective, we show that greater size creates challenges for individual-level learning because it restricts opportunities for individuals to influence the organizational decision. The size of crowds in organizations is, thus, a double-edged sword: if a key objective is to develop smarter individuals, focusing on greater size and information aggregation may be counterproductive.
Our work also intersects with the related, but very different, body of work on crowdsourcing. Although both tap into the potential of the crowd, models of information aggregation design structures that utilize redundancy, whereas crowdsourcing thrives on diversity (Girotra et al. 2010, Jeppesen and Lakhani 2010, Afuah and Tucci 2012, Boudreau 2012, Felin et al. 2017). Our research illustrates how these streams can inform one another. Behavioral research on crowdsourcing illustrates that organizations succeed in eliciting a pool of diverse ideas, but typically end up selecting redundant ideas (Piezunka and Dahlander 2015). Despite the appeal of the idea that organizations may thrive on diversity, organizations seem to value redundancy when they try to leverage the wisdom of the crowds and fail to benefit from crowdsourcing as a consequence (Dahlander and Piezunka 2020). Our results illustrate that commonly used decision-making structures, such as plurality voting, which, on the surface, seem to encode redundancy, tend to marginalize contrarians and, in doing so, undermine individuals’ learning.
5.2. Managerial Implications
A number of managerial implications flow from our theoretical insights. Most notably, our paper has implications for how managers should design their organization, that is, which decision-making structure they should pick. In settings in which individual learning over time is feasible, our work suggests that long-term performance is optimized by choosing an organization structure that engages in greater message transformation. Managers should also carefully examine the number of people involved in decision making given that increasing size is costly and its positive effect may be smaller than that associated with facilitating learning. The outlined mechanism on the integration of contrarians should caution managers in how they can engage with contrarians. Even if a manager is certain that a contrarian favors the wrong alternative, the manager would still benefit from tapping into the contrarian’s knowledge on other alternatives.
An organization not only makes choices about the design of decision making premised on its aspired level of performance, but also how this performance is generated—via information aggregation or individual learning. This suggests implications for the types of organizations individuals may wish to join. Decision-making structures vary in the degree to which they foster the learning of their members. An individual who considers joining an organization should carefully consider what effect the individual’s set of beliefs will have on an organization given the set of beliefs of current members of the organization as well as the organization’s design. This also implies that managers should consider how they cope with contrarians. Instead of marginalizing contrarians and allowing them to become a disgruntled minority, managers might allow them to influence the organizational decision in order to integrate their knowledge and learning for the benefit of the organization.
5.3. Limitations and Future Research
We have made progress toward examining the dual role of structure in shaping both organizational performance as well as individual-level learning in organizations by holding fixed mechanisms of learning beyond learning-by-participating that may occur within organizations. Incorporating other (nonexperiential) learning mechanisms into future theory development efforts, such as social learning among members of the organization, and other contingencies outside the scope of the present paper, may offer fruitful opportunities for richer theoretical insights.
One avenue for future research may be to study the implications of relaxing the assumption that individuals’ votes are equally weighted (either within a period or over time). This is related to the issue of power dynamics in organizations. In a simple sense, this may be reflected in our model via heterogeneity in voting rights across individuals (i.e., differences in heterogeneity among individuals with respect to their decision-making weights). Of course, this may become much more complicated when voting rights emerge endogenously from effective (or ineffective) outcomes from prior voting. Not only may voting rights emerge endogenously, but so too may the groups of individuals participating in decision making. The formation and dissolution of groups (e.g., Carley 1991) has received relatively little attention in the management literature (likewise with work on the closely related idea of coalitions in Cyert and March 1963). However, group formation may have important implications for the efficacy of learning by participating. This relates to the question of who is in the room (Dobrajska et al. 2014). More empirical data on this underlying process would complement insights on how decisions are made and the role of learning by participating in this regard. Future research may also endogenize individuals’ voting behavior as the decision-making structure may affect people’s willingness to vote sincerely (Sah and Stiglitz 1986, Piezunka and Schilke 2021).
Another possibly fertile avenue for future research would be to examine the trade-offs that arise among different decision-making structures when learning by participating occurs. Plurality voting, two-stage voting, and average beliefs, for example, exhibit similar performance in the long run but differ with respect to how much individuals in the respective organizations have learned. Future research might build on a logic of value creation and value capture to further explore these trade-offs. In addition, numerous contingencies may shape our understanding of the trade-offs across decision-making structures. Beyond the evident short- versus long-run trade-off, the size of the organization also plays an important role. Future work may examine issues such as environmental turbulence and differences in individual rates of learning. It may be the case, for example, that individuals learn differently by observing organizational outcomes in which they themselves are contrarians versus decisions in which they are a part of the dominant organizational coalition. Understanding the differential trajectories of individual learning that arise in such a situation can add further color to our understanding of the aggregation–learning trade-off.
In summary, we examine the trade-off between aggregation and learning in organizations. To do so, we bridge work on information aggregation and organizational learning by examining the implications of learning by participating for the efficacy of different structures of organizational decision making. Using a computational model, we find that the efficacy of information aggregation and the extent of individual learning are inversely related outcomes whose ultimate impact on organizational performance is adjudicated by the way in which organizational contrarians, individuals who favor choices that differ from that of the organization, influence organizational choices. Our insights have implications for future research on organizational decision making across a range of organizational contexts, including groups, teams, boards, and crowds.
The authors thank Felipe Csaszar, Javier Gimeno, Henrich Greve, Thorbjørn Knudsen, Stephen Mezias, Phanish Puranam, Mooweon Rhee, Violina Rindova, and two anonymous reviewers as well as seminar participants at the Max Planck Institute, University of Pennsylvania, University of Toronto, Seoul National University, and Yonsei University as well as conference participants at the Strategic Management Society special conference in Frankfurt for valuable feedback and suggestions. All authors contributed equally.
1 This assumption can be thought of in a number of different ways. It may reflect an organization making a series of independent decisions with no learning possible across them. It may also reflect the time scale of learning in the sense that, in some settings, individuals may reach steady-state knowledge rather quickly such that further experience does not meaningfully change their beliefs.
2 Of course, the idea that decision-making structures shape the knowledge of organizational members over time is itself not new (e.g., Coleman 1990, March 1991). Work in the Sah and Stiglitz tradition has certainly recognized that the choice of decision-making structure may shape and complicate individual learning (e.g., Sah and Stiglitz 1986, Knudsen and Levinthal 2007, Christensen and Knudsen 2009, Knudsen et al. 2018).
4 Plurality and two-stage voting follow naturally from work on polyarchy and hierarchy (Sah and Stiglitz 1986, Christensen and Knudsen 2010). In hierarchy, all participants must vote in favor although only one needs do so in a polyarchy. The conditions under which either of these structures is optimal, even in the simple no-learning case, are restrictive (Ben-Yashar and Nitzan 1997). This has given rise to interest in intermediate structures (i.e., G*) in which the decision is determined by a threshold that is some subset of votes (e.g., plurality voting).
5 Despite these precedents, rotating dictatorship is probably the most novel organizational structure as the theoretical debate has typically not examined the random allocation of decision rights (Puranam et al. 2013). In typical (and typically studied) organizations, decision rights are allocated following hierarchical or lateral principles (e.g., O’Mahony and Ferraro 2007, Dahlander and O’Mahony 2011, Klapper et al. 2021).
6 Plurality voting, average beliefs, and two-stage voting are settings in which individuals’ beliefs are given equal weighting that does not change over time. That is, in each period, all individuals’ messages are included—to be aggregated into an organizational decision. Individual inclusion in decision making is interesting in settings with repeated decision making with inclusion weights that change over time. The simplest version of time-varying inclusion is that of rotating dictatorship, in which one individual is randomly selected in each period and given a weight of one, and all others are given weights of zero. Information aggregation is only indirect in that it functions intertemporally, mediated by individual learning by participating. In each period, only one individual’s messages are considered, but over time, every individual’s messages are included in organizational decisions. More complex inclusion settings, which may be interesting to explore in future research, feature endogenously varying fractional weights that evolve over time, perhaps because of emergent differences in power, status, or ability (e.g., Ben-Yashar and Nitzan 1997).
7 In the case of the two-stage decision-making structure, the message transformation and output procedure occurs twice: the first time including all alternatives and the second time including only the top two vote getters.
8 Of course, this is not the only challenge that may be faced by organizational decision making. For instance, one might consider the challenge of complexity rather than uncertainty as in the single agent model of Levinthal (1997) or the organizational models of Rivkin and Siggelkow (2003).
9 Our model, thus, abstracts away from social learning, such as the sharing of knowledge and debates, which also occurs in organizations. We discuss implications for work on social learning in the final section.
10 By 200 periods, individual learning is approaching steady state. For example, for all decision-making structures, at least 98.9% of the performance in period 1,000 has already been reached by period 200.
11 In the “no individual learning” case, individuals make choices based on their beliefs, but individuals’ beliefs are not updated based on the outcome of the organizational choice (labeled “no learning”). In the learning-by-participating case, individuals do learn experientially by updating their beliefs based on the outcome of the organizational choice (labeled “with learning”).
12 The pattern is qualitatively similar in later periods although the cell densities vary over time.
13 The difference across plurality, two-stage voting, and average beliefs is due to the difference in message transformation. The stronger the message transformation, the smaller the alignment (or correlation) among organizational members’ messages. A reduction of alignment increases the chance of a contrarian to influence the organization’s decision.
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Henning Piezunka is an assistant professor of entrepreneurship and family enterprise at INSEAD based in Fontainebleau, France. He received his PhD from Stanford University. His research explores embedded dyadic relationships and crowdsourcing.
Vikas A. Aggarwal is an associate professor of entrepreneurship and family enterprise at INSEAD, based in Fontainebleau, France. He received his PhD from the Wharton School of the University of Pennsylvania. He uses empirical and computational modeling methods to study strategy, organization design, and innovation, focusing on venture capital–backed start-ups as well as on established firms adapting to widespread industry change. His teaching is in the area of private equity and venture capital.
Hart E. Posen is a professor of management at the University of Wisconsin–Madison. He received his PhD from The Wharton School, University of Pennsylvania, before which he was an entrepreneur in the technology and retail sectors. Studying strategy, innovation, and entrepreneurship from a behavioral perspective, he develops computational models of how collective intelligence emerges and evolves in organizations via learning processes. He is an associate editor at the Strategic Management Journal.