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Summer solstice arcidosso 2012 (poster)

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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

  • 3IntroductionFrom 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 subjects 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)

  • 4Features 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.

  • 5Communication 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

  • 6Emerging 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

  • 8Community

    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 tijt

    cti = (Wt)2ii

    bti =

    j,kN,j =k

    #Stjk(i)#Stjk

    P tij =W tijtW

    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

    Norm

    alize

    d Fr

    eque

    ncy

    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

    Norm

    alize

    d Fr

    eque

    ncy

    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

    Norm

    alize

    d Fr

    eque

    ncy

    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

    Norm

    alize

    d Fr

    eque

    ncy

    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

    Norm

    alize

    d Fr

    eque

    ncy

    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

    Norm

    alize

    d Fr

    eque

    ncy

    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 VotingExp 05 : Public Messages

    Time

    Weig

    hted

    Cen

    trality

    Deg

    ree

    of th

    e ag

    ent

    0 15 30 450

    0.005

    0.01

    0.015

    0.02

    0.025

    Centrality Degree TopicExp 01 : Public Messages

    Time

    Weig

    hted

    Cen

    trality

    Deg

    ree

    of th

    e ag

    ent

    0 15 30 450

    0.005

    0.01

    0.015

    0.02

    0.025

    Centrality Degree BlankExp 05 : Public Messages

    Time

    Weig

    hted

    Cen

    trality

    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 BlankExp 01 : Private Messages

    Time

    Weig

    hted

    Cen

    trality

    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 TopicExp 01 : Private Messages

    Time

    Weig

    hted

    Cen

    trality

    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 VotingExp 04 : Private Messages

    Time

    Weig

    hted

    Cen

    trality

    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 45Activity 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) = 1(CposM )45Betw + 2(C

    posM )

    45Cent + 3(CM )

    15Act + 4(PUBRad)

    15Betw

    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) = 1(PRIRad)30

    Act + 2(CNegM )

    15Betw

    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) = 1(CM )45

    Cent + 2(PUBRad)15Betw + 3(P

    NegM )

    45Act

    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

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