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The Small Group DynamicsA minority voting game experiment
A. Cini(1) and A. Guazzini(1,2)1) CSDC, University of Florence, via S. Marta 3, I-50139 Firenze, Italy.
2) Department of Psychology, University of Florence, Via di San Salvi 12, 50100, Firenze, Italy.
Summer Solstice 2012 - Arcidosso - Italy
26 - 29 June 2012
2Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
From Psychology...
The Small Group Communication and Structure
From Physics...
Group as a Complex System Relationships as Complex Networks
Small Group Dynamics Experiment
Framework Introduction Method Results Conclusion
3
IntroductionFrom Psychology...
From Physics...Small Group Dynamics Experiment
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
The main goal of the present work is the characterization of how a small group of people builds and structures their communication network and the related affinities, during a short virtual group interaction, and what differences can be revealed by comparing different conditions.
We show how our experimental framework captures some fundamental aspects of the subject’s behaviour in a small group virtual dynamics.
We present here the results of a minority game situation
(Voting modality), in which there is no winning strategy for reaching consensus
in the majority of participants, and we confront the outcome of
this experiments with that of similar set-ups without
any task (Blank modality) and a majority game (Topic modality)
4
Features of the small group
Size of the Group (10 - 12 persons)
Goals sharing
Frequent and regulars interactions
Social and affective relationships
Strong interdipendence among the members
High sense of belonging
Clearly differentiation of roles
Dyad
Collective
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
The small group is an intermediate space, where coexist and meet the dynamics, norms and expectations of the dual relationship and
the relationship with the collective.
5
Communication is a relevant relational aspect to assess the group
dynamics
Importance of the structure in the group communication
Communication features
Sender - Message - Receiver
Sintax - Semantics - Pragmatics
Non-verbal communication
Topology of communication
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
6
Emerging Properties
Individual-Environment Interaction
Group Phenomena
Totality dynamics
Group Evolution
Interdependence
Phase Transitions
Sensitivity to Initial Conditions
Complex Trend
The whole as more than the sum of the parts
Equilibrium
Dynamics Evolution
Stability
Hierarchy
Self-Organization
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
It is possible to find some similarities between the groups and complex systems...
7
Group StructureRelevance of the dynamics changes in the group structure (i.e. the emergence of the clusters, the modifying of the nodes’ density)
Relationships TopologyEvolution of the network configuration and nodes’ position
Sociogram Grafical representation of the socio-emotional bonds within the group(i.e. sympathy, antipathy, indifference)
Network Parameter Centrality degree
Betweenness degree
Cluster
Closeness
Density
Network diameter
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
8
Community
Chat Structure
Communication environment
Mood Choice
Recipient Choice
Interface DefinitionInteraction Environment
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
The chat room has been divided into two separate spaces, one for public communications, where everyone could interact with every others (i.e. community), and one for peer to peer communications, where everyone could exchange textual messages only with another person at once (i.e. private). The subjects could accompany the textual messages with some information about their mood (i.e. mood
choice). Moreover, to permit an interaction closer to the real social experience, we added two bi-dimensional spaces (i.e. public or private radar), manipulable by the subjects.
9
Public Radar
A change in its configuration will be instantaneously visible to all participants, and in this sub-environment one can only move his/her own avatar symbol. This is reflected by a change in the visibility (transparency) of the messages appearing in the public chat. Namely, the farther is the receiver avatar from the sender's one, the lighter is the message. This allows a more realistic simulation of a real environment, simulating the different loudness of a spoken message due to the `physical’ distance among the participants.
Interface DefinitionRadar Environment
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
10
Private Radar
Subjects can modify others positions, depending on the perceived agreement with them. Everyone has his/her own private personal radar. A change in its configuration will be visible only by the individual who handles this space
Interface DefinitionRadar Environment
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
11
Order Parameters Formalization
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
The components of the matrix W are defined by the counters elements for the
communicative dimensions and by the distances between the coordinates
for the radar dimensions.
The activity is the average of the events produced by the subject i and directed to the
subject j over time, the centrality degree indicates the probability of the number of
elements linked to the node i at instant t, and the Betweenness degree, calculated as the ratio among the number of shortest paths
passing through the node i and the sum of all shortest paths present, it provides
some indications regarding the importance of the node to the topological structure
of the network considered
ati =
N�
j=1,i �=j
W tij
t
cti = (W t)2ii
bti =
�
j,k∈N,j �=k
#Stjk(i)
#Stjk
P tij =
W tij�
t W ti.
Probability Space
Activity
Centrality Degree
Betweenness Degree
12
Dimensions Considered
Communicative Dimension
GM. Messages globally sent, both in the public and private side
CM. Messages sent in the community chat area
PM. Messages sent in the private side
Quality of the Interaction
CPosM. Messages sent with positive mood in the public side
CNegM. Messages sent with negative mood in the public side
CNulM. Messages sent with the neutral mood in the public side
PPosM. Messages sent with positive mood in private side
PNegM. Messages sent with negative mood in private side
PNulM. Messages sent with neutral moods in private side
Spatial Dimension
PUB Radar. (x,y) are the coordinates of the subject within the public radar
PRI Radar. (x,y) are the coordinates of the subject within the prvate radar
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
13
Sample
48% 52%
MaleFemale
Age 24 ±3
Years of Schooling 16 ±1
5' dedicated to the collection of
socio-demographic data
10' standardized training
45' virtual interaction
10 subjects per experimental
session
15 several sessions
60’ per experimental session
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
The common task required to the subjects was to configure their private radar for the entire duration of the experiment, depending on the degree of
perceived affinity toward others, moving away from the center who is perceived as disagreeable and bringing in the likeable.
Furthermore, they must choose the mood and the recipient/s for each message sent
14Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
The TasksBlank Modality vs Topic Modality vs Voting Modality
Blank Modality Voting ModalityTopic ModalityIn this modality it was required to the subjects to talk about a
specific topic, in particularabout animals experimentation. The choice of this argument has
been designed to strongly polarize the group, to lead and to force the subjects’ opinion
toward two contraries opinions. In this modality the subjects could interact freely, without any specification about the topic of
the conversation. The experimental task asked to the
subjects was to represent themselves and to configure the
private radar based on the perceived feeling of affinity with others for the entire
duration of the experiment.
This modality consists in a frustrated minority game. It was
required to the subjects to discuss about three different
features, and for each of these. choose their own preference,
expressed through three different phases of voting (i.e one every 15
minutes of discussion), with the aim to belong in the last vote to the
second largest cluster.
15
Voting Modality Distribution of Cluster Size
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
Standardized Colour Voting Distribution of the clusters size : First (Colour) Voting
Size of the Cluster
Nor
mal
ized
Fre
quen
cy
Exp1Exp2Exp3Exp4Exp5Cumulate
1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
7
Standardized Shape Voting Distribution of the clusters size : Second (Shape) Voting
Size of the Cluster
Nor
mal
ized
Fre
quen
cy
Exp1Exp2Exp3Exp4Exp5Cumulate
1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
7
8
9
10
Standardized Acronym Voting Distribution of the clusters size : Third (Acronym) Voting
Size of the Cluster
Nor
mal
ized
Fre
quen
cy
Exp1Exp2Exp3Exp4Exp5Cumulate
The graphs show the trend of the clusters size related to the voting preferences for what concern the 5 experimental sessions of voting modality.
It's interesting to observe how the size of the clusters decrease during the three votes of preference, up to the closest size to the probability of winning the game in the last vote,
when the subjects indicate their choice on the acronym.During the first two votes the subjects apparently adopt other kind of strategies to vote,
and the distribution of the final clusters size reveals that only in the third vote the subjects try to win, determining only small clusters composed by one, two or three components.
16
Voting ModalityExperimental vs Random Generated Data
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
First Vote (Color) Comparison between Experimental and Random generated data
Size of the Cluster
Nor
mal
ized
Fre
quen
cy
Size distribution (Random)Win Probability (Random)Size distribution (Experimental)Win Probability (Experimental)
1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Second Vote (Shape) Comparison between Experimental and Random generated data
Size of the Cluster
Nor
mal
ized
Fre
quen
cy
Size distribution (Random)Win Probability (Random)Size distribution (Experimental)Win Probability (Experimental)
1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Third Vote (Acronym) Comparison between Experimental and Random generated data
Size of the Cluster
Nor
mal
ized
Fre
quen
cy
Size distribution (Random)Win Probability (Random)Size distribution (Experimental)Win Probability (Experimental)
All the participants are able to belong in the third vote to a cluster with an high probability of victory.Subjects’ strategies seem to approximate effectively the distribution of the probability
of victory of the clusters size in the case of a random process of vote, but making a sort of correction on it and voting not at random.
The first third of the experimenta seems to correspond to the characteristic time for the construction of the first “social structure”, which is also in this experiment
maintained until the end of the experiments.
17
Order Parameters TrendPublic Messages Centrality Degree
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
0 15 30 450
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Centrality Degree Voting−Exp 05 : Public Messages
Time
Wei
ghte
d C
entra
lity
Deg
ree
of th
e ag
ent
0 15 30 450
0.005
0.01
0.015
0.02
0.025
Centrality Degree Topic−Exp 01 : Public Messages
Time
Wei
ghte
d C
entra
lity
Deg
ree
of th
e ag
ent
0 15 30 450
0.005
0.01
0.015
0.02
0.025
Centrality Degree Blank−Exp 05 : Public Messages
Time
Wei
ghte
d C
entra
lity
Deg
ree
of th
e ag
ent
This measure tends quickly to a state of order, and gives us a first indication about the structure of the network. All individuals, regardless to the task required, its will stabilize
around the value of 0.11, which indicates the presence of a full-connected network, where each person exchanges messages with all other people within the network. Each node has equal probability of being connected with any other node. All 15 small groups
that participated at the experiments reach in the first third of each experimental session a state of equilibrium, which remain until the end of the experiment.
18
Order Parameters TrendPrivate Messages Centrality Degree
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
0 15 30 450
0.02
0.04
0.06
0.08
0.1
0.12
Centrality Degree Blank−Exp 01 : Private Messages
Time
Wei
ghte
d C
entra
lity
Deg
ree
of th
e ag
ent
0 15 30 450
0.02
0.04
0.06
0.08
0.1
0.12
Centrality Degree Topic−Exp 01 : Private Messages
Time
Wei
ghte
d C
entra
lity
Deg
ree
of th
e ag
ent
0 15 30 450
0.02
0.04
0.06
0.08
0.1
0.12
Centrality Degree Voting−Exp 04 : Private Messages
Time
Wei
ghte
d C
entra
lity
Deg
ree
of th
e ag
ent
The measure of the centrality degree in the private space clearly shows an evolution explicitly different from that shown in public space. In this space, which allows only
the dyadic relationships between individuals, the trends are highly unstable and it never reached an equilibrium state detectable during the 45 'of interaction. The task does not
appear to affect the dynamics of relationships in the private space, since this appears similar (i.e. out of a state of equilibrium) for all the three tasks and for the 15 experimental sessions
19Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
Exp. Modality BlankBlank Topic
Mean Diff. Topic Mean Diff. Voting Mean Diff. Voting
Observables 45’ 45’ 45’Activity GM 81.7* -107.1**Activity CM 73.8* -95.7**
Activity CposM 106.3** -127.4**
Activity CneuM -46.8* 44.1*
Activity PM 7.8* -11.3**
Activity PposM 5.2** -7.6**
Activity PRIRADAR -20.1**
**: p. < .01, *: p. < .05 (Test Bonferroni for ANOVA)
The data suggest that there is significant differences between the Topic modality and, respectively, the Blank modality and the Voting modality. The data also suggest that the only observable significantly different between the Blank modality and the
Voting modality regards the activity in the private radar (i.e. the average number of movements made by the subjects in their own private radar)
Experimenta ComparisonAnova for Activity
20
Experimenta ComparisonAnova for Betweeness Degree
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
Exp. Modality BlankBlank Topic
Mean Diff. Topic Mean Diff. Voting Mean Diff. Voting
Observables 45’ 45’ 45’
Betweenness CposM .015** - -.15**
Betweenness CneuM - - .020**
Betweenness CnegM .051** .032* -
Betweenness PM .078* -.068* -.146**
Betweenness PposM .056** -.049** -.105**
Betweenness PneuM - - -.109****: p. < .01, *: p. < .05 (Test Bonferroni for ANOVA)
The Betweenness degree for private messages appears to be significantly different for all three experimental conditions, confirming the highest number of clusters that emerges in this space.
The data presented in the table suggest us that there are some differences regarding the communicative strategies depending on the task required, expressed by the significant
differences in the averages of messages exchanged with positive, negative or neutral mood.
21
Correlations in Different SessionPrivate Radar Betweenness Centrality Degree
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
Exp. Modality Blank Topic Voting
Observables Pri Rad Betweenness Pri Rad Betweenness Pri Rad Betweenness
Pri Rad Centrality (45’).516* (45’).398* (45’).515*Activity CM (15’) .508* ns (30’) .368*
Activity CposM (30’) .505* ns (15’) .385*Degree CM (45’) .463* ns (45’) .511*
Degree CposM (45’) .487* ns (45’) .444*
Betweenness CposM (45’) .673* ns ns
Activity PRIRADAR ns (30’) .533* ns
Betweenness CnegM ns (15’) .350* ns
Activity PnegM ns ns (15’) .364*Betweenness PM ns ns (30’) .459*
Betweenness PnegM ns ns (30’) .386*
The best correlation between the observables, with higher values gathered in the 15’, 30’ or 45’ from the begin of the sessions and the betweenness in the private radar (i.e. the affinity space).
Regarding to the community space, the Blank and the Voting modality show some similar results, with the exception of the Betweenness in the positive community messages.
The private space seems to distinguish the Voting modality from the others two conditions.
22
Betweenness Affinity Space in Blank ModalityAffinity assessment strategy regression model
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
r. Adj r. St. Err Sum of SquaresModel ResidualSum of Squares
Model Residual F
0,843 0,686 0,02 0,085 0,035 27.727**
Predictor Beta t
Betweenness Degree in Community Positive Messages (45’) 0,574 7.004**
Centrality Degree in Community Positive Messages (45’) 0,248 2.623**
Activity in Community Messages (15’) 0,303 3.190**
Betweenness Degree in Public Radar (15’) 0,189 2.309*
B(i) = β1(CposM )45
�
Betw + β2(CposM )45
�
Cent + β3(CM )15�
Act + β4(PUBRad)15�
Betw
The value of Betweenness in private radar, interpreted as a measure of affinity, depends on the frequency with which the subject is involved and he is crucial in conversations with
positive mood, how many messages with positive mood are exchanged in the community space at the end of the session, on the activity in first 15’ in the community space and on the
structural importance for the conformation of the group defined in the public radar.
23Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
r. Adj r. St. Err Sum of SquaresModel ResidualSum of Squares
Model Residual F
0,598 0,330 0,035 3,84 5,26 8.210**
Predictor Beta t
Activity Private Radar (30’) 0,517 4.410**
Betweenness Community Negative Messages (15’) 0,271 2.310**
B(i) = β1(PRIRad)30�
Act + β2(CNegM )15
�
Betw
Betweenness Affinity Space in Topic ModalityAffinity assessment strategy regression model
The Betweenness degree depends on the activity, expressed with the frequency of the private radar manipulation, in the first 30’ and on the
structural centrality of the subjet involved in the messages exchanges with negative mood in the first 15’ of interaction
24Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
r. Adj r. St. Err Sum of SquaresModel ResidualSum of Squares
Model Residual F
0,656 0,431 0,07 0,179 0,224 11.592**
Predictor Beta t
Centrality Degree in Community Messages (45’) 0,508 4.534**
Betweenness Degree in Public Radar (15’) -0,280 -2.488*
Activity Private Negative Messages (45’) 0,267 2,365
Betweenness Affinity Space in Voting ModalityAffinity assessment strategy regression model
B(i) = β1(CM )45�
Cent + β2(PUBRad)15�
Betw + β3(PNegM )45
�
Act
The Betweenness degree in the affinity space depends on the number of the messages with positive mood sended and received by a subject at the end of the session, on the structural importance for the conformation of the group defined in the public radar in
the first 15’ of interaction and on the activity on the production of messages with negative mood in the private space at the end of the session
25
We have shown that different tasks elicited different cognitive strategies of the subjects. In particular, in unstructured task the affinity among subjects seems to play a fundamental role, while this is not true for more polarized tasks. The development of the affinity seems to be
consistent with sociophysics models (in unstructured tasks).In the minority game modality we observed that most of participants developed the “most
rational” behaviorn, despite the absence of a clear rewarding perpective.
Summer Solstice 2012 - Arcidosso - Italy A.Cini, A.Guazzini26 - 29 June 2012
Defining a
Framework Reasearch
Setting up of the
survey instrument
Relationship between
Microscopic / Macroscopic levelGroup Individual
Task