Summer solstice arcidosso 2012 (poster)

The Small Group Dynamics
A 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

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

26 - 29 June 2012 A.Cini, A.Guazzini Summer Solstice 2012 - Arcidosso - Italy 2

Introduction
From Psychology...
From Physics...
Small Group Dynamics Experiment

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)

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.


The small group is an intermediate space, where coexist and meet
Dyad the dynamics, norms and expectations of the dual relationship and
the relationship with the collective.

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
Collective
Clearly differentiation of roles


Communication is a relevant
relational aspect to assess the group
dynamics

Communication features
Sender - Message - Receiver

Sintax - Semantics - Pragmatics

Non-verbal communication

Topology of communication

Importance of the structure in the
group communication


It is possible to ﬁnd some similarities between the groups and
complex systems... Emerging Properties

Sensitivity to Initial
Conditions
Totality dynamics
Phase Transitions

Group Evolution Self-Organization
Hierarchy
Equilibrium
The whole as more than
the sum of the parts Dynamics Evolution
Group Phenomena Stability
Interdependence Complex Trend

Individual-Environment
Interaction


Group Structure
Relevance of the dynamics changes in the group structure
(i.e. the emergence of the clusters, the modifying of the nodes’ density)

Relationships Topology
Evolution 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


Interface Deﬁnition
Interaction Environment

Chat Structure

Communication Community
environment

Mood Choice

Recipient Choice

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.

Radar Environment

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.


Radar Environment

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


Order Parameters Formalization

The components of the matrix W are deﬁned
t by the counters elements for the
Wij
Probability Space Pij =
t
t communicative dimensions and by the
t Wi. distances between the coordinates
for the radar dimensions.
N
t
Wij The activity is the average of the events
Activity at =
i
t produced by the subject i and directed to the
j=1,i=j
subject j over time, the centrality degree
indicates the probability of the number of
elements linked to the node i at instant t, and
Centrality Degree ci = (W )ii
t t 2
the Betweenness degree, calculated as the
ratio among the number of shortest paths
passing through the node i and the sum
#Sjk (i) of all shortest paths present, it provides
t
Betweenness Degree bt = some indications regarding the importance
i
#Sjk
t
j,k∈N,j=k of the node to the topological structure
of the network considered


Dimensions Considered

Communicative Dimension Quality of the Interaction
GM. Messages globally sent, both in CPosM. Messages sent with positive
the public and private side mood in the public side

CM. Messages sent in the community CNegM. Messages sent with negative
chat area mood in the public side

CNulM. Messages sent with the neutral
PM. Messages sent in the private side
mood in the public side

Spatial Dimension PPosM. Messages sent with positive
mood in private side
PUB Radar. (x,y) are the coordinates of the PNegM. Messages sent with negative
subject within the public radar mood in private side
PRI Radar. (x,y) are the coordinates of the PNulM. Messages sent with neutral
subject within the prvate radar moods in private side


Sample

Male Age 24 ±3
Female 48% 52%
Years of Schooling 16 ±1

10 subjects per experimental 5' dedicated to the collection of
session socio-demographic data
15 several sessions 10' standardized training
60’ per experimental session 45' virtual interaction

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


The Tasks
Blank Modality vs Topic Modality vs Voting Modality

Blank Modality Topic Modality Voting Modality
In this modality it was required
to the subjects to talk about a
specific topic, in particular
about animals experimentation.
The choice of this argument has
been designed to strongly
polarize the group, to lead and
to force the subjects’ opinion
In this modality the subjects toward two contraries opinions. This modality consists in a
could interact freely, without any frustrated minority game. It was
specification about the topic of required to the subjects to
the conversation. The discuss about three different
experimental task asked to the features, and for each of these.
subjects was to represent choose their own preference,
themselves and to configure the expressed through three different
private radar based on the phases of voting (i.e one every 15
perceived feeling of affinity minutes of discussion), with the aim
with others for the entire to belong in the last vote to the
duration of the experiment. second largest cluster.

Voting Modality
Distribution of Cluster Size
Standardized Colour Voting Standardized Shape Voting Standardized Acronym Voting
Distribution of the clusters size : First (Colour) Voting Distribution of the clusters size : Second (Shape) Voting Distribution of the clusters size : Third (Acronym) Voting
6 7 10
Exp1 Exp1 Exp1
Exp2 Exp2 Exp2
Exp3 Exp3 9 Exp3
Exp4 6 Exp4 Exp4
5 Exp5 Exp5 Exp5
Cumulate Cumulate 8 Cumulate

5
7
4
Normalized Frequency


6
4

3 5

3
4

2
2 3

2
1
1
1

0 0 0
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Size of the Cluster Size of the Cluster Size of the Cluster

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.


Voting Modality
Experimental vs Random Generated Data
First Vote (Color) Second Vote (Shape) Third Vote (Acronym)
Comparison between Experimental and Random generated data Comparison between Experimental and Random generated data Comparison between Experimental and Random generated data
0.7 0.7 0.7
Size distribution (Random) Size distribution (Random) Size distribution (Random)
Win Probability (Random) Win Probability (Random) Win Probability (Random)
Size distribution (Experimental) Size distribution (Experimental) Size distribution (Experimental)
0.6 Win Probability (Experimental) 0.6 Win Probability (Experimental) 0.6 Win Probability (Experimental)

0.5 0.5 0.5


0.4 0.4 0.4

0.3 0.3 0.3

0.2 0.2 0.2

0.1 0.1 0.1

0 0 0
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Size of the Cluster Size of the Cluster Size of the Cluster

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.


Order Parameters Trend
Public Messages Centrality Degree
Centrality Degree Centrality Degree Centrality Degree
Blank−Exp 05 : Public Messages Topic−Exp 01 : Public Messages Voting−Exp 05 : Public Messages
0.025 0.025 0.045

0.04
Weighted Centrality Degree of the agent


0.02 0.02
0.035

0.03

0.015 0.015
0.025

0.02
0.01 0.01

0.015

0.01
0.005 0.005

0.005

0 0 0
0 15 30 45 0 15 30 45 0 15 30 45
Time Time Time

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.


Order Parameters Trend
Private Messages Centrality Degree
Centrality Degree Centrality Degree Centrality Degree
Blank−Exp 01 : Private Messages Topic−Exp 01 : Private Messages Voting−Exp 04 : Private Messages
0.12 0.12 0.12

0.1 0.1 0.1


0.08 0.08 0.08

0.06 0.06 0.06

0.04 0.04 0.04

0.02 0.02 0.02

0 0 0
0 15 30 45 0 15 30 45 0 15 30 45
Time Time Time

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


Experimenta Comparison
Anova for Activity

Exp. Modality Blank 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 Comparison
Anova for Betweeness Degree

Exp. Modality Blank 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.


Correlations in Different Session
Private Radar Betweenness Centrality Degree

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.

Betweenness Affinity Space in Blank Modality
Affinity assessment strategy regression model

Sum of Squares
r. Adj r. St. Err
Model Residual F
0,843 0,686 0,02 0,085 0,035 27.727**
pos 45 pos 45 15 15
B(i) = β1 (CM )Betw + β2 (CM )Cent + β3 (CM )Act + β4 (P U BRad )Betw

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*

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.


Betweenness Affinity Space in Topic Modality

Sum of Squares
r. Adj r. St. Err Model Residual F
0,598 0,330 0,035 3,84 5,26 8.210**

30 N eg 15
B(i) = β1 (P RIRad )Act + β2 (CM )Betw
Predictor Beta t
Activity Private Radar (30’) 0,517 4.410**
Betweenness Community Negative Messages (15’) 0,271 2.310**

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


Betweenness Affinity Space in Voting Modality

Sum of Squares
r. Adj r. St. Err Model Residual F
0,656 0,431 0,07 0,179 0,224 11.592**

45 15 N eg 45
B(i) = β1 (CM )Cent + β2 (P U BRad )Betw + β3 (PM )Act

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

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


Defining a Setting up of the
Framework Reasearch survey instrument

Relationship between
Microscopic / Macroscopic level
Group Individual

Task

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 arcidosso 2012 (poster)

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