MEASURING “GROUP COHESION” - Ricerca sull'intelligenza artificiale specializzata al MIT

MEASURING “GROUP COHESION”

TO REVEAL THE POWER OF SOCIAL RELATIONSHIPS IN TEAM PRODUCTION

SIMON GÄCHTER, CHRIS STARMER AND FABIO TUFANO*

University of Nottingham and University of Leicester**

30 novembre 2022

We introduce “group cohesion” to study the economic relevance of social relationships in

team production. We operationalize measurement of group cohesion, adapting the “oneness

scale” from psychology. A series of experiments, including a pre-registered replication,

reveals strong positive associations between group cohesion and performance assessed in

weak-link coordination games, with high-cohesion groups being very likely to achieve

superior equilibria. In exploratory analysis, we identify beliefs rather than social preferences

as the primary mechanism through which factors proxied by group cohesion influence group

performance. Our evidence provides proof-of-concept for group cohesion as a useful tool for

economic research and practice. JEL Classification: C92, D91

IO.

introduzione

A vast array of economic and social activity occurs in groups and teams. People need to

coordinate and cooperate as colleagues in the workplace, teams on sports fields, army units on

the battlefield, and across a host of less formal interactions with relatives, friends, E

neighbors. In this paper, we report an extensive program of conceptual and experimental

research building from the arguably plausible idea that the ‘qualities’ of social relationships

within households, firms, or other organizations, collectively constitute an important factor of

production. While various strands of existing literature hypothesize that social relationships

may matter for economic outcomes (see Section II below), our motivation stems from the

absence of any systematic approach to measuring the productive value of social relationships.

Our primary contribution is to develop and test a measurement tool, based on a new concept

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012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 Internazionale (CC BY 4.0) licenza.

of group cohesion, with a view to providing foundations for the study of social relationships

as factors of production.

We proceed via two main steps. The first is to introduce a simple, but conceptually well-

grounded, approach to characterizing any real group in terms of a group cohesion index,

intended as a summary statistic for aspects of social relationships that matter for team

production. Our second main step is to test the predictive power of the group cohesion index

in a large-scale program of experiments and accompanying analysis investigating (weak-link)

team production in real groups that vary in terms of their pre-existing social relationships.

Since group cohesion is a novel concept in economics, in Section III, we explain the rationale

for the concept, our approach to measuring it and some of its key properties. To preview briefly,

our starting point is that members of any real human group inevitably have some relationships

to other group members: for example, to begin with a very simple idea which we later

operationalize, some people might feel “close” to other group members, whereas others may

feel quite “distant.” In our approach, we use the term “group cohesion” (or sometimes just

“cohesion” for brevity) to refer to the state of the aggregate closeness ties within a group.

Because closeness is an essentially subjective concept, it is natural to wonder whether it can be

reliably measured either for pairs of individuals or aggregated to form a meaningful group-

level statistic. Our research supports positive answers to both questions. Our measurement of

group cohesion is based on the well-established “oneness scale” (Cialdini et al. (1997)) whose

psychometric properties we replicated successfully in previous research (Gächter, Starmer and

Tufano (2015)). The oneness scale uses simple, and very portable methods to assess how close

one person feels to another, based on their own self-reports. From a measurement viewpoint,

our innovation is to develop an aggregate statistic, based on oneness, to characterize the set of

relationships within a group. Specifically, in our experiments, we ask each group member,

privately, to indicate their oneness with every other group member. The group cohesion index

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is then calculated as an average of individual oneness ratings (full details of our measurement

approach and its psychological foundations are in Section III.A).

This seemingly modest measurement innovation generates a tool with considerable

predictive power: Across a set of six experiments (see Appendix Table 3 for a summary of key

aspects), we demonstrate that group cohesion is strongly associated with group outcomes. Noi

explain the main experimental setup in Section IV. A key feature is that we study the behavior

of real groups – not artificially created ones – achieved by recruiting groups of friends to

participate. Hence, we observe real closeness ties based on pre-existing sociological and

psychological characteristics that are absent (by construction) in groups set up on the spot in

the lab, including those using minimal group manipulations (Goette, Huffman and Meier

(2012)). 1 As we will show, measured cohesion tracks tangible sociological features of the real

groups we study (see Section III.B).

Our workhorse to study group outcomes is a weak-link game, chosen to model coordination

problems endemic to real organizations and teams (per esempio., Camerer and Weber (2013)). In our

version of the weak-link game, group members simultaneously choose an “effort level”.

Payoffs to each group member then depend on their own effort and the lowest effort chosen by

anyone (the “weakest link”) in the group. The game has multiple strict Pareto-ranked Nash

equilibria in material payoffs reflecting two dimensions of group success: coordination

(matching the effort level of other group members) and cooperation (achieving Pareto-superior

equilibria). Building on the approach of Brandts and Cooper (2006), we designed our game to

be “harsh” in the sense that groups lacking pre-existing social relationships would be expected

to collapse to the Pareto-worst equilibrium.

Section V presents the key behavioral patterns in our data. We identify a strong positive

association between group cohesion and performance and, while the likelihood of coordinating

on some equilibrium is largely independent of the level of cohesion, it is crucial for equilibrium

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selection: low cohesion groups usually descend rapidly to the worst Pareto-ranked equilibrium;

high cohesion groups typically achieve higher Pareto-ranked equilibria. We replicate these

patterns via an independently conducted, pre-registered, experiment (Study 2, Tavolo 3,

Appendix). We also confirm that our results are robust to the timing of oneness measurement

(before or after play of the weak-link game), eliminating the interpretation that experience of

game play explains variation in cohesion.

While our results clearly establish that groups with high cohesion systematically outperform

low cohesion groups, one must be cautious about causal interpretation. In definitiva, our results

are correlational, but we think a plausible interpretation of our findings is that group cohesion

is a summary statistic for tangible features of real groups that matter, causally, for team

production (at least in the context of the weak-link settings we study). Interpreted in that way,

the group cohesion index as a new tool would be much less valuable if one could predict group

performance, just as well, using a small number of easily measured group characteristics; our

risultati, Tuttavia, cast doubts on the prospects for doing that.

In Section VI, we present econometric analysis showing that group cohesion is a powerful

and dominant predictor of group performance even when controlling for a large range of

measured group characteristics – moreover, those characteristics become insignificant as

predictors of group outcomes, once cohesion is present as a regressor. In the last game period,

the model predicted effects of cohesion on group outcomes are also substantial: minimally

cohesive groups are almost certain to collapse to a minimum effort of 1; maximally cohesive

groups almost never fall to a minimum effort of 1; and large financial incentives are needed to

promote the levels of effort expected for high cohesion groups.

In Section VII, we discuss the interpretation of our results considering two main avenues.

Primo, we consider the possibility that, because our experiments involve groups of friends, IL

association between effort and cohesion might be explained by subjects having planned to

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share their earnings with participating friends. We test and discount this as a plausible account

of our main findings. Secondo, exploiting data on participants’ beliefs and social preferences

gathered in our replication study, we explore the extent to which the association between group

cohesion and minimum effort is mediated through beliefs or social preferences. In contrast to

results found elsewhere (per esempio., Chen and Chen (2011)), we find that the effects of cohesion

operate mainly via the channel of beliefs with only a limited influence of social preferences.

To preview our conclusion of Section VIII, our studies establish proof of concept for group

cohesion as a useful new tool of economic analysis to capture and reveal the, previously hidden,

power of social relationships as factors of production.

II. Related Literature and Our Contribution

Before presenting the substance of our paper we briefly place it in the literature. In the broadest

sense, we contribute to the literature on social capital (per esempio., Putnam (2000); Glaeser, Laibson

and Sacerdote (2002)) by tackling one of its central problems. In a recent typology of that

literature, Jackson (2020) argues that “[M]easuring various forms of social capital is especially

difficult as they are dependent upon relationships between people, which are often intangible

and only indirectly observed” (P. 333). We demonstrate how (social) relationships can be

observed and measured to provide quantitative assessments of the (psychological) quality of

social network links (Goyal (2005)), thereby providing a micro-foundation of social capital.

We do this by introducing the novel psychological concept of group cohesion. As we will

explain, group cohesion builds on the concepts of “relationship closeness” and “oneness”.

These concepts are firmly established in the psychology literature (see Section III.A) but are

less considered in economics, with the possible exception of “social distance” (per esempio., Akerlof

(1997)). In the experimental economics literature, social distance has mainly been juxtaposed

to complete anonymity and manipulated experimentally by giving participants cues about the

identity of other individuals, for instance, via visual identification (Bohnet and Frey (1999)) O

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via their names (Charness and Gneezy (2008)). By contrast, we measure the closeness of

relationships between group members and construct the concept of group cohesion on such

measurements. To our knowledge, this is an entirely new approach in economics.

Another contribution is to the experimental literature on coordination games, which –

following seminal papers by van Huyck, Battalio and Beil (1990; 1991) – has largely studied

coordination among anonymous individuals without considering the role of social

relationships. This research (see Cooper and Weber (2020) for a recent survey), highlights

primarily the importance of structural features that facilitate coordination on efficient equilibria

ad esempio: communication (Cooper et al. (1992); Brandts and Cooper (2007)); leadership (Weber

et al. (2001)); individual incentives (Brandts and Cooper (2006)); group size (Weber (2006));

choice of group members (Riedl, Rohde and Strobel (2016)); and organizational or societal

culture (Weber and Camerer (2003); Engelmann and Normann (2010)). By studying a fixed

weak-link game, we keep structural features constant and show that the socio-psychological

property of group cohesion is an independent and powerful predictor of group outcomes.

We also contribute to a growing literature on the economic impact of groups and group

identity (Charness and Chen (2020)). This includes studies investigating in-group favoritism

(per esempio., Currarini and Mengel (2016)); interactions among friends (per esempio., Glaeser et al. (2000);

Leider et al. (2009); Babcock et al. (2019); Chierchia, Tufano and Coricelli (2020); Gächter et

al. (2022)); and the role of identity in organizations (per esempio., Akerlof and Kranton (2005); Ashraf

and Bandiera (2018)), including social-psychological dimensions of employment relationships

(per esempio., Baron and Kreps (2013)). Our work builds most directly on prior experimental work

which has established the impact of group identity on behavior in various contexts including

in prisoner’s dilemma and battle of the sexes games (Charness, Rigotti and Rustichini (2007)),

in trust games (Hargreaves Heap and Zizzo (2009)) and in weak-link games (Chen and Chen

(2011)). While the last of these comes closest to our work in studying weak-link games, relative

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to all three studies, our work breaks new ground: we study real groups, not artificially

constructed ones; and we do this for the novel purpose of developing and providing proof of

concept for a tool to measure the quality of behaviorally relevant features of extant socio-

psychological relationships within real groups.

III. Group Cohesion in Real Groups

Since group cohesion is a novel concept in economics, we devote subsection A to explaining

the concept, its roots in established psychological literature and our approach to its

measurement. Subsection B shows that measured group cohesion passes a basic test of

construct validity in varying coherently with tangible sociological properties of real groups.

UN. Group Cohesion: psychological foundations and measurement

Our study involves the development and application of a new tool: A simple and portable

measure of group cohesion designed to summarize the social and psychological relationships

that exist between members of any group. A tal fine, we build on an established literature

which has developed tools to measure the nature and strength of bilateral relationships between

pairs of individuals. This literature demonstrates that important features of possibly complex

bilateral relationships can be summarized by simple measurement tools, which ask subjects to

report how “close” they feel towards another focus person (Aron, Aron and Smollan (1992)).

Our strategy builds on and extends this literature by assuming that important aspects of

relationships that exist within groups can be summarized in terms of the set of pairwise

closeness relationships within them. On our measure, a group will be more cohesive to the

extent that its members feel, collectively, closer to one another. Since individual judgments of

relationship closeness will be its foundation, we now describe the key properties of tools for

measuring bilateral relationship closeness.

According to psychologists Kelley et al. (1983), relationship closeness increases with

people’s frequency of interactions, the diversity of activities people undertake together, and the

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strength of influence people have on one another. In an effort to measure these determinants of

relationship closeness, Berscheid, Snyder and Omoto (1989) developed a 69-item

“Relationship Closeness Inventory” to assess, in detail, the frequency of interactions, diversity

of jointly undertaken activities and the influence a pair exerts on each other. While the

Relationship Closeness Inventory is fine-grained, it is not practical for many purposes. A

provide a handy measurement technique, in a highly cited paper, Aron, et al. (1992) proposed

a simple tool: the “Inclusion of the Other in the Self” (IOS) scale depicted in Fig. 1UN. The IOS

scale “is hypothesized to tap people’s sense of being interconnected with another. That sense

may arise from all sorts of processes, conscious or unconscious” (Aron, et al. (1992), P. 598).

Essentially, it aims to measure relationship closeness without examining its detailed

determinants (cioè., frequency or diversity of activities; strength of mutual influence).

Aron, et al. provide statistical evidence that the IOS scale successfully tracks key dimensions

of relationship closeness: people tend to pick more overlapping pairs of circles for a given

other, the more frequent or diverse their interactions, and the stronger their perceptions of

mutual influence. Subsequent research, most notably by Starzyk et al. (2006), developed an

18-item “Personal Acquaintance Measure” intended for application to a wider range of

relationships including acquaintances. Their measure also correlates strongly with the IOS

scala. Together, these results make the IOS scale a very promising tool for our purposes. It also

has the decisive advantage of being intuitive for respondents and very simple to implement.

[Figura 1 here]

Since our research relies critically on the IOS scale, in a background paper (Gächter, et al.

(2015)), via a study with 772 subjects, we assessed the psychometric validity of the IOS scale

for a wide range of relationships (from strangers to close friends), by testing whether we could

replicate key findings in the foundational psychological research that validated the IOS scale

as a reliable predictor of relationship closeness. Our results replicate, remarkably closely, IL

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correlations of the IOS scale with the Relationship Closeness Index reported by Aron et al. IL

IOS scale also varies coherently with the form of the relationship (lowest for acquaintances,

medium for friends, and highest for close friends), with the Personal Acquaintance Measure of

Starzyk, et al. and with Rubin’s Loving and Liking Scale. In Gächter, et al. (2015), we also

find that the principal components of the questionnaire-based measures correlate strongly

(0.85) with the IOS scale. Hence, we conclude that the IOS scale is a psychologically

meaningful and reliable tool for measuring bilateral relationship closeness.

In our measurement of relationship closeness, we follow Cialdini, et al. (1997) who combine

the IOS scale with the “We scale,” depicted in Fig. 1B. The Cialdini et al. measure is calculated

as the average of responses on these two scales. They call this the “oneness scale,” which they

interpret as reflecting a “sense of shared, merged, or interconnected personal identities” (P.

483). In Gächter, et al. (2015), we confirmed Cialdini et al.’s claim that oneness correlates

slightly better with the questionnaire-based measures than the IOS scale alone and, hence, we

use the oneness scale for our analysis.

We deployed the oneness scale as follows (wider procedural details are in Section IV).

Subjects participated as groups of four and each person rated three other visually identified

group members, separately and privately, on the IOS and We scales as depicted in Fig. 1; group

members knew they would not receive feedback about each other’s ratings. Both IOS and We

scale responses are scored on a scale from 1 A 7. Oneness is the average of the two measures

and hence ranges from 1, “lowest oneness”, A 7, “highest oneness.”

Since groups contain four people, who each rate the three other members in their group, any

group generates twelve bilateral oneness ratings. We construct our group cohesion index by

selecting, for each group member, the oneness score for the person they rated lowest. We then

compute group cohesion as the average of these four scores. Hence, our index can be thought

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of as summarizing the minimum envelope of oneness in a group. Our results are not sensitive,

Tuttavia, to different ways of averaging the individual oneness reports (see Section VI.B).

B. Group Cohesion and the Sociological Properties of Naturally Occurring Groups

In much of this paper, we focus on whether or how well group cohesion predicts performance

in stylized “production tasks”. Before pursuing this, Tuttavia, we briefly probe the validity of

our measurement tool via some simple tests examining whether measured cohesion varies as

expected with tangible, socio-demographic, features of the groups in our experiments.

[Figura 2 here]

The simplest approach to this exploits the procedures we used to assemble groups. To create

variation in how well members of groups knew one another prior to our experiments, we

recruited participants as groups of four self-selecting friends who were then either matched

into new groups of four members (Non-friends, N-matching) or kept together as friends to

proceed to the experimental tasks (Friends, F-matching) (see Section IV for further details). If

cohesion is tracking the pre-existing relationships within groups, we should expect that already

existing groups (F-matching) will tend to have higher measured group cohesion than the ones

we constructed fresh (N-matching). Fig. 2 plots the distribution of measured group cohesion

separately for N- and F-matching. It is evident that group cohesion tends to be higher in the F-

matching groups as compared to N-matching groups (means are 3.81 E 1.84, resp.; IL

distributions differ according to a Mann-Whitney test, z = 5.896 P < 0.001). Note that, with measured group cohesion ranging from 1 to 5.5, there is good scope for observing its association with group behavior, if such association exists. For a more sophisticated test of construct validity, we use individual-level data on 15 characteristics of our participants, collected via post-experimental questionnaires. The characteristics range from self-reports of relatively concrete variables (e.g., age or gender) through to more subjective self-assessments of dispositional traits (e.g., political attitudes or 10 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. happiness). An established literature related to “homophily” and the sociology of friendship (e.g., Baccara and Yariv (2013); Dunbar (2018); McPherson, Smith-Lovin and Cook (2001)) shows that “like-befriends-like” hence members of self-assorted groups are expected to be more similar in terms of socio-demographic characteristics than members of other groups. This is clearly true of our self-selected groups (i.e., the F-matching groups): Based on both parametric and non-parametric tests, the null of equal variance between and within F-matching groups is rejected in the expected direction at p < 0.05 for 11 of the 15 characteristics (see Table SM2.1 in the supplemental materials, henceforth “SM”). In contrast, no significant differences are found for N-matching groups. This analysis demonstrates that homophily is an indicator of pre-exiting relationships among group members. Hence, if group cohesion measures what we intend, we should expect that group cohesion and group homophily will be correlated. To test this prediction, we construct a simple homophily index that increases with the similarity of group members on each of the fifteen variables we measured to capture tangible sociological features of group members. We explain the construction of the Homophily Index in detail in Section VI, where it features as a control variable. For now, however, we note that an OLS regression of group cohesion on the homophily index produces a highly significant coefficient (p < 0.001) with an R2 of 0.37. We take this as reassuring evidence that, as well as being a simple, intuitive, and portable group-level statistic capturing bilateral assessments or relationship closeness, the group cohesion index also reflects homophily within groups, consistent with the literature on the sociology of friendship. IV. Experimental Setup A. The Test Environment: The Weak-link Game Our workhorse for studying team performance is the so called weak-link game. Since the seminal papers by van Huyck et al. (1990; 1991), it has been widely studied in the lab, partly because it represents a form of coordination problem endemic to organizations (Camerer and 11 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. Weber (2013)). A classic example is workers preparing an aircraft for takeoff: the plane can only leave once the slowest worker has fulfilled their task (Knez and Simester (2001)). We use a version of the weak-link game due to Brandts and Cooper (2006). In a group of four, players simultaneously choose one of five “effort levels” 1 to 5. The payoff to each player i is given by πi = 190 – 50ei + 10b∙[min(e1, …, e4)] where ei is player i’s own effort, min(∙) is the lowest effort in the group, and b is a “bonus” rate controlling the marginal return to changes in minimum effort. In our main experiment, we set b = 6 mimicking Brandts and Cooper’s baseline treatment. Table 1 illustrates the payoff matrix as generated by the payoff function πi. [Table 1 here] Each player chooses an effort level (i.e., a row of Table 1) and their payoff then depends on their own choice and the minimum effort among all members of their group (given by the column). The key tension embodied in the weak-link game is easy to see: everyone prefers that everyone chooses maximum effort (of 5) because this is the unique social optimum, which simultaneously maximizes everyone’s payoff (at 240 points); but the optimum may not be achieved because it is costly for any individual to exceed the minimum of efforts. On standard analysis, rational players will match their expectation of the minimum of others’ efforts. The game has five strict Pareto-ranked equilibria on the diagonal of Table 1. Notice that the achievement of high payoffs requires elements of coordination (choosing the same effort level as other group members) and cooperation (groups achieving Pareto-superior Nash equilibria). We chose this specification of a weak-link game as our baseline setup in the expectation that – in the absence of aids to cooperation (e.g., communication) – low cohesions groups, typical of those used in prior experimental implementations of this game (e.g., Brandts and Cooper (2006; 2007)), would rapidly descend to the worst equilibrium.2 B. Sampling Strategy and Sequence of Events 12 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. Since our goal was to study the performance of real groups, invitations to prospective participants asked each invitee to bring three additional people who all knew each other and the invitee. Hence, participants (n = 260 students, “Study 1”) arrived at the lab in sets of four acquaintances. Upon arrival, we assigned them to one of two matching protocols, the F- matching (47 groups) or the N-matching (18 groups). In the F-matching, each quartet of acquaintances was allocated to the same group (“Friends”). By contrast, in the N-matching, each set of four acquaintances was split up so that each was randomly assigned to become a member of a different experimental group (“Non-friends”). Thus, the only difference between the two matching protocols is that, under F-matching, group members are selected to have some prior history of social interactions with each other, whereas the N-matching aims to minimize the likelihood of prior social interaction but keeping the recruitment procedures constant. Using these two matching protocols, we achieved the desired variation in pre-existing cohesion across groups (Fig. 2). Since our setup required participants to both provide oneness ratings of other group members and to play a (repeated) weak-link game, a very important issue is whether the experience of one type of task might affect behavior in the other. We addressed this issue in two ways. First, pilot experiments revealed that measuring oneness before the weak-link game does have some influence on minimum effort. A key question is then whether prior play of the game affects subsequently measured oneness. To test this, we ran a within-subject experiment (172 new subjects; 27 F-matching groups and 16 N-matching ones) conducted in two stages. We refer to this as our “two-week experiment” (see Table 3, Appendix). In week 1, we measured oneness and elicited various individual characteristics. In week 2, the same subjects in the same groups played the weak-link game followed by elicitation of oneness. Since relationship closeness should not change systematically over the course of one week, any systematic changes in oneness ratings would be likely due to effects of the experience of game play. 13 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / . / 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. Our results show that the oneness scores are not significantly different between week 1 and week 2 (individual average ratings as observations, Wilcoxon signed ranks test, z = -1.033, p = 0.302). At the group level, the Spearman rank order correlation between week 1 and week 2 group cohesion is 0.928 (n = 43; p < 0.001). This demonstrates an encouraging degree of test-retest reliability at the level of the individual. To further test the impact of game play on oneness ratings, we regressed changes in group cohesion on average minimum effort. The coefficient on minimum effort is insignificant (ordered probit, β = -0.032, z = -0.28, p = 0.783).3 We conclude that prior play of the weak-link game has no detectable impact on subsequent measurement of oneness. This provides strong support for the sequence where we elicit the oneness ratings, for the construction of group cohesion, after the weak-link game. C. Procedures In all matching conditions, each group sat at a block of four computer workstations with partitions to prevent them from seeing each other’s screens and responses. Each session started with an introduction read aloud by the experimenter. After that, each group of four participants was asked to stand up – one group at a time – so that each of its members could see the other members of their group.4 Subjects then followed computerized instructions, via their own screens. These first introduced the weak-link game followed by questions to test subjects’ understanding of it. After the test, subjects played eight periods of the weak-link game. In each period, after each group member had (privately) entered their own effort level, their computer screen reported their own choice, their group’s minimum, their own points for the current period, and their own accumulated points for all completed periods. Subjects knew that total accumulated points across the eight periods would be converted to cash at an exchange rate of 500 points = £1.00. For oneness measurements (elicited after game play for reasons explained above) after computerized instructions, each participant was asked to focus on each other group 14 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. member in turn and to respond, in sequence, to both the IOS scale and the We scale (Fig. 1) tasks. The full experimental instructions are in the supplemental materials (see section SM14). We recruited participants via ORSEE (Greiner (2015)) and ran the experiments with z-Tree (Fischbacher (2007)) in the CeDEx lab at the University of Nottingham. Sessions lasted about one hour. Participants received task-related payoffs plus a £2.00 show-up fee (the mean payment was £7.88). Payments were made privately. V. Associations between Group Cohesion and Weak-Link Team Production Before presenting our primary results, we note that our experimental environment is “harsh”, as intended, in that groups whose participants have no significant history of prior social interaction tend to quickly gravitate towards the lowest ranked equilibrium of the weak-link game. Using data from the N-matching, we find that, by period 8, 90 percent of groups collapse to minimum effort = 1; only two groups do better, achieving effort levels 2 and 3, respectively.5 These results confirm existing evidence (e.g., Brandts and Cooper (2006, 2007)) and establish that there is ample scope for improvement in cooperation in our environment, if the factors captured in the group cohesion index measure matter for team production. A. Group Cohesion, Minimum Effort and Wasted Effort Fig. 3 presents scatter plots of minimum effort against group cohesion with separate panels for the first and last periods of the weak-link game. Each plot also includes a line of best fit (OLS) and the 95% confidence interval. We find a significant positive association between group cohesion and effort for both periods. Medium-to-high levels of group cohesion appear necessary for selecting high effort levels (i.e., minimum effort > 3). There is also evidence of

some dynamic component revealed both by the change in concentration of observations across

periods and picked up by the regression line which is both steeper and more strongly significant

in period 8 (see p values in note to Fig. 3).

[Figura 3 here]

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To further examine the dynamics suggested by Fig. 3UN, we separate the full set of 65 groups

into three subsets of “low”, “medium” and “high” cohesion groups (for details of partitions see

Fig. 3 caption). Fig. 3b reveals marked differences in the dynamics by showing the time path

Di (average) minimum effort, separately by partition. This reveals differences in both the initial

levels of and trends in minimum effort across partitions: in contrast to low and medium

cohesion groups, high cohesion groups cooperate more effectively in the initial period and do

not experience a decay of minimum effort over time.

È interessante notare, the dynamics of “wasted effort” (cioè., the total of effort in a group above the

group minimum in a particular period) seem largely independent of cohesion levels and the

uniformly low rates of wasted effort by period 8 imply strong convergence on equilibrium play

for all levels of cohesion.6 As Fig. 3c shows, average wasted effort in period 1 is around 5 E

collapses to about 1 by period 8. The analyses of Figs. 3b and 3c suggest that group cohesion

is primarily associated with cooperation (decisions consistent with higher ranked equilibria),

with relatively little connection to coordination success (group members coordinating on the

same equilibrium, regardless of its ranking).

A natural question to ask is whether our results are robust to the timing of the oneness

elicitation. We use the data generated by our “two-week” experiment (where oneness is also

elicited one week before the weak-link experiment, see Section IV.B) to conduct a simple but

informative check comparing average minimum effort across experiments (original vs two-

week experiment) using the partitions for group cohesion (cioè., low, medium, and high)

introduced in Fig. 3B. These tests show that for both low and high cohesion groups, IL

achieved levels of minimum effort are statistically indistinguishable across the two

esperimenti. For groups with mid-range cohesion, minimum effort is somewhat higher for the

two-week experiment. For both experiments, Tuttavia, we identify a strong positive association

between cohesion and minimum effort, regardless of the timing of the oneness elicitation. Questo

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holds regardless of whether we include observations from groups with mid-range cohesion (for

more details of analysis see supplemental material, Section SM4).

B. A Pre-Registered Replication

While the results presented in the last subsection are encouraging, they are also novel.

Therefore, replicability is of first order importance to establish confidence in the behavioral

patterns just reported (per esempio., Camerer, Dreber and Johannesson (2019)). We therefore replicated

the experiment and report the results in this sub-section. In the following, we sometimes use

“Study 2” as a convenient label for the replication study and refer back to the original study as

“Study 1”. To provide a credible replication, we pre-registered the experiments7 for Study 2

and we hired an independent contractor (the University of Birmingham Experimental

Economics Laboratory (BEEL)) to implement them. We provided the experimental protocol,

software, and instructions, but we were not involved in data collection. BEEL followed our

original recruitment procedures but with a new subject pool from Birmingham University. IL

protocols and instructions were as for Study 1 except that, to probe the relationship identified

in Study 1, we introduced two further sets of measurements. Primo, subjects’ beliefs about the

minimum effort in their group were elicited in each round of the weak-link game. Secondo, IL

post-experimental questionnaire

included

incentivized elicitation of “Social Value

Orientation” (Murphy and Ackermann (2014)) as a measure of group social preferences. Noi

discuss the details of these measures and the associated results in Section VII.

The main results of Study 2 (276 participants; 49 F-matching groups and 20 N-matching

ones) are described in Figure 4. A comparison with the corresponding Fig. 3 for Study 1 reveals

Quello, qualitatively, the results are remarkably similar.8 Panel 4a replicates the positive

relationships between group cohesion and minimum effort though with the difference that, In

the replication, the relationship is strongly significant for both the first and the last period. Fig.

4b confirms the ability of higher cohesion groups to achieve and sustain higher minimum effort

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levels over time while Fig. 4c confirms the finding that the dynamics of wasted effort are

largely independent of cohesion levels.9 In sum, the results of Study 2 confirm that group

cohesion has a replicable association with cooperation in the weak-link game.

[Figura 4 here]

C. Individual-Level Effort Choice

In this sub-section, we dig down to examine the association between individual level effort and

group cohesion using pooled data from Studies 1 E 2 (see Fig. SM6.1, for corresponding

analysis separately by study). Fig. 5 shows the distribution of individual effort comparing

individuals in groups with low (panel a) and high (panel b) group cohesion (these correspond

with the two extreme partitions of Figs. 3 E 4). In these panels, for each period, color coding

shows the distribution of efforts while the average of individual effort is indicated with a circle.

[Figura 5 here]

Notice that the time profile of average individual effort is clearly different comparing low

and high cohesion groups: for low cohesion groups, it starts just above 3 and descends close to

the minimum of 1 by period 8; whereas, for high cohesion groups it starts higher (close to 4)

and descends less steeply converging by period 8 to an average effort level of around 3.

Persistent differences in the distributions of effort are also apparent comparing low and high

cohesion panels (for instance, there is markedly more incidence of efforts above 3 in the high

cohesion panels). An econometric analysis also finds a highly significant positive influence of

individual average oneness on individual effort choices.10

We further examine these dynamics by focusing on each individual’s change in effort

following rounds in which they delivered above minimum effort. A subject who did not choose

the minimum effort in period t is modelled as having a choice between three (mutually

exclusive and exhaustive) options in period t + 1 which we label nice, moderate, or harsh: nice

agents deliver at least as much effort as before; moderate agents reduce effort but no lower

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than the previous period minimum; harsh agents reduce their effort below the previous

minimum. We conjectured that subjects with high average oneness ratings of their fellow group

members would be more likely to be nice, with the reverse true for individuals with low average

oneness ratings of their fellow group members. An ordered probit analysis (using cases where

a subject did not choose the minimum effort in period t) shows that their reaction in t + 1 (coded

1, 0 O -1 for nice, moderate, or harsh) varies positively with their average oneness ratings of

the other three group members (β = 0.067, p = 0.002, pooled for Studies 1 E 2).

VI. The Predictive Power of Group Cohesion for Minimum Effort

The combined results of the two studies presented in Section V establish a strong and replicable

positive association between group cohesion and minimum effort. In this section, we probe the

robustness and scale of that relationship through two sets of additional analyses.

UN. Does Group Cohesion Outperform Homophily Measures as a Predictor of Effort?

This sub-section presents regression analysis assessing the power of group cohesion as a

predictor of minimum effort with a particular focus on the impact of controls for homophily.

Via this analysis we address an issue raised in the introduction: since we interpret group

cohesion as capturing the effects of real relationships that exist between group members, could

we achieve comparable or better predictive power through use of information about observable

individual characteristics? The main analysis we report makes use of the homophily index, first

introduced in Section III, but here we provide more details of its construction.

Tavolo 2 reports results for three models of group-level minimum effort which feature either

group cohesion or the homophily index or both as independent variables. The homophily index

combines data on 15 individual characteristics that we measured for this purpose (see SM1 for

details).11 For each of these 15 variables, we construct an homophily sub-index by first coding

observations for each variable into a small number of mutually exclusive categories (per esempio., two

genders; three nationality groups). For each variable, we then assign a homophily sub-index to

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each group calculated as the proportion of group members associated with the highest-

proportion category (per esempio., suppose that, in a group, 3 members are female and 1 is male then,

by definition, the gender homophily sub-index for that group is 3/4=0.75). The homophily

index used in the regressions of Table 2 is then the average of the 15 sub-indices for each

group. The models are estimated using standard ordered probit with clustering at group-level,

since groups make multiple decisions.12 The regressions pool data for all 8 periods with

separate panels for Study 1 (Panel A), Study 2 (Panel B) and the combined data set (Panel C).

[Tavolo 2 here]

The estimated models that include group cohesion without homophily (models 1, 4 & 7 In

Tavolo 2) show that cohesion is a stable and strongly significant predictor across the two subject

pools and the pooled data set. Allo stesso modo, when the homophily index enters without cohesion,

consistent with our prior expectation, we find a strongly significant association for homophily

in each case (models 2, 5 & 8). Critically, Tuttavia, when both variables enter together, IL

homophily index is never significant while group cohesion remains strongly significant and

with a coefficient very similar to that in the regression without the homophily index. As

robustness checks, we conducted similar analysis along two further routes either entering all

15 homophily sub-indices as separate variables in regressions alongside group cohesion, or by

using the 6 main principle components of the 15 homophily sub-indices as regressors alongside

group cohesion (see SM8 for details).13 The consistent outcome of this analysis is that various

homophily-inspired measures do not match the performance of the group cohesion index in

predicting group minimum effort.

B. Assessing the Magnitude of Cohesion-Related Cooperation

In this sub-section, we consider the magnitude of the effects of group cohesion on minimum

effort, observed in our data. As one approach to this, we explore the predictive power of group

cohesion by regressing it on minimum effort in the last period (period 8) to generate the

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predicted probabilities for each possible level of minimum effort, conditional on different

levels of group cohesion. The results (presented in detail in SM9) demonstrate a very sizeable

predicted impact of group cohesion on minimum effort as we move between the extreme points

of the group cohesion scale. Per esempio, imagine a group characterized by minimum cohesion

(equal to 1): such a group is almost certain to be at minimum effort of 1 (the actual probability

of minimum effort in this case is approximately 93 per cento, based on pooled data from Studies

1 E 2). By contrast, a group with maximum possible group cohesion (equal to 7) is unlikely

to end up at minimum effort of 1 (probability of less than 12 per cento) and is predicted to achieve

minimum effort of at least 3 with a probability of about 83 per cento.

One might wonder how far these results depend on the specification of the group cohesion

variable. Recall that we calculate group cohesion as the average of the minimum oneness

ratings in a group. While this minimum “envelope” seems a natural statistic, particularly in the

context of the weak-link game, there is no “special sauce” involved here: Infatti, using the

group average of individual oneness ratings as an alternative cohesion metric delivers very

similar results (see supplemental material, Table SM10.1).

As a second approach to assessing the scale of cohesion effects, we ran a series of new

experimental treatments which varied the bonus (cioè., b in the payoff function πi of the weak-

link game – see Section IV.A). In these treatments, in line with the earlier research by Brandts

and Cooper (2006) and others, we recruited unrelated individuals (not groups of friends) E

they completed 8 rounds of the weak-link game. The bonus rates in four between-subjects’

treatments (60 subjects each) were set at 6, 14, 22 E 30, rispettivamente (see supplemental

Materiale, Table SM3.1, for the respective payoff tables). The first two bonus levels correspond

with the lowest and highest bonus payments implemented by Brandts and Cooper (2006), while

the other two go substantially higher in steps of 8 (the highest more than doubles their

maximum). Increasing the bonus monotonically increased the average minimum effort. A

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bonus level 6, it was close to the minimum possible value of one and corresponds with the

expected minimum effort associated with low cohesion groups (cioè., a cohesion level of

approximately 3, see Fig. SM12.1). Our results show that substantial increases in the bonus,

beyond those used by Brandts and Cooper, are needed to induce average minimum effort levels

comparable to those associated with high cohesion (see SM12 and Fig. SM12.1 for details).

For example, a bonus level of 22 in the Bonus Study produces an average minimum effort

comparable to that expected from groups with a cohesion level of approximately 6. These

results show that the economic value of group cohesion – or more precisely the value of the

factors it proxies – is substantial, when gauged by the financial incentives needed to induce

effort levels comparable to those of high cohesion groups.

VII. Towards an Explanation of the Power of Group Cohesion

Bringing real groups to the lab, as we have done, is a departure from classic lab experiments

which might, initially, trouble those who presume that (at least approximate) anonymity is a

sine qua non principle for experimental games, required to avoid the shadow of the future

“infecting” strategic behavior in the lab. We aim to convince readers otherwise. A key rationale

for our approach comes from the fact that real groups, and the real relationships that have

developed within them, are our object of study. Yet working with real groups does create some

methodological challenges and issues of interpretation, one of which we address next.

A possible interpretation of the relation between cohesion and effort is that the members of

high cohesion groups – by virtue of tending to know one another – might have agreed to share

their payoffs, thus changing the payoff structure of the weak-link game making cooperation

easier.14 In the post-experimental questionnaire, we asked participants whether they planned to

share their earnings with other group members and whether their expectation of sharing had

affected their game decisions. Our robustness tests extend the analysis of Table 2 by adding

controls for self-reports of sharing. While this reached significance in some specifications, Esso

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had only a very modest impact on the coefficient for group cohesion which remained strongly

significant in all cases (see SM11 for details). While this is reassuring, self-reports of sharing

may not be entirely reliable and they may also be partly endogenous to game play.

With these limitations in mind, we ran a further set of treatments that we call the Sharing

Study (Tavolo 3, Appendix). For this study, we recruited fresh participants individually (hence,

subjects typically did not know any other participant). Subjects played the weak-link game of

Tavolo 1 (where b = 6) following other standard procedures used across our studies but with the

distinguishing feature that, before making their game decisions, subjects were told that there

was some probability that we would pool all individual earnings within each group and share

them equally among group members. We implemented three versions of this protocol (n = 60

each) with the known probability of sharing being either 0.5, 0.8 O 1. This allows us to assess

an upper bound for the impact of sharing (when sharing is certain) and its sensitivity to different

levels of uncertainty associated with any potential sharing arrangement.

The treatment where sharing is certain generated an average minimum effort of 2.73 Quale

is comparable to the expected minimum effort associated with a group cohesion of close to 5

(see SM12). While introducing a little uncertainty about sharing (by setting the sharing

probability at 80%) depressed average minimum effort a little (to a value just below 2.5), Quando

the likelihood of sharing was only 50%, average minimum effort fell dramatically to a level

only slightly above 1 (see Fig. SM12.1). While this evidence does not eliminate the possibility

that expectations of sharing played some role, it counts against it being a convincing

explanation of the broad patterns in our data: this is so because the ceiling of the sharing effect

is well below the predicted effect of maximal cohesion (=7) and because uncertainty about

sharing – quite likely in any actual sharing arrangements – rapidly diminishes its impact.

The results of the Sharing Study are interesting for the further reason that the treatment where

sharing is certain can be interpreted as implementing an extreme form of social preferences in

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which each agent places the same weight on the earnings of all group members, including

themselves. Viewed in this way, the results are consistent with some explanatory role for social

preferences, albeit a limited one. A natural question is then, what is the relative importance of

social preferences versus beliefs in mediating the impact of cohesion on effort?15

We offer some tentative insight to this, exploiting data on beliefs and social preferences

collected as part of Study 2. Specifically, immediately after entering their effort decision for

each round of the weak-link game, but before knowing what others had done, each participant

entered their best guess about what would be the minimum effort in that round.16 Then, at the

end of the study, we measured participants’ social preferences via a set of standard Social Value

Orientation tasks: the “Social Value Orientation Slider Measure” due to Murphy, Ackermann

and Handgraaf (2011).17 We use responses to these two sets of tasks as key inputs to a

decomposition analysis based on the following simultaneous equation model:

𝑀𝑀𝑀𝑀𝑀𝑀_𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 𝛼𝛼1 + 𝛽𝛽1 𝐵𝐵𝐵𝐵𝐵𝐵𝑀𝑀𝐵𝐵𝐸𝐸𝐵𝐵 + 𝛽𝛽2 𝑆𝑆𝐸𝐸𝑆𝑆𝑀𝑀𝑆𝑆𝐵𝐵_𝑃𝑃𝐸𝐸𝐵𝐵𝐸𝐸𝐵𝐵𝐸𝐸𝐵𝐵𝑀𝑀𝑆𝑆𝐵𝐵𝐵𝐵 + 𝛽𝛽3 𝐺𝐺𝐸𝐸𝐺𝐺_𝐶𝐶𝐸𝐸ℎ𝐵𝐵𝐵𝐵𝑀𝑀𝐸𝐸𝑀𝑀 + 𝜀𝜀1 (1)

𝐵𝐵𝐵𝐵𝐵𝐵𝑀𝑀𝐵𝐵𝐸𝐸𝐵𝐵 = 𝛼𝛼2 + 𝛽𝛽4 𝑆𝑆𝐸𝐸𝑆𝑆𝑀𝑀𝑆𝑆𝐵𝐵_𝑃𝑃𝐸𝐸𝐵𝐵𝐸𝐸𝐵𝐵𝐸𝐸𝐵𝐵𝑀𝑀𝑆𝑆𝐵𝐵𝐵𝐵 + 𝛽𝛽5 𝐺𝐺𝐸𝐸𝐺𝐺_𝐶𝐶𝐸𝐸ℎ𝐵𝐵𝐵𝐵𝑀𝑀𝐸𝐸𝑀𝑀 + 𝜀𝜀2 (2)

𝑆𝑆𝐸𝐸𝑆𝑆𝑀𝑀𝑆𝑆𝐵𝐵_𝑃𝑃𝐸𝐸𝐵𝐵𝐸𝐸𝐵𝐵𝐸𝐸𝐵𝐵𝑀𝑀𝑆𝑆𝐵𝐵𝐵𝐵 = 𝛼𝛼3 + 𝛽𝛽6 𝐺𝐺𝐸𝐸𝐺𝐺_𝐶𝐶𝐸𝐸ℎ𝐵𝐵𝐵𝐵𝑀𝑀𝐸𝐸𝑀𝑀 + 𝜀𝜀3 (3)
The first equation posits beliefs, (social) preferences and group cohesion as determinants of

minimum effort. Group cohesion is treated as the unique (a priori) exogenous variable which

can influence minimum effort directly (Eq. 1) E, indirectly, via beliefs (Eq. 2) or social

preferences (Eq. 3).18 In the spirit of models linking social preferences and beliefs (per esempio.,

Dufwenberg, Gächter and Hennig-Schmidt (2011)), the model also allows social preferences

to influence beliefs (Eq. 2). Although very simple from a psychological point of view, IL

model is presented in the spirit of a tool for assessing the relative importance of beliefs and

social preferences as channels mediating the impact of group cohesion on effort, in our data.19

The estimated model produces significant coefficients (at 5% O 1% levels) for every β

coefficient except one: specifically, we find no direct effect from social preferences to

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minimum effort (cioè., β2 is not significantly different from zero). Hence, group cohesion

impacts minimum effort through three active channels: it operates directly (via β3) and through

its impacts on both beliefs and social preferences, though the last of these channels works

entirely through the secondary effect of social preferences on beliefs. Detailed estimation

results are in the supplemental material, Table SM13.1.

[Figura 6 here]

Figura 6 summarizes decomposition analysis conducted to assess the relative contributions

of these three channels. While the pie chart provides a summary of the complete decomposition

for the whole model, our primary interest is in the relative sizes of the partial effects (listed on

the right-hand side of Fig. 6) which decompose the total effect of group cohesion into its three

constituent paths. The path from group cohesion through beliefs accounts for about 56% del

total effect of group cohesion on minimum effort. While the impact via social preferences also

accounts for a non-trivial proportion (Di 27%) of the total effect, this path operates only

indirectly via the beliefs channel suggesting that the role of social preferences is secondary to

beliefs in both scale and mechanics (cioè., no direct effect of social preferences). Finalmente, IL

direct effect from group cohesion to minimum effort accounts for 16.7% of the total effect of

group cohesion. We interpret the small size of this direct effect as “good news” in the sense

that the impact of the factors proxied by group cohesion can be largely explained through its

influence on the familiar rational choice concepts of beliefs and preferences.

For a variety of reasons, we suggest that the results of this decomposition be treated as

tentative, absent further replication or other support. For example, we note a difference

between the status of our measurements of beliefs and social preferences: specifically, while

elicited beliefs measure something intrinsic to the weak-link games played by our participants,

the measured social preferences capture something external to the game context. This might

have led to underestimation of the role of social preferences.20 We could also measure social

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preferences in multiple different ways and an approach combining alternative ways of

measuring them (à la Gillen, Snowberg and Yariv (2019)) could be an interesting avenue for

checking the robustness of our conclusions from the mediation analysis. Inoltre, we cannot

rule out the possibility that measured social preferences were to some extent influenced by

experiences in play of the weak-link games although, conditional on there being such an effect,

it seems most plausible to assume that success in the weak-link game would have encouraged

more generous allocations in SVO tasks. In that case, our decomposition analysis should be

interpreted as identifying an upper bound on the contribution of social preferences.

Notwithstanding these potential reservations, Tuttavia, the fact that the lion’s share of the work

is done by beliefs in our data stands in distinct contrast to results based on experiments using

artificially-induced groups (see Chen and Chen (2011)). At minimum, we therefore suggest

that our results should unsettle any presumption that social preferences are the primary channel

through which within-group relationships affect success in team production.

VIII. Conclusions

It is hard to deny that social relationships may affect many variables that naturally interest

economists. An open question is how much they matter and whether economic analysis could

take account of them in a sufficiently parsimonious way to render the undertaking tractable and

worthwhile. The research presented in this paper sheds new, and positive, light on these issues.

In this paper, we have explored the power of group cohesion – a hitherto unobservable

characteristic and potential “production factor” of any real group – as a tool for predicting

strategic behavior, adopting the weak-link setting as a workhorse for proof of concept. Nostro

previous related research has established that the oneness scale, on which our measurement of

group cohesion is based, is simple to implement, highly portable and correlates extremely well

with more detailed measures of personal relationships (Gächter, et al. (2015)). We used our

measure of group cohesion, which is a group-level statistic of the oneness scale, to study the

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cohesion of real groups. We showed that group cohesion varies across groups as predicted by

relevant sociological and psychological literature and is stable based on test-retest

measurement.

Using an extensive set of experiments involving 1160 participants and including a variety of

robustness tests, benchmarking exercises, and an independent pre-registered replication, we

examined the predictive power of group cohesion in the context of experimental weak-link

coordination games played by real groups which vary in the extent of pre-existing social

relationships among their members. Despite no possibilities for communication, high cohesion

groups do much better in terms of the equilibria they achieve in weak-link games, and low

cohesion groups rarely, if ever, do well. We used an econometric approach to explore possible

mechanisms underpinning the association between group cohesion and group minimum effort

and found that, in our model, group cohesion shapes both beliefs and social preferences but

with beliefs emerging as the primary channel. We have also presented evidence that the

changes in effort associated with variation in cohesion can be considered “large” in the context

we have studied.

While we cannot directly extrapolate to predict the scale of comparable effects in other lab

or in field contexts beyond those we have studied, our results do provide motivation for

exploring such issues using our group cohesion index. On the assumption that our results do

translate to the field, they have particular potential significance in the context of organizational

performance (per esempio., Akerlof and Kranton (2005); Ashraf and Bandiera (2018)). If group

cohesion is associated with desirable team or group outcomes across a variety of organizational

settings, then our tool may facilitate a wide range of productive applied research. E, for those

with interests in engineering better organizational or team performance, oneness measurement

techniques may be valuable for assessing the impact of interventions, including the variety of

team building-activities in which so many organizations already invest.

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More generally, beyond the new evidence we have presented, we believe we have provided

proof of concept for a new simple and portable tool designed to facilitate the quantitative study

of social relationships as factors of team production.

Data availability

Data and analysis code are available at https://osf.io/g9u3e.

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APPENDIX

TABLE 3: List of Experimental Studies

Research Objectives

Predictive Power of

Group Cohesion

Construct reliability

IO.

Study 1

Two-week

Incentive

Structure

Recruitment

b=6

Friends

II.

(Test-retest reliability;

b=6

Friends

Study

Task sequencing)

Replicating Study 1;

III. Study 2

Mediational channels:

b=6

Friends

Beliefs, Social Prefs.

50-period

Random

Allocation

F- or N-

matching

F- or N-

matching

F- or N-

matching

260

172

276

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IV.

Long horizon

b=6

Strangers

Groups

Study

To compare the cooperation

b=6, Pr{S}=0.5 Strangers

Groups

enhancing effects of group

b=6, Pr{S}=0.8 Strangers

Groups

cohesion with sharing rules

b=6, Pr{S}=1

Strangers

Groups

To compare the cooperation

b=6

Strangers

Groups

Bonus

enhancing effects of group

b=14

Strangers

Groups

VI.

Study

cohesion with financial

bonuses

b=22

b=30

Strangers

Groups

Strangers

Groups

NOTE.— Study 2 was a pre-registered (see footnote 7) replication independently conducted at the BEEL

lab (University of Birmingham, UK) by in-house experimenters. All the other studies were conducted at

the CeDEx Lab (University of Nottingham, UK). Total overall sample: 1160 participants. b is the bonus

rate controlling the marginal return to changes in minimum effort. Pr{S} stands for probability of sharing.

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Please, look at the circles diagram provided on your desk. Then, consider

which of these pairs of circles best represents your connection with this

person before this experiment. By selecting the appropriate letter below,

please indicate to what extent you and this person were connected.

UN. ☐ B. ☐ C. ☐ D. ☐ E. ☐ F. ☐ G. ☐

UN. The “Inclusion of the Other in the Self” (IOS) scala

Please, select the appropriate number below to indicate to what extent,

before this experiment, you would have used the term “WE” to

characterize you and this person.

Not at all ☐

☐

☐ ☐ ☐ ☐

Very much

FIG. 1.—Oneness elicitation as explained to the participants.

B. The We Scale

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N-matching
F-matching

1.0

1.5

1.8

2.0

2.3

4.1

4.6

5.0

5.5
5.3

2.9

3.6

3.9
3.4
2.5
Group Cohesion

FIG. 2.—The distribution of group cohesion under F- and N-matching. The N-matching bars are

stacked over the F-matching ones.

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Period 1

Period 8

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1.5

3.5

2.5
Group Cohesion

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4.5

5.5

1.5

N-matching
Fitted values

F-matching
95% CI

3.5

2.5
Group Cohesion

4.5

5.5

3UN. The link between group cohesion and group-minimum effort in Period 1 E 8

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High Cohesion
Medium Cohesion
Low Cohesion

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7
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High Cohesion
Medium Cohesion
Low Cohesion

4
5
Period

3B. Group minima across periods

3C. Wasted effort

FIG. 3.—Group Cohesion, Minimum Effort and the Dynamics of Coordination. Fig. 3UN: Size of

symbols proportional to no. of observations; in Period 1, two N-matching observations are not

displayed because they coincide with F-matching circles with coordinates (2.25, 1) E (2.5, 2);

in Period 8, one N-matching observation is not displayed because it coincides with the F-

matching circle at (2.5, 2). OLS Regression (65 groups), Period 1: β = 0.313 (se = 0.123, p =

0.014, R2 = 0.092); Period 8 dati: β = 0.547 (se = 0.123, P < 0.001, R2=0.240); an ordered probit estimation generates qualitatively similar results. Fig. 3b and 3c: “Low Cohesion” Partition (13 groups): group cohesion ∈ [1, 2]; “Medium Cohesion” Partition (36 groups): group cohesion ∈ (2, 4]; “High Cohesion” Partition (16 groups): group cohesion ∈ (4, 7]. Fig. 3b: average group minimum effort over time. Fig. 3c: wasted effort per period, calculated as the sum of efforts in a group above the group minimum, averaged across groups. 37 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / . / 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. A pre-registered replication Period 1 Period 8 t r o f f E m u m i n i M 5 4 3 2 1 0 t r o f f E m u m i n i M 5 4 3 2 1 0 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Group Cohesion Group Cohesion N-matching Fitted values F-matching 95% CI 4a. The link between group cohesion and group-minimum effort in Period 1 and 8 t r o f f E m u m i n i M 5 4 3 2 1 High Cohesion Medium Cohesion Low Cohesion t r o f f E d e t s a W 7 6 5 4 3 2 1 0 High Cohesion Medium Cohesion Low Cohesion 1 2 3 5 4 Period 6 7 8 1 2 3 5 4 Period 6 7 8 4b. Group minima across periods 4c. Wasted effort FIG. 4.—Study 2: pre-registered replication independently conducted at University of Birmingham. Fig. 4a: Size of symbols proportional to the number of observations; in Periods 1 and 8, three N-matching observations are not displayed as they coincide with F-matching circles at coordinates (2, 1), (2.375, 2) and (2.875, 1); OLS Regression (69 groups), Period 1: β = 0.321 (se = 0.099, p = 0.002, R2 = 0.135); Period 8: β = 0.405 (se = 0.108, p < 0.001, R2=0.175); ordered probit estimation generates qualitatively similar results. Fig. 4b and 4c: “Low Cohesion” Partition (19 groups): group cohesion ∈ [1, 2]; “Medium Cohesion” Partition (25 groups): group cohesion ∈ (2, 4]; “High Cohesion” Partition (25 groups): group cohesion ∈ (4, 7]. Fig. 4b: average group minimum effort over time. Fig. 4c: wasted effort per period is the sum of efforts in a group above the group minimum, averaged across groups. 38 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. e g a t n e c r e P 100 90 80 70 60 50 40 30 20 10 0 a. Low Cohesion b. High Cohesion 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 0 5 4 3 2 1 M e a n E f f o r t 1 2 3 4 5 Period 6 7 8 1 2 3 4 5 Period 6 7 8 Effort levels 2 3 1 4 5 FIG. 5.—Study 1 and 2 combined: distribution of individual efforts over periods. Panel a: “Low Cohesion” Partition (32 groups): group cohesion ∈ [1, 2]; Panel b: “High Cohesion” Partition (41 groups): group cohesion ∈ (4, 7]. The bars represent the percentage of each effort level ranging from 1 to 5. The y-axes show the relevant percentages. The connected dots represent mean efforts (individual level and measured on the secondary y-axes). Supplemental Material SM6 provides further analysis for all three partitions, separated by study. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / . / 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 39 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Decomposition of Total/Partial Effect on Minimum Effort FIG. 6.—Study 2: modelling how group cohesion affects minimum effort. The panel reports the decomposition of the total/partial effect on minimum effort based on estimates derived from estimation of equations 1-3 above. 40 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. TABLE 1 THE PAYOFFS (IN POINTS) FOR THE WEAK-LINK GAME Minimum Effort 1 2 3 4 5 200 150 210 100 160 220 50 0 110 170 230 60 120 180 240 Effort by Player i 1 2 3 4 5 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / . / 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 41 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. ORDERED PROBIT REGRESSIONS OF MINIMUM EFFORT ON GROUP COHESION AND HOMOPHILY TABLE 2 Panel A - Study 1 Dep. var.: Min. Effort (1) (2) (3) Group cohesion 0.448*** (0.105) 0.484*** (0.136) Homophily index 3.871** (1.809) -1.038 (2.315) Log-likelihood -644.2 -681.6 -643.6 # level 1 (resp. 2) units 520 (65) 520 (65) 520 (65) Panel B - Study 2: Pre-registered replication independently conducted at the BEEL Lab. Dep. var.: Min. Effort (4) (5) (6) Group cohesion 0.388*** (0.099) 0.325** (0.128) Homophily index 6.400*** (2.468) 2.640 (2.883) Log-likelihood -569.0 -592.8 -565.3 # level 1 (resp. 2) units 552 (69) 552 (69) 552 (69) Panel C - Study 1 and 2 combined Dep. var.: Min. Effort (7) (8) (9) Group cohesion 0.414*** (0.074) 0.391*** (0.095) Homophily index 5.025** (1.486) 0.777 (1.803) Study 2 (dummy var.) -0.342* (0.191) -0.303 (0.195) -0.351* (0.191) Log-likelihood -1231.1 -1295.7 -1230.4 # level 1 (resp. 2) units 1072 (134) 1072 (134) 1072 (134) NOTES.—Data from Periods 1 to 8. Variables are at group level. Variable definition and construction are in the supplemental material, section SM1. Period dummies (always included, relative to Period 1) are significantly negative (at p<0.05). Controls for individual effects: group-level clustering. Robust standard errors in parentheses. *** p<0.01, ** p <0.05 * p<0.1. 42 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. * Corresponding authors (chris.starmer@nottingham.ac.uk, fabio.tufano@leicester.ac.uk). We are grateful to Robert Cialdini and John K. Maner for sharing experimental tools. We thank Antonio Aréchar, Michalis Drouvelis, Francesco Fallucchi, Ernesto Gavassa Perez, Jose Vicente Guinot Saporta, Natalia Montinari, Daniele Nosenzo, and Simone Quercia for assistance with experiments. We have benefited greatly from discussions with: Abigail Barr, Jordi Brandts, Leonardo Bursztyn, Colin Camerer, Gary Charness, Yan Chen, David Cooper, Vincent Crawford, Robin Cubitt, Enrique Fatas, Sourafel Girma, John Hillas, John List, Muriel Niederle, Pietro Ortoleva, Carla Rampichini, Al Roth, Marie-Claire Villeval, Roberto Weber, Frans van Winden and Leat Yariv. We thank participants at various conferences, workshops, and seminars. This work was supported by the Economic and Social Research Council [grant numbers ES/K002201/1, ES/P008976/1], the European Research Council [grant numbers ERC-AdG 295707 COOPERATION, ERC-AdG 101020453 PRINCIPLES], and the Italian Ministry of Education. The research was approved by the School of Economics Research Ethics Committee (Univ. of Nottingham). The authors declare no relevant conflict of interest. ** Gächter and Starmer: School of Economics, Univ. of Nottingham, University Park, Nottingham NG7 2RD, UK. Gächter is also affiliated with IZA Bonn and CESifo Munich. Tufano: School of Business, Univ. of Leicester, 266 London Road, Leicester LE2 1RQ, UK. 1 In the taxonomy of Charness et al. (2013), our experiments would classify as “extra- laboratory experiments”. However, a more apt label could be “field-in-the-lab experiment” because we bring naturally occurring groups of friends into a laboratory setting. 2 Relative to other weak-link settings, this one is “harsh” in the sense defined in SM3. 3 We explored various other specifications involving the change in minimum effort between period 1 and 8; the initial minimum effort level; all effort levels; a variable representing the period (to capture a time trend) plus interactions between the period and effort levels. None of them revealed any systematic change in group cohesion in response to game play. 43 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. 4 It was essential for our design that subjects knew who their other group members were and, in particular, that subjects in N-groups realised that they were not grouped with their friends. Hence, in verbal instructions we asked them to “pay attention to the composition of their group” (see oral instructions in SM14). This instruction formed a brief part of the overall instructions, given some time in advance of decisions and we did not provide any signal for how subjects should take account of group membership. A reviewer suggested that this instruction might foster an experimenter demand effect. While we cannot definitively reject such a possibility, studies of experimenter effects suggest that their scale is generally modest (e.g., de Quidt et al., 2018). Nevertheless, direct evidence on this point from further research could be useful. 5 A long-time horizon does not help low cohesion groups escape cooperation failure. We tested this with 32 fresh participants, recruited individually, who played the game of Table 1 for 50 periods in 8 fixed groups of four anonymous members (see Appendix). Six groups were trapped in the Pareto-worst equilibrium by period 4; one by period 10; and one by period 22. 6 We find only a weakly significant relationship between (average) group level wasted effort and group cohesion (Spearman’s ρ = -0.227, p = 0.069; n = 65). 7 See https://www.socialscienceregistry.org/trials/3566 (Reg. no. AEARCTR-0003566). Note that we collected one fewer group in the F-matching than planned due to no-shows. 8 Study 2 also closely replicates the evidence that the cohesion index varies coherently with tangible characteristic of the groups (See Fig. SM5.1 and Table SM2.1). 9 As for Study 1, we find only a weakly significant relationship between (average) Study-2 group level wasted effort and group cohesion (Spearman’s ρ = -0.209, p = 0.085; n = 69). 10 In a nested random model (GLLAMM, Rabe-Hesketh et al., 2005) individual effort increases with the mean oneness rating of others in their group (β=0.106; p<0.001; Study 1 and 2 combined). Period dummies are negative (p<0.01); the oneness ratings’ standard deviation is positively signed and significant at 5-percent level (β=0.132; p= 0.022; Study 1 and 2 44 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / . / 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. combined). Ordered probit analysis (clustered on individuals) confirms these conclusions with the only exception that the oneness ratings’ standard deviation is insignificant. 11 The 15 variables are: gender; age; field of study; nationality; no. of siblings; income; city size; no. of cohabitees; monthly budget; extent of self-finance; no. of club/group memberships; religiousness; political attitude; current happiness; future happiness. 12 We reach consistent conclusions if instead we account for interdependence of observations by estimating nested random models using GLLAMM (for details see Table SM7.1). 13 We are grateful to an anonymous referee for suggesting these robustness checks. 14 While the Nash equilibria are unchanged, the risks of cooperating are substantially reduced in groups committed to “full sharing” of payoffs, making cooperation easier to achieve. 15 In practice, it will be difficult to separate these roles clearly. For example, if groups with higher cohesion care more about each other’s payoffs, in theory this reduces strategic risk, which in turn supports the expectation of higher effort levels within a group. 16 In line with Schlag, Tremewan and van der Weele (2015), p. 484, we use non-incentivized belief elicitation because ours were fresh subjects with no clear incentive to misreport, facing a straightforward elicitation task embedded in a multi-task experiment in which hedging could otherwise have been a problem. See the supplemental material, section SM14.c, for details. 17 Each participant made 15 dictator style allocation decisions for an identified recipient from their group. The participant knew that one of the other two group members would make allocations to them (hence eliminating reciprocity considerations) but they did not know which one. See the supplemental material, section SM14.c, for further details. 18 The analysis is conducted at group level. We use the average of the individual beliefs in each group and the average of the individual social value orientations in each group. 19 The approach is similar in spirit to the mediation analysis reported in Kosse et al. (2020). 20 We are grateful to an anonymous referee for highlighting this possibility. 45 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 2 8 3 2 0 7 0 3 7 1 / r e s t _ a _ 0 1 2 8 3 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 012832023Review of Economics and Statistics Just Accepted MS.restby the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative CommonsAttribution 4.0 International (CC BY 4.0) license. MEASURING “GROUP COHESION” image

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