Collective benefit in joint perceptual judgments: Partial roles of shared environments, meta-cognition, and feedback

Abstract

Recent research has demonstrated that two persons can optimally combine their observations to make better decisions when they can verbally communicate their confidence to each other. The present study investigated whether non-verbal interaction in a shared environment can be sufficient to achieve similar collective benefit. Pairs of individuals performed a localization task in a shared virtual 3D environment. In Experiments 1 and 2, partners had access to orthogonal viewpoints providing complementary information. The results showed robust collective benefit compared to individual performance from a single viewpoint, which could be obtained without any opportunity for verbal communication and even when no feedback about joint accuracy was provided (Experiment 2). When partners shared the same viewpoint (Experiment 3), collective benefit was achieved only when feedback on accuracy was provided (Experiment 3a). The findings indicate that sharing an environment can be sufficient for achieving integration of complementary perceptual information. Communicating confidence might not be necessary when an environment is shared. Another possibility is that processes for integrating interpersonally continuous information generally differ from the processes invoked when making a joint dichotomous choice.

1. Introduction

Are two people more accurate in their perception than a single individual? Few would doubt that multiple watchmen are better able to monitor a crowded site for a target than an individual watchman, especially if each of them is aware of where the others are looking (Brennan, Chen, Dickinson, Neider, & Zelinsky, 2008). Indeed, recent studies suggest that integration of perceptual information across multiple individuals (Bahrami et al., 2012a, Bahrami et al., 2012b, Ernst, 2010) can be as effective as integration of inputs from multiple sensory modalities within a person (Ernst & Bülthoff, 2004). In these studies, two individuals were quickly flashed the same perceptual information, such as an array of Gabor patches, on two separate screens, and were then asked to decide jointly after a verbal discussion which patch is the odd one out (Bahrami et al., 2010, Bahrami et al., 2012a, Bahrami et al., 2012b).

It has been claimed that collective benefits are obtained through a meta-cognitive process that enables people to verbally communicate to each other their individual confidence in their own judgment (Bahrami et al., 2012a). If confidence is communicated properly, close to optimal interpersonal integration can be achieved (Bahrami et al., 2010). Although communicating confidence may be a powerful strategy to integrate quickly fading perceptual information that cannot be re-accessed, there may be alternative ways of integrating perceptual information in a stable shared environment.

To illustrate, consider putting up a Christmas tree alone and together with another person. In both cases the aim is to put up the tree straight (perpendicular to the floor plane). This is a challenging task for a single individual because visual perception of distance is quite accurate on the left-right dimension but much less accurate on the front-back dimension corresponding to the line of sight (Foley, 1980, van Beers et al., 1998). Recruiting a second person to help with adjusting the tree may lead to a large collective benefit if she positions herself in a way that allows her to compensate for the inaccurate depth perception of the first person (because the two viewpoints complement each other). In the present study, we asked whether acting together in a shared environment can lead to collective benefits in spatial judgments. This could be the case because individuals inhabiting a shared environment may have access to complementary perceptual information, e.g., because they have different viewpoints on the same object. Alternatively, communicating confidence in one’s judgments may be a necessary condition to obtain such benefits (Bahrami et al., 2012b).

1.1. How interpersonal integration leads to collective benefit

Previous research addressing collective benefits in joint judgment and decision-making works from the assumption that when observers judge the value of a continuous property such as age, height, weight, temperature, distance, etc., their judgment is likely to contain a random estimation error (Clarke and Yuille, 1990, Knill et al., 1996, Ma, 2010). When two observers make independent judgments of the same property, simple averaging of their judgments has the statistical effect of filtering out random error, thereby making the combined judgment more accurate (Larrick, Mannes, & Soll, 2012). This effect has been demonstrated in many early psychological experiments which used simple perceptual tasks, such as estimating the number of beans in a jar or classroom temperature (for reviews, see Lorge, Fox, Davitz, and Brennar, 1958; Voinov, 2017).

Because simple averaging gives the same weight to all individual judgments, collective benefit for joint judgments decreases if the contributing individuals differ a lot in the precision of their judgments, for example due to differences in expertise. The problem of combining judgments from independent observers with unequal reliability is conceptually similar to the problem of combining information from different sensory modalities (Bahrami et al., 2012a, Ernst and Bülthoff, 2004), where each sensory modality is modelled as an observer providing independent information. This conceptual similarity made possible adopting models developed for the problem of multi-sensory integration to inter-individual information integration (Bahrami et al., 2010, Ernst, 2010, Sorkin and Dai, 1994, Voinov, 2017). In line with the principles of multi-sensory integration, statistically optimal or close to optimal solutions that guarantee maximum reduction of random error in individual observations, weight individual judgments proportionally to their reliability (the inverse of variance observed across multiple individual judgments, see Voinov, 2017).

Adopting perceptual signal-detection tasks (e.g. Bahrami et al., 2010; Sorkin, Hays, & West, 2001) further allowed for a direct comparison between the processes of intra- and inter-individual information integration. A series of studies by Bahrami et al., 2010, Bahrami et al., 2012a, Bahrami et al., 2012b), where participants were required to identify among two arrays of Gabor patches the one with a high-contrast patch, suggest that individuals providing joint decisions can achieve close to optimal performance unless the gap in performance between two partners is too big.

At present, it is an open question how different individuals integrate continuous information to arrive at joint judgements. Accordingly, in the present study we investigated whether similar mechanisms that allow groups of individuals to integrate information to make more accurate decisions may also allow groups of individuals to integrate information to make more accurate judgments on continuous perceptual dimensions.

1.2. Metacognition versus shared environments

From a psychological perspective, optimal weighting models require that two or more individuals not only share with each other information about the content of each other’s judgments but also about the reliability with which these judgments were made (Bahrami et al., 2012a). This is in analogy to optimal weighting models for intra-individual integration of sensory information which assume that sensory systems act like independent observers sharing their reliability in an appropriate format (Ernst and Bülthoff, 2004, Ma, 2010). But how can such a sharing be achieved interpersonally? One possibility is that each individual accesses a meta-representation of reliability of evidence underlying their judgment and communicate the content of this meta-representation to all others involved in the joint judgment. As Ernst (2010) has pointed out this would require that different individuals use the same reference systems and the same scale to communicate the estimated reliability of their judgment. This can be tricky due to differences in cultural background and learning histories. For instance, if two people use different metric systems, they will have problems to communicate the reliability of their judgments about the length of objects.

Bahrami et al., 2010, Bahrami et al., 2012a proposed that, instead of communicating reliability, individuals communicate their confidence in a decision or judgment as a unit free proxy of estimated reliability. This could establish the kind of common ground needed for optimal interpersonal weighting of individual contributions to joint judgments and decisions. Accordingly, weighing of perceptual information during interpersonal integration should rely on how well meta-cognitive confidence information is exchanged within a pair (Fusaroli et al., 2012).

This assumption was tested using a perceptual decision task where pairs were asked to jointly judge which of two successively displayed arrays of Gabor patches contained a patch that differed in its contrast from all other patches in the array. Participants communicated to agree on a joint judgment. When both participants performed individually at near equal levels, they jointly reached optimal performance. However, when additional noise was added to one of the participants’ displays, joint performance was systematically below optimal. According to the confidence sharing model of joint decision-making (Bahrami et al., 2010) this happens because confidence is a sub-optimal measure of reliability associated with one’s judgment (for a detailed account on how the processes of perception, judgment, and decision are related, see Voinov, 2017). Bahrami et al. (2010) concluded that communication of confidence is necessary to obtain collective benefit, while, counterintuitively, feedback about the accuracy of a joint decisions is not necessary (p. 1084).

However, there is another mechanism that could enable groups to achieve accurate weighting: Perceiving each other’s judgments in a shared environment as expressed through actions performed in the shared environment and agreeing (reaching a compromise) on a joint outcome. Perceptual information in shared environments is normally not fleeting (in contrast to communication) but it persists. At the same time, the shared environment provides a common spatial reference and a common scale creating a natural medium for information exchange. Together, these two features of shared environments may remove the need for explicit verbal communication of confidence. A first indications that this could be the case come from studies addressing joint action coordination. Ganesh et al. (2014) demonstrated that establishing a haptic connection between two individuals had a beneficial effect on accuracy of their tracking a moving object. Wahn, Schmitz, Koenig, and Knoblich (2016) showed that, when participants were given joint control over an object in a target location task, they displayed collective benefit in their performance, even though they could not verbally communicate. Thus, shared environments may be sufficient to successfully integrate individual perceptions into joint perceptual judgments.

Actually, there is a potential advantage of integrating interpersonally information in shared environments. Partial overlap of perceptual content is sufficient to produce potential benefits for joint judgments just as partial overlap of perceptual content from different perceptual modalities is sufficient to produce benefits in multi-sensory integration (Stein & Meredith, 1993), e.g., when vision and proprioception complement each other in localizing objects on a 2D surface (van Beers, Sittig, & van Der Gon, 1999), or when vision and touch complement each other in object recognition (Ernst & Bülthoff, 2004; Newell, Ernst, Tjan, & Bülthoff, 2001). To date, studies addressing joint judgment and decision making in an optimal weighting perspective have addressed interpersonal integration of redundant information where multiple individuals received the same perceptual stimuli with different levels of noise added (Bahrami et al., 2010). In the present study we investigated whether the findings obtained in these studies generalize to perception in shared environments where different individuals receive complementary perceptual information.

1.3. The present study

The present study aimed to investigate two questions: (a) whether pairs of participants sharing the same environment show collective benefit for perceptual judgments, and (b) whether the mere necessity to agree on a joint judgment in a shared environment is sufficient to obtain collective benefit. One hypothesis is that achieving collective benefit hinges on verbal communication of confidence. An alternative hypothesis is that collective benefits hinge on a shared feedback from the environment. We tested these hypotheses with a joint target localization task (Voinov, Sebanz, & Knoblich, 2017) that required two individuals to agree on the location of a target in a plane, looking from orthogonal viewpoints or from the same viewpoint. Locating a target from the same viewpoint implied that both partners provided their judgments based on the same redundant perceptual information. Locating a target from different viewpoints implied that both partners provided their judgments based on complementary perceptual information.

The joint localization task capitalized on the finding that human depth perception on a front-back dimension along the participants’ line of sight is less accurate (liable to high variability of judgment errors, see van Beers et al., 1998) than perception on the left-right dimension (liable to low variability of judgment errors). When two partners look at a shared environment from orthogonal viewpoints one partner’s inaccurate front-back dimension may be compensated by the other’s accurate left-right dimension and vice versa (see Fig. 1B).

Fig. 1.

(A) Schematic depiction of the virtual environment used for the location task (the size of the pointer and the target were much smaller during the actual experiment, see Supplementary Video 1). Participants were asked to locate a POINTER above a TARGET so that it would point exactly to its center. FEEDBACK was only provided once at the end of each trial. It consisted of a line that projected the position of the pointer on the upper plane to the lower plane, visualizing the distance between pointer and target on the lower plane (ERROR). (B) Schematic illustration of the four visual viewpoints used in the experiments as seen from the top of the 3D container (see main text). Two viewpoint sets, each with a pair of orthogonal viewpoints, were used (listed from top-left counter-clock-wise): 160°/250°, and 290°/20°). Ellipses visualize idealized uncertainty of participants with respect to the correct location of the pointer. Dashed lines are aligned with participants’ virtual lines of sight.

We predicted that the necessity to reach an agreement in a shared environment would require each individual to move somewhat away from the location they believed to be correct, leading to joint locations located in between participants’ initial judgments. If the joint judgment is located exactly in between initial judgments, this would amount to averaging initial judgment vectors. This should cancel out random error inherent in individuals’ internal estimations and in this way improve the accuracy of joint judgments (Larrick et al., 2012), even if the agreed upon location does not coincide with the exact mid-point between the two initial judgments (Soll & Larrick, 2009). This implies that dyads should reach higher accuracy (smaller error) than their average member without communicating to one another. Alternatively, if communication plays an essential role in the process if inter-individual integration, improved accuracy of joint judgments should only be enhanced if communication is allowed.

A stronger hypothesis is that individuals weight the contributions of their individual judgments to the joint judgments proportionally to the precision of their internal estimates of the true location. This would require that the two individuals in a dyad are sensitive to the geometric properties of each other’s uncertainty and give higher weight to those dimensions of the judgment of the partner that reflect the partner’s more reliable perception. Accordingly, we predicted that members of a dyad perceiving a shared environment should achieve close to optimal weighting of two-dimensional perceptual information (target location on the front-back dimension and the left-right dimension) even if they have no opportunity to verbally communicate to each other their confidence in the judgment on each dimension. If this is the case, the accuracy of joint judgments should be higher than the judgments of the most accurate dyad member, even if the members of the dyad have no opportunity to communicate.

To address our research questions, we conducted four experiments with two factors crossed: the viewpoints that the two partners had access to (complementary vs. same) and availability of feedback on the accuracy of joint judgments (provided vs. not provided). Opportunity for communication (allowed vs. disallowed) was manipulated within subjects in each experiment. Additionally, we introduced an Individual Double (ID) condition where one participant had access to both viewpoints. The purpose of this condition was to investigate how well individuals can integrate information from two viewpoints when they have access to both viewpoints. The key features of the experiments are summarized in Table 1.

Table 1.

Summary of the key parameters varied across experiments.

Experiment	Difference between the two viewpoints (Joint and ID* condition).	Availability of feedback on accuracy
Experiment 1	90° (Complementary viewpoints)	Available on each trial
Experiment 2	90° (Complementary viewpoints)	Absent
Experiment 3a*	0° (Same viewpoint)	Available on each trial
Experiment 3b*	0° (Same viewpoint)	Absent

^*In Experiments 3a and 3b the ID condition is essentially identical to an individual baseline where judgments are based on information from a single viewpoint.

In the next section we’ll specify three possible integration schemes that could formally account for the process of integrating individual observations into a joint judgment. These schemes predict different amount of collective benefit resulting from such integration.

1.4. Models for multi-dimensional information integration

Deriving three different models for multi-dimensional information integration enabled us to predict different statistical properties of the distribution of joint judgments based on the statistical properties of distributions of the contributing individuals’ judgments. These three models included ‘Simple Averaging’, ‘Take-the-Best’, and ‘Multidimensional Optimal Weighting’ (see below).

Our research strategy was to compare the fits of the three models to empirical data to specify in more detail how participants formed their joint judgments under different conditions. In analogy to the work obtained in the domain of intra-individual sensory information integration (Ernst and Bülthoff, 2004, van Beers et al., 1996, van Beers et al., 1999), all models predict that joint judgments should be more reliable (precise). However, the models differ in their quantitative predictions regarding the variability of joint judgments and its geometric properties. Using the model predictions as benchmarks for the accuracy of joint judgments, we could exclude out models where the accuracy of joint judgments exceeded the accuracy predicted by a model and conclude that a more effective process must have taken place.

In the ensuing description of the three models we will use the following notation: individual location judgments are denoted with vectors ${\mathbf{j}}_{\mathrm{i}}={\left[x_{\mathrm{i}},y_{\mathrm{i}}\right]}^{\text{'}}$ where i ∈ {1, 2} is an individual member of a dyad, and X and Y are the two dimensions of a Cartesian coordinate system. Each member’s judgment is modeled as a true location θ $=\left[x_0,y_0\right]\text{'}$ with added random error sampled from a bivariate distribution parameterized with mean μ_i $={[\overline{x}}_{\mathrm{i}},{\overline{y}}_{\mathrm{i}}]\text{'}$ and the following variance-covariance matrix:

$${\mathbf{\Sigma }}_{\mathrm{i}}=\left[\begin{array}{cc}{\sigma }_{\mathrm{i},\mathrm{x}}^2& {\rho }_{\mathrm{i},\mathrm{x}\mathrm{y}}{\sigma }_{\mathrm{i},\mathrm{x}}{\sigma }_{\mathrm{i},\mathrm{y}}\\ {{\rho }_{\mathrm{i},\mathrm{x}\mathrm{y}}\sigma }_{\mathrm{i},\mathrm{x}}{\sigma }_{\mathrm{i},\mathrm{y}}& {\sigma }_{\mathrm{i},\mathrm{y}}^2\end{array}\right]\text{,}$$ (1)

where σ_i,d is the standard deviation of random error on dimension d ∈ {x, y}, and ${\rho }_{\mathrm{i},\mathrm{x}\mathrm{y}}$ is the correlation between X  and Y errors for individual i. Thus, the mean of the distribution μ_i reflects perceptual bias for individual i, and ∑_i characterizes variability in individual i’s judgments and reflects his or her perceptual uncertainty about the correct target location. Note that individual judgments ${\mathbf{j}}_{\mathrm{i}}$ do not need to be made explicitly but are assumed to arise in the mind of an observer in response to the external stimulus with the true parameter value equal to θ.

Individual judgments are then combined to form the joint judgment with one of the following integration schemes.

Simple averaging. This model implies that individuals in a dyad give equal weights to each other’s judgment on both dimensions. The joint judgment is derived by averaging individual judgments of the two dyad members: ${\mathbf{j}}_{\mathrm{j}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}=0.5{\mathbf{j}}_1+0.5{\mathbf{j}}_2$. The distribution of joint judgments is expected to have the following variance-covariance properties¹:

$${\mathbf{\Sigma }}_{\mathrm{j}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}=0.25{\mathbf{\Sigma }}_1+0.25{\mathbf{\Sigma }}_2\text{,}$$ (2)

where ∑₁ and ∑₂ is the variance-covariance matrix (Eq. (1)) of random error characterizing variability in judgments of the first and second dyad member respectively. In a scenario where individuals judge the same stimulus (for example, when making observations from one viewpoint), this simple strategy is expected to substantially reduce random error in joint judgments (Larrick et al., 2012), and allow dyads to reach higher accuracy than their average member.

Take-the-best. This model assumes that the joint judgment on each trial is equal to the judgment of the individual with the highest overall precision: ${\mathbf{j}}_{\mathrm{j}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}={\mathbf{j}}_1$. This predicts that the distribution of the joint judgments will have the same variability properties as the distribution of the more accurate member’s individual judgments: ${\mathbf{\Sigma }}_{\mathrm{j}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}={\mathbf{\Sigma }}_1$, where $({\sigma }_{1,\mathrm{x}}^2+{\sigma }_{1,\mathrm{y}}^2)<({\sigma }_{2,\mathrm{x}}^2+{\sigma }_{2,\mathrm{y}}^2)$. Note that this model requires that individuals assess and evaluate the precision of each other’s judgments.

Multidimensional optimal weighing. Optimal weighting models provide a quantitative benchmark for how much collective benefit can be expected given the precision of the contributing individual judgements. This model is the multidimensional extension of the optimal model for integrating redundant observations (Ernst & Bülthoff, 2004), where individual judgments are weighed by their reliability. The derivation of the joint judgment can be written out as the linear combination of individual judgments:

$${\mathbf{j}}_{\mathrm{j}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}={\left({\mathbf{W}}_1+{\mathbf{W}}_2\right)}^{-1}\left({\mathbf{W}}_1{\mathbf{j}}_1+{\mathbf{W}}_2{\mathbf{j}}_2\right)\text{.}$$ (3)

This model assumes that participants in a dyad have full access to the structural properties of their uncertainties about the location and combine them in a statistically optimal fashion. This implies that the weight matrix W_i applied to a judgment from individual i is the inverse of the variance-covariance matrix ∑_i that characterizes variability in individual i’s judgments (van Beers et al., 1999): ${\mathbf{W}}_{\mathrm{i}}={\mathbf{\Sigma }}_{\mathrm{i}}^{-1}$. In this way, weight matrix W_i accommodates all information about the extent of an individual’s uncertainty and its geometric properties. If the weights are combined in a statistically optimal way, the precision of joint judgments is expected to be always at least as high as that of the more precise dyad member or higher. The predicted composition of the variance-covariance matrix of joint judgments in this case is

$${\mathbf{\Sigma }}_{\mathrm{j}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}={\left({\mathbf{\Sigma }}_1^{-1}+{\mathbf{\Sigma }}_2^{-1}\right)}^{-1}\text{.}$$ (4)

The model also provides the upper bound for the level of precision a particular dyad can reach in their joint judgment based on statistically optimal integration of information given the individual uncertainties associated with the two dimensions of the judgment.

2. Experiment 1

The first experiment addressed two questions. First, we investigated whether the need to agree on joint judgments that are informed by complementary perceptions from orthogonal viewpoints leads to collective benefit. This should lead to higher accuracy and lower judgments variability when locating a target together from different viewpoints than when locating it alone from one viewpoint. Based on individual performance from one viewpoint we derived model predictions for joint performance that enabled us to establish whether the interpersonal integration used to obtain joint judgements is Simple Averaging, Take-the-Best, or Multidimensional Optimal Weighting. To investigate whether interpersonal integration of perceptual information from different viewpoints is more accurate or less accurate than intrapersonal integration (Avraamides et al., 2012, van Beers et al., 1999) we compared the accuracy of joint judgements to the accuracy of judgments of one individual with access to both viewpoints.

Finally, we investigated whether the opportunity to verbally communicate increases collective benefit. This is predicted if communicating confidence is crucial for obtaining benefits from joint judgments (Bahrami et al., 2012a, Bahrami et al., 2012b).

2.1. Method

2.1.1. Participants

Thirty-two students (18 female), aged between 19 and 27 years (M = 22.9) were tested in pairs. Participants provided informed consent and received fixed payment for their participation (corresponding to roughly $4 per hour). The two participants in a pair were always of the same gender. One dyad was replaced due to poor accuracy (3 SDs above average in one of three experimental conditions). Participants in all dyads reported to not have known each other prior to participating in the experiment.

2.1.2. Material and apparatus

The experiment used two Apple iMac computers (2.5 GHz Intel Core i5 with a 21.5″ Display and AMD Radeon HD 6750 M 512 MB graphics) and an additional external monitor (BenQ RL2240H 21.5). The screen resolution was 1600 × 900 pixels on all displays and color output was matched. Location judgments were provided with two joysticks (Thrustmaster T16000M ambidextrous).

The perspective mode of MatLab (The Mathworks, Natick, MA) was used to generate a two-dimensional projection of a three-dimensional square-based rectangular cuboid with a length × width × height ratio of 2 × 2 × 1 (see Fig. 1A). The cuboid was centered on the screen area (263 × 204 mm) and simulated a real-world cuboid (256 × 256 × 128 mm). The target location was displayed inside of the inner area of the cuboid’s bottom plane (minimum distance of 51 mm from each side). The upper and lower planes of the cuboid were colored in a shade of cyan and were semi-transparent. The side planes of the cuboid were fully transparent. To provide cues to different orientations of the cuboid the delineating lines of one of the cuboid’s vertical planes were colored green and thicker than other lines (colored black).

The length of the cuboid’s sides on the screen followed the laws of perspective projection. Two sets of two viewpoints were used (all four viewpoints had equal distance from the center). Each set included two orthogonal viewpoints. If seen from the top of the cuboid, virtual camera positions of the four viewpoints were at 20°/290° (Set 1) and 160°/250° (Set 2) with respect to the horizontal axis. All viewpoints provided a slanted view on the cuboid, with a 14° angle between the container’s bottom plane and the virtual line of sight. The camera view angle was set to a constant 6.3° to minimize angular distortions in the scene.

2.1.3. Design and procedure

The experiment had two within-subject factors. The first factor varied the way in which participants performed the task. In the Joint (J) condition the two individuals in a pair had simultaneous access to one of two orthogonal viewpoints and provided a joint location judgment. In the ID condition individual participants had sequential access to two orthogonal viewpoints and provided one location judgment. The second factor varied whether communication was available during the Joint task performance (Com+) or not (Com−). This resulted in a nested design with factor Communication being nested within the factor Condition. Furthermore, we included an additional baseline where individual participants provided one location judgment from a single viewpoint (IS).

The two participants in a pair were seated in different rooms with separate monitors and joysticks. Each participant received an initial video instruction explaining the setup and the task (see Supplementary Video 1). The main experiment was run in two sessions. Each session consisted of a block of 20 J trials and a block of 20 ID trials. In one session communication was allowed in J trials and in the other session communication was not allowed in J trials. The order of sessions, the order of blocks within sessions, and the viewpoint sets used for the Joint and Individual Double condition were counterbalanced across pairs of participants.

At the beginning of each of the four blocks participants received further instructions. In J blocks participants were instructed to visit each other’s rooms to look at their partner’s setup so that they knew which viewpoint their partner had on the cuboid. Further instructions specified whether communication was allowed. At the beginning of each ID block participants were instructed how to switch between different viewpoints on the cuboid. Before and after the main experiment both individuals in a pair were asked to provide a location judgment from a single viewpoint (IS, 20 trials before and 20 trials after). The whole experiment took about 2 h.

At the beginning of each trial a randomly positioned target on the cuboid’s bottom was displayed together with a pointer randomly positioned in one of the four corners of the cuboid’s upper plane. Participants had 120 s to judge the target location by moving the pointer with the joystick. If no judgment had been provided after 110 s warning beeps sounded each second afterwards. After the judgment was delivered or after the time limit was reached, participants received immediate feedback in the form of a colored line connecting the apex of the pointer with the bottom plane of the cuboid visible for 5 s (see Fig. 1A).

In the J blocks, the two partners observed the same cuboid from orthogonal viewpoints. The inputs from their two joysticks were summed up resulting in joint control of the pointer. If two partners tilted their joysticks by the same angle in the same direction, the pointer moved twice the distance compared to one partner tilting the joystick in the same way. Each participant in a pair could make a location proposal by pressing a joystick button that froze the pointer at its current location. Their partner could either accept the proposal leading to a consensual judgment, or she could continue moving the pointer after 5 s. If the two partners did not agree within the time limit, the pointer’s position at the end of the trial was coded as not consensual. In the communicative J block the partners talked to each other via headsets with no constraints on the content of their communication. In the non-communicative J block headsets were disabled.

In ID blocks both individual participants could switch between two different viewpoints and provided an individual judgment based on sequentially integrated information. The initial perspective corresponded to the one participants worked from in the J condition of the respective experimental session. Participants initiated a change in perspective (camera rotation) using keyboard keys. There was no limit on the number of switches per trial. As in the J condition pressing a joystick button froze the pointer, and participants chose to either confirm the judgment or to continue moving the pointer. The ID blocks were the same in the communicative and non-communicative sessions of the experiment because there was nobody to communicate with.

In the IS baseline participants provided their judgment from one viewpoint. A single press on the joystick button was required for the location judgment.

2.1.4. Data preparation

From the raw data (two-dimensional coordinates in the cuboid’s x-y plain) the Euclidean distance between the judged and true location of the target was computed. This “absolute error” provides a measure of the overall accuracy of participants’ judgments. To obtain a variability measure of participants’ location coordinates that reflects participants’ uncertainty (Gigone & Hastie, 1997) about the target location we removed the bias component from the directional error coded in a two-dimensional vector format. The most prominent bias in the present experiment was to overshoot on the depth dimension and this is in line with biases observed in individual performance (e.g. van Beers et al., 1998, van Beers et al., 1999). Such biases are thought to occur when participants observe a visual layout under a slant angle as was the case in the present experiment. The same transformation also removed variability that resulted from participants’ gradual learning from feedback to compensate for the overshooting bias, which results in a drift of the geometrical center of their judgments within a condition.

In order to achieve this we subtracted variance resulting from such drifts from the total variance of judgments (e.g. van Beers et al., 1996, van Beers et al., 1998, van Beers et al., 1999). The drifts were calculated through linear fits that determined drifts in each of the two spatial dimensions (left-right, depth) across consecutive trials. The drifting center coordinates were subtracted from the raw egocentric coordinates to derive the unbiased coordinates. This procedure removes both the constant bias and variance resulting from learning.

We then applied Chauvenet’s criterion (Taylor, 1997, p. 166–168) to the unbiased coordinates to identify errors that resulted from accidentally pressing the joystick button. According to this criterion, in a sample consisting of n data points, a data point may be discarded as a measurement error if the probability of obtaining a deviation from the mean at least as large as the data point in question is lower than 1/(2n). After removing the outliers, drifting centers were re-calculated and subtracted from the data.

We adopted an established scalar measure for assessment of variability for the two-dimensional spatial data: the area under the standard deviational (SD) ellipse (Ebdon, 1988, Kent and Leitner, 2007). This is an ellipse in which the semi-axes are equal to the square roots of the eigenvalues of the sample variance-covariance matrix. We used square root of the area as the dependent measure.

We used individual judgments provided from one viewpoint at the end of the experiment (IS) as a baseline and for generating model predictions for the variability of errors in joint judgments resulting from the three integration schemes. Including only these judgments leads to an optimistic estimate of participants’ individual performance from one viewpoint in the course of the experiment. This is because by the end of the experiment when the baseline was collected, participants had already received ample feedback and were very familiar with the task. We chose this procedure to avoid underestimating the precision of individual judgments when deriving model predictions, and to rule out the alternative explanation that observed benefits in the Joint condition are due to gradual learning and extensive experience with the task. Note, though, that this leads to a conservative estimate of collective benefits for joint judgments.

Prior to testing how well different integration models fit the empirical data we analyzed whether location judgments could be accurately modeled with bivariate normal distributions, which is a necessary condition for the validity of the three models’ predictions. The Henze-Zirkler's Multivariate Normality tests (Trujillo-Ortiz, Hernandez-Walls, Barba-Rojo, & Cupul-Magana, 2007) confirmed that there were no gross violations of normality in the individual data (out of n = 32 individual distributions of errors, only four distributions were not normal at p ≤ .05 level of significance).

Individual performance parameters of participants in the IS and ID condition belonging to one dyad were averaged when comparing them to the performance of the corresponding dyads in the J condition. This enabled us to compare performance of a dyad to the average performance of its members.

In addition, to these main variables of interest, we collected participants’ RTs and number of judgment proposals they made in the Joint condition. Analyses of these variables did not reveal any systematic differences relevant to the theoretical focus of the current article, and, therefore, are not reported. Details of these analyses and results are available in Voinov (2017).

2.2. Results

Participants came to a consensual joint judgment in 99.35% of trials in the condition with communication, and in 99.68% of trials without communication. Data where dyads did not reach a consensual judgment by the time limit were excluded. After excluding these trials and removing outliers (see data preparation section) 97.1% of original data were retained.

2.2.1. Absolute error

First, we analyzed absolute error of the location judgments (see Fig. 2A). We first conducted an analysis of variance (ANOVA) with the factor Communication (Communication vs. No-Communication) nested within the factor Condition (ID vs J), and dyad as a random factor. No main effects of fixed factors were significant (ps > .174). The difference in absolute error between Communicative and Non-Communicative Joint condition was also not significant (p = .819). As Fig. 2A illustrates, absolute error in the J condition (M = 7.14 mm, SD = 4.60 mm) was significantly lower than absolute error in the IS condition (M = 21.1 mm, SD = 6.18 mm), t(15) = −11.0, p < .001. Absolute error in the ID condition (M = 8.92 mm, SD = 5.24 mm) was also significantly lower than absolute error in the IS condition, t(31) = −8.21, p < .001.

Fig. 2.

Absolute error data from the three experiments. Data from the ID condition is averaged across two blocks. Error bars represent SEs of the means. (A) Experiment 1. (B) Experiment 2. (C) Experiment 3a. (D) Experiment 3b.

In a second step, we compared the absolute error of dyads in the J condition with the absolute error of the better individual in the dyad, i.e., the individual with lower absolute error (see Fig. 3A). Paired-sample t-tests showed that dyads achieved lower absolute error than the more accurate individuals in the IS condition (M = 16.0 mm, SD = 5.08 mm) both with communication (M = 7.26 mm, SD = 5.68 mm), t(15) = -5.81, p < .001, and without communication (M = 7.03 mm, SD = 4.28 mm), t(15) = −6.82, p < .001.

Fig. 3.

Comparison of performance between the better individual from a dyad and the joint performance from that dyad in Experiment 1 and Experiment 2. “Com+” – Communication condition, “Com−” – No-communication condition. Error bars are SE of the means. (A) Experiment 1. (B) Experiment 2.

2.2.2. Variability (square root of the area under the SD ellipse)

An ANOVA with the factor Communication (Communication vs. No-Communication) nested within the factor Condition (ID vs J) revealed no significant main effects (ps > .406). The difference between Communicative and Non-Communicative levels of the Joint condition was not significant either (p = .316). Variability of judgment errors in the J condition and in the ID condition were smaller than in the IS condition (M = 7.14 mm, SD = 4.60 mm), t(15) = 6.15, p < .001 and t(31) = 6.08, p < .001 respectively. This is illustrated in Fig. 4A. Generally, participants could make use of the available complementary information and effectively distributed the two dimensions in the Joint condition. This is evident from the distributions of individual judgment errors in the Joint condition provided in the Supplementary Fig. S1.

Fig. 4.

Variability of judgment errors from four experiments. Data from the ID condition is averaged across two blocks. Error bars stand for SE of the means. (A) Experiment 1. (B) Experiment 2. (C) Experiment 3a. (D) Experiment 3b.

Because there were no differences in accuracy between the Communication and the No-communication condition, square roots of SD ellipses were averaged across these two conditions. Fig. 5A plots the difference in variability predicted by the three integration models and the empirical data. Pair-wise t-tests showed that the variability was smaller than predicted by the Simple Averaging model, t(15) = −8.85, p < .001; and smaller than predicted by the Take-the-Best model, t(15) = −3.21, p = .006. However, it was still larger than predicted by the Multidimensional Optimal Weighting model, t(15) = 2.69, p = .01. Fig. 6 plots observed versus predicted variability of dyadic judgments for the three modes. A visual inspection of the graphs together with the results of goodness-of-fit tests (see Table 2) indicates that while the Simple Averaging and the TTB model substantially underestimated participants’ performance, while the MOW model overestimated it. In the latter case, the discrepancy was somewhat larger for the dyads with larger expected variability of judgment errors (see Fig. 6C).

Fig. 5.

Comparisons with model predictions from four experiment. Average differences between the predictions for the area of the SD ellipse from different integration schemes and empirical data obtained from dyads in the joint judgment condition J. Asterisks indicate whether these differences were significantly different from 0 (paired samples t-test). Error bars stand for the standard error of the mean difference. Averaging – Simple Averaging, TTB – Take-the-Best, MOW – Multidimensional Optimal Weighing. (A) Experiment 1. (B) Experiment 2. (C) Experiment 3a. (D) Experiment 3b. For Experiment 2 data from the Communication (“Com+”) and No-Communication (“Com−”) conditions are plotted separately.

Fig. 6.

Variability of dyads’ judgment errors in the Joint condition averaged between Communicative and Non-Communicative conditions (Experiment 1). Smaller values mean higher precision. Observed data is plotted against predictions of three models of information integration: (A) Simple Averaging. (B) Take-the-Best. (C) Multidimensional Optimal Weighing.

Table 2.

Results of Goodness-of-fit tests for the models of information integration.

	Simple Averaging		Take-the-Best		Multidimensional Optimal Weighing
	t	R2	t	R2	t	R2
Experiment 1	−8.85***	−3.83	−3.21**	−0.002	2.69*	0.041
Experiment 2 (Com)	−6.38***	−1.26	−3.56*	0.452	2.84*	0.505
Experiment 2 (No-Com)	−6.58***	−0.376	−1.03	0.678	3.99***	0.253
Experiment 3a	1.87	0.505	0.68	0.487	4.89***	−0.110
Experiment 3b	2.88***	−0.859	2.16**	−0.426	4.08***	−2.29

^***p < .001.

^**p < .01.

^*p < .05.

2.3. Discussion

The results clearly demonstrate that two individuals providing joint judgements took advantage of being able to observe a shared environment from two orthogonal viewpoints. They integrated information available to them to form joint judgments which were much more accurate than judgments from one individual provided with one viewpoint. The comparison of errors variability predicted by different models of interpersonal integration and the empirical data allowed us to rule out Simple Averaging and Take-the-Best models because the empirically observed variability of errors was considerably smaller than the variability predicted by these models. This implies that both individuals contributed to joint judgments on both spatial dimensions. However, the reduction in variability of errors was still smaller than predicted by the statistically optimal Multidimensional Weighting model. Despite falling short of theoretically optimal performance, dyads were not less accurate in locating the target from orthogonal viewpoints than individuals who had access to both viewpoints.

There was no indication that interindividual integration was less or more efficient than intraindividual integration. There was also no indication that the opportunity to engage in verbal communication further improved the accuracy of joint judgments. This indicates that minimal means for negotiating a collective judgment in a shared environment can be sufficient to produce collective benefits for joint judgments.

3. Experiment 2

The first aim of this experiment was to investigate whether successful integration of complementary information across participants requires that participants perceive how accurate their joint judgment was. Therefore, we provided no feedback about the accuracy of location judgments in this experiment. We predicted that participants would still benefit from complementary perceptual information provided by orthogonal viewpoints because they would weigh information on the two spatial dimensions in a way that reflected their different uncertainties of judging location on each of these dimensions.

The second aim was to investigate whether verbal communication would lead to an enhancement of collective benefit in a situation that implied higher uncertainty regarding the accuracy of the judgments provided. When feedback is lacking, collective benefit may only be achievable through verbal communication because communicating one’s confidence in individual judgments on each spatial dimension could be an efficient way to compensate for the increased uncertainty about the accuracy of one’s judgments.

3.1. Method

3.1.1. Participants

Thirty-two English-speaking students (16 females) aged between 20 and 30 years (M = 22.6) were tested in pairs. The two participants in a pair were always of the same gender. Participants provided informed consent and received payment for their participation (corresponding to roughly 4$ per hour). Participants in all dyads reported to not have known each other prior to participating in the experiment.

3.1.2. Materials and apparatus

The same stimuli and set-up as in Experiment 1 were used.

3.1.3. Procedure

The same procedure as in Experiment 1 was applied with the exception that no feedback about the accuracy of participants’ judgments was provided.

3.2. Results

Participants came to a consensual joint judgment in 98.75% of the trials in the condition with communication, and in 100% of the trials without communication. After excluding joint trials where no consensual judgment was reached, joint trials where the response exceeded the time limit, and outliers (see data preparation section of Experiment 1), 97.75% of the trials were retained for the ensuing analyses. Because statistical analyses were structurally identical to Experiment1, we’ll report the summary of the results in a tabular format (see Table 3, Table 4, Table 5) so that results can be compared across experiments.

Table 3.

Effect of Condition on Absolute Error and Area under SD ellipse. Analyses were conducted with a 2 × 2 ANOVA with the factor Communication (Communication vs. No-Communication) nested within the factor Condition (Joint vs ID). Df1 = 1, df2 = 15 for all tests.

	Absolute error			Area under SD ellipse
	F	p	ηp2	F	p	ηp2
Experiment 1	2.04	.174	0.119	0.906	.356	0.057
Experiment 2	0.009	.925	0.001	3.15	.096	0.173
Experiment 3a	11.6	.004	0.437	13.9	.002	0.481
Experiment 3b	0.01	.920	0.001	<0.001	.992	<0.001

Table 4.

Results of a one-way ANOVA with three levels (J Comminicative vs. J Non-Communicative vs IS) with Absolute Error as the dependent variable. For omnibus test df1 = 2, df2 = 30. For individual contrasts df1 = 1, df2 = 15.

	Omnibus ANOVA			Joint Com vs Joint No-Com			Joint vs IS
	F	p	ηp2	F	p	ηp2	F	p	ηp2
Experiment 1	81.7	<.001	0.845	0.054	.819	0.004	120	<.001	0.889
Experiment 2	24.2	<.001	0.617	0.716	.411	0.046	26.9	<.001	0.642
Experiment 3a	1.67	.205	0.100	2.22	.156	0.129	0.595	.452	0.038
Experiment 3b	4.97	.014	0.249	0.034	.856	0.002	10.2	.006	0.404

Table 5.

Results of a one-way ANOVA with three levels (J Comminicative vs. J Non-Communicative vs IS) with Area under SD Ellipse as the dependent variable. For omnibus test df1 = 2, df2 = 30. For individual contrasts df1 = 1, df2 = 15.

	Omnibus ANOVA			Joint Com vs Joint No-Com			Joint vs IS
	F	p	ηp2	F	p	ηp2	F	p	ηp2
Experiment 1	39.6	<.001	0.845	0.009	.926	0.001	71.9	<.001	0.827
Experiment 2	33.3	<.001	0.689	5.66	.031	0.274	51.5	<.001	0.775
Experiment 3a	7.34	.003	0.329	0.363	.556	0.024	12.0	.003	0.444
Experiment 3b	1.33	.28	0.081	2.12	.166	0.124	0.518	.483	0.033

3.2.1. Absolute error

Neither the effect of Communication nor the effect of Condition reached significance (see Table 3). There was no difference between the Communicative and Non-Communicative Joint condition (see Table 4). Fig. 3B illustrates that absolute error in the J condition was lower than the error of the more accurate dyad member in the IS condition both with communication, t(15) = −3.48, p = .003, and without communication, t(15) = −4.28, p = .001.

3.2.2. Variability (square root of the area under the SD ellipse)

An ANOVA with the Communication factor (Communication vs. No-Communication) nested within the Condition factor (ID vs J) revealed a significant main effect of Communication, F(2, 30) = 3.99, p = .029, partial η² = 0.21. Dyads overall performed better in the No-Communication Block (M = 10.6, SD = 8.27) than in the Communication block (M = 10.7, SD = 8.38) if the J and ID conditions are collapsed. As Fig. 4 illustrates, dyads provided more precise judgments in the Communicative J condition (M = 8.79 mm, SD = 6.66 mm) than in the Non-Communicative J condition (M = 10.4, SD = 7.19, also see Table 5). Supplementary Fig. S2 plots individual judgment errors for each dyad to illustrate that a high proportion of participants could effectively and near-optimally distribute the two dimensions within the dyad without feedback and without communication. This figure along with Fig. 7 demonstrates that for certain dyads (e.g. dyad 9, 11, 12, 16) judgments were more precise when communication was available.

Fig. 7.

Variability of dyads’ judgment errors in the Joint condition (Experiment 2). Smaller values mean higher precision. Observed data is plotted against predictions of three models of information integration: (A) Simple Averaging. (B) Take-the-Best. (C) Multidimensional Optimal Weighing. Data points are labeled by the dyad number.

Because there was a significant difference in variability of judgment errors between the Communicative and the Non-Communicative J condition, we analyzed these two conditions separately (see Figs. 5B, 7, and Table 2). Variability of errors in joint judgments in the Communication condition was significantly smaller than predicted by the Simple Averaging model, and smaller than predicted by the Take-the-Best model, but significantly larger than predicted by the MOW, t(15) = 2.84, p = .012. In the Non-Communication condition variability was significantly lower than predicted by the Simple Averaging model and significantly larger than predicted by the MOW model, but in contrast to the Communication condition, variability of errors was not significantly lower than predicted by the Take-the-Best model. As indicated by the coefficients of determination (see Table 2), Take-the-Best model provided a better fit to the observed data in the Joint Communication condition than in the No-Communication condition. At the same time, the MOW model provided a rather poor fit to the data from the Joint No-Communication condition, while it provided the best fit for the data from the Joint Communication condition.

3.3. Discussion

The results of Experiment 2 demonstrated that individuals successfully integrated complementary information available to them into a joint judgment. They reached a collective benefit even when feedback was absent. Complementary information and minimal means of negotiating the collective judgment were sufficient to obtain collective benefits and to reach a comparable level of accuracy observed in intrapersonal integration of perceptual information from different viewpoints

However, other than in Experiment 1, verbal communication facilitated inter-individual information integration in Experiment 2 where feedback was lacking. The comparison of variability of errors predicted by different models of interpersonal integration and the empirical data showed that only when verbal communication was allowed joint judgments were less variable than the judgements of the more accurate individual in a dyad. Note, however, that dyads in the non-communication condition still produced less absolute error than the more accurate dyad member.

4. Experiment 3a

In the first two experiments the two partners providing joint judgments had complementary information about the target location because they were looking from different viewpoints. Previous research on joint decisions (Bahrami et al., 2010) has focused on two individuals who perceived the same fleeting information. With Experiment 3 we attempted to establish whether the results obtained in this research generalize to a situation where individuals have access to the same perceptual information in a stable shared environment. Accordingly, the first aim of Experiment 2a was to assess whether there is collective benefit from joint perceptual judgments in a stable perceptual environment where two participants have the same viewpoint. The second aim of Experiment 2a was to investigate whether such benefits depend on verbal communication as demonstrated in previous research on perceptual decision-making (Bahrami et al., 2010, Bahrami et al., 2012a, Bahrami et al., 2012b).

4.1. Method

4.1.1. Participants

Thirty-two English-speaking students (14 males) aged between 20 and 26 years (M = 22.1) were tested in pairs. The two participants in a pair were always of the same gender. Two additional dyads were replaced due to poor performance (accuracy lower than 3 SD from sample average). Participants provided informed consent and received payment for their participation (corresponding roughly to 2–5$ per hour). Participants in all dyads reported to not have known each other prior to participating in the experiment.

4.1.2. Materials and apparatus

These were the same as in the previous experiments except that only two viewpoints (160° and 250°) were used, one in the Communication condition and one in the No-communication condition. The assignment of viewpoints to conditions was counter-balanced across dyads.

4.1.3. Procedure

The procedure was the same as in Experiment 1 and 2 except that the two individuals belonging to a dyad were assigned to the same viewpoint and thus had identical perceptual input in the Joint condition. In the Individual Double condition participants were provided with only one viewpoint which made this condition practically equal to the Individual Single condition. However, the same judgment-confirmation dialog appeared upon pressing the joystick button as in the ID conditions of Experiment 1 and Experiment 2. This ensured that the response procedure was identical to the previous two experiments, and that the difference was only in the amount of perceptual information available to an individual participant. In Experiment 3, the ID condition controlled only for the amount of perceptual experience that participants had with the task by the time when they performed one of the two J conditions. This made the experiment comparable to Experiments 1 and 2.

4.2. Results

Participants came to a consensual joint judgment in 98.44% of the trials in the No-communication condition and in 100% of the trials in the Communication condition. After excluding non-consensual trials, trials where the response exceeded the time limit, and outliers, 97.56% of original data was retained for the ensuing analyses.

4.2.1. Absolute error

The Condition factor (J vs ID) had a significant effect on Absolute error (see Table 3). Absolute error in the J condition (M = 15.8 mm, SD = 7.35 mm) was smaller than in the ID condition (M = 18.5 mm, SD = 6.65 mm). The difference between Communicative and Non-Communicative Joint conditions was not significant (p = .156). Absolute error in the IS condition was not different from the J condition (p = .452), however, it was significantly lower than in the ID condition, t(15) = −2.04, p = .049.

4.2.2. Variability (square root under the area of the SD ellipse)

The effect of Condition on variability of judgment errors was significant (see Table 5): errors were less variable in the J condition (M = 8.53 mm, SD = 2.59 mm) than in the ID condition (M = 10.3, SD = 3.03 mm). The difference between Communicative and Non-communicative Joint conditions was not significant (p = .556).

Although variability of judgment errors in the J condition was on average larger than variability of the more precise dyad members in the IS condition (M = 7.91 mm, SD = 3.0 mm), it should be mentioned that 7 out of 16 dyads reached a higher level of precision (smaller area under the SD ellipse in the J condition) than the more precise dyad member.

In this experiment the ID condition was practically equivalent to the IS condition. We, therefore, took individual judgments from the ID condition of the respective block to generate predictions on performance in the J condition from the three models. These should be best comparable to the individual abilities when performing the J condition. Because there was no difference in judgment accuracy between the Communication and the No-communication J condition, the empirical data and model predictions were collapsed across the two conditions. In contrast to the first two experiments variability of errors in joint judgments was not smaller than predicted by the Simple Averaging model and the Take-the-Best model (ps > .08). Both models provided a relatively good fit (see Table 2 and Fig. 8). However, variability was significantly larger than predicted by the Multidimensional Optimal Weighing model, t(15) = 4.89, p < .001.

Fig. 8.

Variability of dyads’ judgment errors in the Joint condition (Experiment 3a). Observed data is plotted against predictions of three models of information integration: (A) Simple Averaging. (B) Take-the-Best. (C) Multidimensional Optimal Weighing.

4.3. Discussion

As in the case of collaboration performed from orthogonal viewpoints, participants took advantage of the opportunity to integrate individual perceptions when they shared the same viewpoint receiving redundant information. This is evident from the smaller error in joint judgments compared the average individual error in the ID condition. The latter would not be possible without some process of information integration or distribution.

From the comparison of the present data with the predictions of three information integration models we can conclude that joint judgments were less precise than predicted by the statistically optimal model. We cannot conclude whether both participants averaged their private estimations on each trial or whether the more accurate member dominated in the final judgment on most trials (Hastie & Kameda, 2005): both strategies could result in the empirically observed pattern of accuracy and variability of judgment errors.

In contrast to previous findings which pointed to a crucial role of verbal communication as a determinant of collective benefit in integrating perceptual information (Bahrami et al., 2010), we did not find any effect of communication on collective benefit in the present task. This discrepancy might be due to a difference in inter-individual processes in decision-making and judgment tasks. We’ll return to this issue in the general discussion.

5. Experiment 3b

Previous research on perceptual decision-making (Bahrami et al., 2010, Bahrami et al., 2012b) has demonstrated that verbal communication can be especially helpful when integrating redundant information in the absence of feedback on the accuracy of the decisions. When people are allowed to communicate their confidence, they can obtain the same collective benefit with and without feedback about the accuracy (Bahrami et al., 2010, Bahrami et al., 2012b, Fusaroli et al., 2012). This led the authors to conclude that one of the functions of meta-cognition is to overcome the limitations of simultaneous uncertainties about the environment and one’s decisions by replacing objective feedback from the environment (2012a). To investigate whether this conclusion holds in shared environments, Experiment 3b provided no feedback about the accuracy of joint judgments from the same viewpoint. If verbal communication can substitute feedback in a joint multidimensional location judgment collective benefit should hinge on the opportunity to communicate one’s confidence to each other.

5.1. Method

5.1.1. Participants

Thirty-two English-speaking students (16 males) aged between 19 and 25 years (M = 22.6) were tested in pairs. The two participants in a pair were always of the same gender. Participants provided informed consent and received payment for their participation (corresponding roughly to 2–5$ per hour). Participants in all dyads reported to not have known each other prior to participating in the experiment.

5.1.2. Materials and apparatus

These were the same as in the previous experiments except that only two viewpoints (160° and 250°) were used, one in the Communication condition and one in the No-communication condition. The assignment of viewpoints to conditions was counter-balanced across dyads.

5.1.3. Procedure

The procedure was the same as in Experiment 3a except that no feedback about the accuracy of location judgments was provided.

5.2. Results

Participants reached a consensual joint judgment in 96.88% of the trials in the No-communication condition and in 100% of the trials in the Communication condition. After exclusion of joint trials where a no consensual judgment was reached, trials where the response was exceeded the time limit, and outliers, 97.8% of the trials were retained for the ensuing analyses.

5.2.1. Absolute error

There was no difference across ID and J conditions (see Table 3, Table 4). As can be seen in Fig. 2D, absolute error in the IS condition (M = 27.9 mm, SD = 16.1) was smaller than in the J condition (M = 33.2 mm, SD = 12.7), t(15) = −3.19, p = .006; and smaller than in the ID condition (M = 33.4 mm, SD = 9.91), t(31) = −2.89, p = .007.

5.2.2. Variability (square root of the area under the SD ellipse)

There was no difference in variability of judgment errors across J and ID conditions (see Table 5). Pair-wise comparisons showed that variability of judgment errors in the J condition was significantly larger than predicted by all three models (ps ≤ .001, see also Figs. 5D and 9).

Fig. 9.

Variability of dyads’ judgment errors in the Joint condition (Experiment 3b). Observed data is plotted against predictions of three models of information integration: (A) Simple Averaging. (B) Take-the-Best. (C) Multidimensional Optimal Weighing.

5.3. Discussion

The results demonstrate that when feedback on accuracy was not available, participants were not able to integrate redundant perceptual information obtained from the same viewpoint. This is surprising, considering that simply averaging the two judgments would already have increased joint accuracy. However, the performance results and model comparisons both indicate that participants simply did not integrate in this experiment. In contrast to findings reported in previous research on collective decision making (Bahrami et al., 2010), the opportunity to communicate one’s confidence could not compensate for the lack of feedback.

One possible explanation for the difference in results is that feedback is more important for successful inter-personal integration when dyads judge continuous perceptual information than when they make binary choices in joint decision-making. Another possibility is that participants in the present experiment did not have sufficient time to align their linguistic practices to find a common scale for expressing confidence (Fusaroli et al., 2012). In Bahrami et al.’s (2012b) study collective benefit from interaction was based on 80 joint decisions or more with feedback. It took dyads even longer to establish a reliable collective benefit without immediate feedback about the accuracy of the joint judgment. In the present experiment participants performed only 40 trials in total that involved joint judgments, 20 in the Communication condition and 20 in the and No-Communication condition. Actually, there is an indication in the present study that verbal communication may have led to collective benefit if sufficient time to more time to align expressions of confidence would have been available: Numerically, dyads who could communicate had smaller variability of errors than individuals in the ID condition (see Fig. 4D).

Surprisingly, participants were most accurate when providing individual judgments from one viewpoint at the end of the experiment. This was not accompanied by a reduction in variability of judgment errors. Therefore, the improvement likely occurred because participants gradually calibrated their sensory system to looking from a slant angle leading to a decrease in their overshooting bias.

6. General discussion

The present study asked whether sharing the same environment can produce collective benefits for perceptual judgments and whether achieving such benefits hinges on verbal communication of confidence. Experiment 1 and 2 bore out our prediction that performing joint judgments in a shared environment is sufficient for dyads to achieve effective interpersonal integration of complementary information available to its members. Dyads systematically outperformed their better members when different viewing perspectives on the shared environment implied different orientations of the scatter of localization errors for the individuals in the dyad. Although, on average, the accuracy achieved by dyads was still significantly lower than optimal, it was also significantly higher than predicted by ‘Take-the-Best”. Thus, collective benefits occurred because the members of the dyad formed a structurally accurate representation of multi-dimensional uncertainty which captured that each observer’s accuracy on the front-back dimension was lower than her accuracy on the left-right dimension. This allowed dyads to come close to optimally weighting complementary spatial information available from different individual viewpoints when agreeing on joint judgments.

When exposed to redundant perceptual information in Experiment 3, dyads systematically reached higher accuracy than the average of the two members if feedback on accuracy was provided (Experiment 3a). As we predicted, the need to agree was sufficient to improve the quality of judgments: either because two partners formed a compromise or let the more accurate partner dominate in the joint judgment. However, when feedback on accuracy was absent (Experiment 3b), they effectively failed to integrate available information. These findings suggest that in a situation of interacting in a shared stable environment objective feedback plays a critical role in the process of information integration.

The role of verbal communication in improving the accuracy of joint judgments was rather limited. In Experiment 1 and 2 where participants occupied orthogonal viewpoints, dyads systematically outperformed the better individuals with an access to only one viewpoint, regardless of whether they had an opportunity to verbally communicate. Furthermore, there was no evidence that the precision of inter-individual information integration differed from intra-individual integration of information across two viewpoints. In Experiments 3a and 3b, where participants shared the same viewpoint, there was also no evidence that the opportunity to communicate increased the precision of information integration. The only indication that verbal communication was beneficial came from Experiment 2 with orthogonal viewpoints, where no feedback was provided. Here, verbal communication aided participants in achieving lower variability of judgment errors. In line with previous research, verbal communication compensated for the lack of feedback (Bahrami et al., 2010, Bahrami et al., 2012b) and helped dyads to correctly adjust weighting of complementary information obtained from different viewpoints.

It is likely that this was achieved because participants were able to communicate their hypotheses (Beppu & Griffiths, 2009) about structural relations between their viewpoints and their ability to precisely locate the target on different spatial dimensions. This is in line Tylén, Weed, Wallentin, Roepstorff, and Frith (2010) claim that verbal communication is particularly efficient in situations requiring coordination of complementary abilities (Sebanz, Bekkering, & Knoblich, 2006) and supports joint attention, perspective-taking (Beveridge and Pickering, 2013, Dietz et al., 2010), and the construction of higher-order situational models of joint tasks. Further experiments controlling the verbal communication channel between collaborating individuals could help to clarify which aspects of verbal communication are useful in improving joint judgments and when.

Surprisingly, in Experiment 3b where participants looked at a shared environment from the same viewpoint verbal communication could not compensate for the lack of feedback. This is in contrast to previous studies on joint decision-making based on perceptual information. For instance, Bahrami et al., 2010, Bahrami et al., 2012b found large benefits of communication when participants received the same perceptual information and no feedback about the accuracy of joint judgments. Thus, whereas previous research has suggested that verbal communication may be both necessary and sufficient for collective benefit (Bahrami et al., 2010, Bahrami et al., 2012b) in joint judgment and decision making, our findings could be taken to suggest just the opposite: Communication was neither necessary nor sufficient to achieve collective benefit from inter-individual integration of perceptual information. Thus, metacognition that is mediated through verbal communication of confidence does not seem to be the only way to optimize joint judgments, at least when joint judgments are derived in a shared environment.

It is an open question whether this conclusion can be generalized to decision making that requires dyads to make a binary choice or whether the present results are restricted to providing estimates on a continuous scale. Although normative theories suggest that judgment and decision making are two sides of the same coin, psychological research suggests that there may be qualitative differences between the psychological processes supporting information integration for continuous judgments and the processes supporting information integration for binary choices (Einhorn and Hogarth, 1981, Hinsz, 1999, Hinsz et al., 1997).

Most relevant for the present purpose is the possibility that the role of communicating confidence might be larger when making choices during decision making. Whereas in Bahrami et al.’s studies on decisions making Bahrami et al., 2010, Bahrami et al., 2012a, Bahrami et al., 2012b verbal communication of confidence was the crucial factor for optimal interpersonal information integration, knowing each other’s confidence did not matter in an earlier group study with continuous judgements (Sniezek & Henry, 1989). In this study groups ignored each other’s confidence when weighting individual judgments to provide a collective judgment, presumably because there was no systematic relationship between individuals’ confidence in their judgments and the actual accuracy of their judgments (see also Sniezek & Henry, 1990). Given these inconsistencies it would be worthwhile to directly compare the role of verbal communication of confidence and the role of objective information (feedback) from a shared environment in joint judgment and decision making. Such studies could help us to understand whether joint judgments and joint decision are based on the same or different integration processes and whether these processes differ in their reliance on metacognition and objective information available from a shared environment.

Another possible source of discrepancy between the present results and previous results might be the source of noise in individual perception. In our task participants had a long time (120 s) to sample the environment, while previous studies presented stimuli very briefly. The difference in time for sampling perceptual information may lead to different ways of dealing with uncertainty. Our results suggest that when a shared environment can be continuously sampled, joint judgments may rely less on communicating one’s confidence to resolve disagreements. One potential reason for this is that participants prioritize assessing the structure of the environment over sharing confidence when they have continuous access to shared perceptual information.

The discrepancy in results between the present study and Bahrami and colleagues earlier studies also raises the question to what extent the results obtained so far are task-specific and to what extent they tap into general psychological processes. Some aspects of the present data can shed some light on this question. The apparent failure of pairs to integrate their judgments without external feedback on accuracy in Experiment 3b indicated that, indeed, some learning must take place within the experimental situation to potentiate joint success. Similarly, in the studies by Bahrami et al. (2012a) in the absence of feedback, it took participants some time until they obtained collective benefit from their interactions. Bahrami et al. (2012b) put forward the hypothesis, that one of the functions of meta-cognition is to substitute objective feedback from the environment and to allow collective learning by means of verbal interaction and exchange of confidence in one’s judgments. As pointed out previously, the fact that communication had no effect on participants’ performance in Experiment 3b might be either to the fact that our experiment was too short for communication to work, or because it is just not as effective in a situation of continuous judgment as opposed to a situation of a dichotomous choice.

Whereas our models for information integration can be considered static in a sense that they do not develop over time on the time scale of an experimental condition, this is certainly a simplifying view on the social processes unfolding between two partners in the task. To properly address the question of how learning from feedback or communication translates into a stable strategy of making joint judgments, one would require process-tracing techniques, where on each trial independent individual judgments and a joint judgement are collected. This would allow one to analyze the relation between individual and joint judgments on a trial to trial basis. However, this would come at the cost of not being able to rule out primacy effects (Anderson, 1991) and biases reflecting individuals’ commitment to sticking to their initial judgment (Sorkin et al., 2001).

At the same time, the fact that in Experiment 2 participants obtained collective benefit in absence of both objective feedback and verbal communication from the beginning, suggests that in certain situations effective means for information integration are available that do not have to be learned. Here, collective benefit was obtained when complementary perceptual information was provided, but in theory the same should apply to integration of continuous information outside of perceptual domain as well (Voinov, 2017). For example, if one financial expert is good at predicting different return rates and another one is good at predicting inflation rates, they should be able to obtain maximum collective benefit in making an investment decision. Such generalizations are tempting but not necessarily warranted. Einhorn and Hogarth pointed out a long time ago that “the elements of a psychological theory of decision making must include a concern for task structure, the representation of the task, and the information processing abilities of the organism” (1981, p. 9). In actual behavioral experiments, while focusing on one element, the influence of the other is often left out as an uncontrolled variable. Building a complete theory capable of making general predictions would require adopting a broader perspective (Carroll, 1980) and investigating influence of contextual factors that are typically ignored (cf. Einhorn & Hogarth, 1981). A way forward would be to replicate various findings across different tasks and domains (e.g. perceptual and cognitive). If the effects in question prove to be stable and replicable across a wide range of domains, the consequential conclusion would be that the cognitive processes responsible for these effects are rather general and fundamental in their nature. This, in turn, would allow one to make more confident predictions based on the empirical findings regarding the applicability of these findings to a wider range of real-life scenarios.

The main conclusion from the current study is that the necessity of reaching agreement in a shared environment is sufficient to achieve close to optimal integration of perceptual information when individuals in a group receive complementary perceptual information and/or feedback about the accuracy of joint judgments. How does the necessity to agree exert its power of optimizing joint judgments? A first factor is that individuals insist more on influencing the dimensions of joint judgments they feel more certain about. A second factor is that shared environments provide opportunities for individuals to exchange implicit confidence, an automatic and non-conscious assessment of individual (un)certainty (Bach & Dolan, 2012). This may be mediated by action kinematics that reflect people’s confidence in their own decisions (Freeman et al., 2011, McKinstry et al., 2008, van der Wel et al., 2014) and inform them about others’ confidence in their decisions (Patel, Fleming, & Kilner, 2012). Both factors are independent of symbolic communication and thus have a potential to lead to large collective benefits in joint judgment and decision making that do not require sharing a common language for communicating confidence in one’s individual judgments.

7. Declarations of interest

None.

Appendix A. Supplementary material

The following are the Supplementary data to this article:

This is open data under the CC BY license (http://creativecommons.org/licenses/by/4.0/).