Summer solstice arcidosso 2012 (poster)

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


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


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


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


8

Community

Chat Structure

Communication environment

Mood Choice

Recipient Choice

Interface DefinitionInteraction Environment


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


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


11

Order Parameters Formalization


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


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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


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 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


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


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


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


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


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


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


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


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


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


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


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


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.



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



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.


Defining a

Framework Reasearch

Setting up of the

survey instrument

Relationship between

Microscopic / Macroscopic levelGroup Individual

Task

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