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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.

                                      CODYM 2012
                           Cultural and Opinion Dynamics Workshop
                                      Bruxelles - Belgium

                                03 - 07 September 2012
Summary
                                                    Starting Point
                                          Experimental Framework
                                 Small Group Dynamics Experiment




   Starting Point
            Small group & Lewin’s field theory
            Physical & Psychologial field
            Complex network of relationships

   Experimental Framework
            Framework introduction
            Interface description
            Parameter & Explored dimensions
            Blank - Topic -Voting modality

   Small Group Dynamics Experiment
           Voting game strategies results
           Comparison between modality
           Affinity strategies assessment
           Conclusion

03 - 07 September 2012 A.Cini, A.Guazzini                            CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   2
Summary
                                                                   The Small Group & Lewin’s Field Theory
                                                 Starting Point
                                                                   Physical & Psychological Field
                                          Experimental Framework
                                                                   Complex Network of Relationships
                                 Small Group Dynamics Experiment



           Dyad                                    Features of the small groups
                                                         Size of the Group          Strong interdipendence
                                                        (10 - 12 persons)	

       among the members
                                                         Goals sharing             High sense of belonging
                                                         Frequent and               Clearly differentiation of
                                                        regulars interactions      roles
                                                         Social and affective      Interest sharing
                                                        relationships


                                                             Lewin’s field theory
                                        Group as a dynamics system	

      Collective                        Individual-environment interaction
                                       Temporal causality
                                                                                            B = f (P, E)
                                        Relationship network


03 - 07 September 2012 A.Cini, A.Guazzini                                  CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   3
Summary
                                                                    The Small Group & Lewin’s Field Theory
                                                 Starting Point
                                                                    Physical & Psychological Field
                                          Experimental Framework
                                                                    Complex Network of Relationships
                                 Small Group Dynamics Experiment



  Physical field
          Short-range interactions
          Local field dependence
          Simmetric interactions
          Inertia as memory term
           i = (x, y) as respectively the spatial coordinates
          and the internal degree of freedom for interaction

                                                                   Small group field
                                                                           Total-range interactions
                                                                           Interdependance between all the elements
                                                                           Asimmetric relations
                                                                           Evolution of affinity as memory term

                                                                           i = (x,y) as respectively a matrix of affinity and
                                                                          the opinion

03 - 07 September 2012 A.Cini, A.Guazzini                                    CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   4
Summary
                                                                   The Small Group & Lewin’s Field Theory
                                                 Starting Point
                                                                   Physical & Psychological Field
                                          Experimental Framework
                                                                   Complex Network of Relationships
                                 Small Group Dynamics Experiment




   Group Structure
       Relevance of the dynamics changes in the group
     structure

   Relationships Topology
      Evolution of the network configuration and
     nodes’ position

   Affinity Network
      Grafical representation of the socio-emotional
     bonds within the group

   Network Parameters
             Nodes’ activity
             Centrality degree
             Betweenness degree


03 - 07 September 2012 A.Cini, A.Guazzini                                  CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   5
Summary        Framework Introduction
                                                    Starting Point     Interface Description
                                   Experimental Framework              Parameters & Explored Dimensions
                                 Small Group Dynamics Experiment       Blank - Topic - Voting Modality


 Advantages of the framework: the virtual community
   Isolation and anonymity guaranteed to the subjects
   Optimal control of the information dynamics
   Effective measures of the group communication
   Comparisons of different task oriented conditions
   Different network topologies impact evaluation
   Detection of both individual and collective features

     Experimental details
       150 unknown and unidentifiable interacting                      60’ per experimental session
     individuals                                                      10’ of standardized training with the tool
       15 Experimental sessions of 10 randomized                     and the task
     subjects                                                         5‘ for the sociodemographic
       3 Task Modality (i.e. cognitive constraints)                  data collection
       15 several sessions                                            45’ of virtual interaction by text messages


03 - 07 September 2012 A.Cini, A.Guazzini                                       CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   6
Summary      Framework Introduction
                                                    Starting Point   Interface Description
                                   Experimental Framework            Parameters & Explored Dimension
                                 Small Group Dynamics Experiment     Blank - Topic - Voting Modality


Interaction Environment
                                 Communication environment




                         Community




                                                                                        Private
                                                                                                                  Mood
                                                                                                                  Choice


      Recipient Choice
03 - 07 September 2012 A.Cini, A.Guazzini                                     CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   7
Summary      Framework Introduction
                                                    Starting Point   Interface Description
                                   Experimental Framework            Parameters & Explored Dimension
                                 Small Group Dynamics Experiment     Blank - Topic - Voting Modality


Radar Environment

Affinity Space
 (Private Radar)
 Each individual has his icon at
 the center of the radar, and
 uses the radar to set up his
 affinity network during all the
 interaction




                                   Each individual can move only his icon,
                                   monitoring the positions of the others.                     Room Space
                                   The distance between the icons affects
                                   the contrast of the textual messages                        (Public Radar)
                                   displayed in the community

03 - 07 September 2012 A.Cini, A.Guazzini                                     CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   8
Summary      Framework Introduction
                                                     Starting Point   Interface Description
                                    Experimental Framework            Parameters & Explored Dimensions
                                  Small Group Dynamics Experiment     Blank - Topic - Voting Modality

Order Parameters Formalization
                                                     t
                                                   Wij
  Probability of interaction         Pij =
                                      t
                                                       t
                                                                 Centrality Degree                       ct = (W t )2
                                                                                                          i         ii
                                                   t Wi.
                                               N
                                                       Wijt                                                         #Sjk (i)
                                                                                                                      t
   Activity                        at =                          Betweenness Degree             bt =
                                    i
                                                        t
                                                                                                 i
                                                                                                                     #Sjk
                                                                                                                        t
                                             j=1,i=j                                                   j,k N,j⇥=k


Considered dimensions

    Communicative Dimension                                           Quality of the Interaction
               GM. Messages globally sent, both in the                         CPosM. Messages with positive mood
              community and private                                           in community
               CM. Messages sent in community                                  CNegM. Messages with negative mood
               PM. Messages sent in private                                   in community
                                                                               CNulM. Neutral messages in
    Spatial Dimension                                                         community
              PUB Radar. (x,y) are the coordinates of                          PPosM. Messages with positive mood
              the subject within the public radar                             in private
               PRI Radar. (x,y) are the coordinates of                         PNegM. Messages with negative mood
              the subject within the private radar                            in private
                                                                               PNulM. Neutral messages in private

 03 - 07 September 2012 A.Cini, A.Guazzini                                   CODYM 2012 - ECCS 2012 - Bruxelles - Belgium      9
Summary      Framework Introduction
                                                     Starting Point   Interface Description
                                    Experimental Framework            Parameters & Explored Dimensions
                                  Small Group Dynamics Experiment     Blank - Topic - Voting Modality




  Affinity                                                                   The common task along all the three
                                                                            modality it was to modify constantly the
   Space                                                                    affinity space for the entire duration of the
                                                                            experiment, depending on the degree of
                                                                            perceived affinity toward others




 Blank Modality                               Topic Modality                             Voting Modality




The subjects could interact freely,          We asked to the subjects to talk          The subjects discuss and choose
The experimental task asked to               about a specific topic, in particular      their own preference through three
the subjects simply to represent             about animals experimentation,            voting sessions, trying to belong to
themselves during the interaction            negotiating their opinion                 the second cluster of majority

 03 - 07 September 2012 A.Cini, A.Guazzini                                    CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   10
Summary       Framework Introduction
                                                     Starting Point    Interface Description
                                    Experimental Framework             Parameters & Explored Dimensions
                                  Small Group Dynamics Experiment      Blank - Topic - Voting Modality

Focusing on Voting modality

            The subjects interacting                                   First vote
             into a minority game.                                        Color (15’)
    The condition to satisfy has been to
      belong to the second cluster of
        majority in the final voting.

Voting rules                                                          Second vote
    Each subject had to select the color, shape                           Shape (30’)
   and the acronym they preferred
    The vote preferences were expressed using
   the apposite voting card
    Only one preference (vote) can be
   expressed
                                                                      Third vote
    After the voting phase, winners were be                             Acronym (45’)
   announced by the responsible of experiment


 03 - 07 September 2012 A.Cini, A.Guazzini                                     CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   11
Summary                                                                                       Voting Game Strategies Results
                                                                                                                          Starting Point                                                                                     Comparison Between Modality
                                                                                                                Experimental Framework                                                                                       Affinity Strategies Assesment
                                                                                                   Small Group Dynamics Experiment                                                                                           Conclusion

                 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
Normalized Frequency




                                                                                                                                       Normalized Frequency




                                                                                                                                                                                                                                                                          Normalized Frequency
                        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


                 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




                                                                                                                                               Normalized Frequency




                                                                                                                                                                                                                                                                              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


                        03 - 07 September 2012 A.Cini, A.Guazzini                                                                                                                                                                                 CODYM 2012 - ECCS 2012 - Bruxelles - Belgium                                                                                               12
Summary                                                                          Voting Game Strategies Results
                                                                                                             Starting Point                                                                        Comparison Between Modality
                                                                                                   Experimental Framework                                                                          Affinity Strategies Assesment
                                                                                      Small Group Dynamics Experiment                                                                              Conclusion

Blank - Topic -Voting: Centrality degree in community comparison
                                                               Centrality Degree                                                                                                  Centrality Degree                                                                                                                        Centrality Degree
                                                            Blank−Exp 05 : Public Messages                                                                                      Topic−Exp 01 : Public Messages                                                                                                      Voting−Exp 01 : Global Messages
                                            0.025                                                                                                               0.025                                                                                                        0.025




                                                                                                                                                                                                                                                                                               0.02




                                                                                                                                                                                                                         Weighted Centrality Degree of the agent
  Weighted Centrality Degree of the agent




                                                                                                                      Weighted Centrality Degree of the agent
                                             0.02                                                                                                                0.02




                                            0.015                                                                                                               0.015                                                                                                        0.015




                                             0.01                                                                                                                0.01                                                                                                                          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


Blank - Topic -Voting: Centrality degree in private comparison
                                                                  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
Weighted Centrality Degree of the agent




                                                                                                           Weighted Centrality Degree of the agent




                                                                                                                                                                                                                                                             Weighted Centrality Degree of the agent
                                            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

                                            03 - 07 September 2012 A.Cini, A.Guazzini                                                                                                                            CODYM 2012 - ECCS 2012 - Bruxelles - Belgium                                                                                               13
Summary     Voting Game Strategies Results
                                                 Starting Point   Comparison Between Modality
                                       Experimental Framework     Affinity Strategies Assesment
                          Small Group Dynamics Experiment         Conclusion


Blank - Topic - Voting
 Anova for Activity: Mean Differences


                                       Blank vs Topic        Blank vs Voting      Topic vs 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**                -107.1**
                                                                                    **: p. < .01, *: p. < .05 (Bonferroni test for ANOVA)




                      The Activity mean differences refers to a different usage of the
                environment, depending on the task required to the subjetcs in interaction.


03 - 07 September 2012 A.Cini, A.Guazzini                                   CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 14
Summary     Voting Game Strategies Results
                                                 Starting Point   Comparison Between Modality
                                       Experimental Framework     Affinity Strategies Assesment
                          Small Group Dynamics Experiment         Conclusion


Blank - Topic - Voting
 Anova for Centrality Degree: Mean Differences


                                       Blank vs Topic       Blank vs Voting       Topic vs Voting

                  Observables                  45’                 45’                       45’
                  Centrality CposM           .017**                 -                      .017**

                  Centrality CneuM           .025**                 -                      .021**

                  Centrality CnegM           .025*                  -                          -
                  Centrality PM               .14*                  -                          -

                  Centrality PposM            .14**                 -                      -.18**
                  Centrality PnegM           .079*                .077*                        -

                                                                                   **: p. < .01, *: p. < .05 (Bonferroni test for ANOVA)




                 The Centrality degree provide us an overview on the system and on the
                  mean state of the subjects in interaction. The mean differences regard
                      the mood of the messages and the private communication.


03 - 07 September 2012 A.Cini, A.Guazzini                                 CODYM 2012 - ECCS 2012 - Bruxelles - Belgium                     15
Summary       Voting Game Strategies Results
                                                 Starting Point     Comparison Between Modality
                                       Experimental Framework       Affinity Strategies Assesment
                          Small Group Dynamics Experiment           Conclusion


 Affinity recipes: linear regression
Betweenness in
                                       r2 = 0,686
Blank Modality
                             150            P OS 450             P OS 450
           B(i) =     1 (CM )Act   +    2 (CM   )Cent   +    3 (CM   )Betw



Betweenness in                         r2 = 0,330
Topic Modality

                                   300              N eg 150
           B(i) =      1 (P RIRad )Act      +   2 (CM )Betw




Betweenness in                          r2 = 0,431
Voting Modality
                            450                      150              N eg 450
           B(i) =    1 (CM )Cent   +    2 (P U BRad )Betw   +     3 (PM )Act



03 - 07 September 2012 A.Cini, A.Guazzini                                   CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   16
Summary     Voting Game Strategies Results
                                                  Starting Point   Comparison Between Modality
                                        Experimental Framework     Affinity Strategies Assesment
                           Small Group Dynamics Experiment         Conclusion

Strategies in Voting modality

  The subjects evolve and negotiate effectively an effective strategy to face with
  the (frustrated) task
  All the participants are able to belong in the third vote to a cluster with an
  high probability of victory (e.g. size 2-4)
  The voting strategy used by the subjects approximate always the best strategy

Group structure
  The average time needed to establish a group structure is about 15’ in
  community communication, for all the tasks.
  The private communication never reached a stationary state
   Different levels of analysis show different structures

Affinity network

  The final affinity space depends on the task, as so as the strategy used by
  the subjects to assess their affinity with others

  The affinity network is affected both from communicative and non-
  communicative factors

 03 - 07 September 2012 A.Cini, A.Guazzini                                  CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   17
Thanks for the attention
  Selected bibliography
            Bagnoli, F., Carletti, T., Fanelli, D., Guarino, A., Guazzini, A. (2007). “Modeling mutual
          affinity in opinion dynamics", Phys. Rev. E, 76, 066105. DOI: 10.1103/PhysRevE.
          76.066105
           Bagnoli, F., Carletti, T., Fanelli, D., Guarino, A., Guazzini, A. (2008). “Meet, Discuss and
          Trust each other: large versus small groups”, proceedings WIVACE 2008 (12 pag).
            Guazzini, A., Liò, P., Bagnoli, F., Passarella, A., Conti, M. (2010) “Cognitive network
          dynamics in chatlines”, Procedia Computer Science, Volume 1, Issue 1, May 2010, Pages
          2349-2356. ICCS 2010. DOI:10.1016/j.procs.2010.04.265

             Guazzini, A., Vilone, D., Bagnoli, F., Carletti, T., Lauro-Grotto, R. (2012) “Cognitive
          network structure: an experimental study”, Vol. 15, No. 6, Advances in Complex
          Systems. DOI: 10.1142/S0219525912500841
             Guazzini, A., Cini, A., Lauro-Grotto, R., Bagnoli, F. (2012) “Virtual small group
          dynamics: a quantitative experimental framework”, Vol.1 Iss.2, pp 10-17, in
          Journal of Review of Psychology Frontier (RPF)

03 - 07 September 2012   A.Cini, A.Guazzini                        CODYM 2012 - ECCS 2012 - Bruxelles - Belgium   18
Summary     Voting Game Strategies Results
                                                 Starting Point   Comparison Between Modality
                                       Experimental Framework     Affinity Strategies Assesment
                          Small Group Dynamics Experiment         Conclusion


Blank - Topic - Voting
 Anova for Betweeness Degree: Mean Differences


                                       Blank vs Topic       Blank vs Voting         Topic vs 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 (Bonferroni test for ANOVA)




                     The Betweenness degree mean differences depending on the tasks
                         required to the subjects in interaction give us information
                            concerning the topology of the network considered


03 - 07 September 2012 A.Cini, A.Guazzini                                   CODYM 2012 - ECCS 2012 - Bruxelles - Belgium                        19

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Eccs2012 small group

  • 1. 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. CODYM 2012 Cultural and Opinion Dynamics Workshop Bruxelles - Belgium 03 - 07 September 2012
  • 2. Summary Starting Point Experimental Framework Small Group Dynamics Experiment Starting Point Small group & Lewin’s field theory Physical & Psychologial field Complex network of relationships Experimental Framework Framework introduction Interface description Parameter & Explored dimensions Blank - Topic -Voting modality Small Group Dynamics Experiment Voting game strategies results Comparison between modality Affinity strategies assessment Conclusion 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 2
  • 3. Summary The Small Group & Lewin’s Field Theory Starting Point Physical & Psychological Field Experimental Framework Complex Network of Relationships Small Group Dynamics Experiment Dyad Features of the small groups Size of the Group Strong interdipendence (10 - 12 persons) among the members Goals sharing High sense of belonging Frequent and Clearly differentiation of regulars interactions roles Social and affective Interest sharing relationships Lewin’s field theory Group as a dynamics system Collective Individual-environment interaction Temporal causality B = f (P, E) Relationship network 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 3
  • 4. Summary The Small Group & Lewin’s Field Theory Starting Point Physical & Psychological Field Experimental Framework Complex Network of Relationships Small Group Dynamics Experiment Physical field Short-range interactions Local field dependence Simmetric interactions Inertia as memory term i = (x, y) as respectively the spatial coordinates and the internal degree of freedom for interaction Small group field Total-range interactions Interdependance between all the elements Asimmetric relations Evolution of affinity as memory term i = (x,y) as respectively a matrix of affinity and the opinion 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 4
  • 5. Summary The Small Group & Lewin’s Field Theory Starting Point Physical & Psychological Field Experimental Framework Complex Network of Relationships Small Group Dynamics Experiment Group Structure Relevance of the dynamics changes in the group structure Relationships Topology Evolution of the network configuration and nodes’ position Affinity Network Grafical representation of the socio-emotional bonds within the group Network Parameters Nodes’ activity Centrality degree Betweenness degree 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 5
  • 6. Summary Framework Introduction Starting Point Interface Description Experimental Framework Parameters & Explored Dimensions Small Group Dynamics Experiment Blank - Topic - Voting Modality Advantages of the framework: the virtual community Isolation and anonymity guaranteed to the subjects Optimal control of the information dynamics Effective measures of the group communication Comparisons of different task oriented conditions Different network topologies impact evaluation Detection of both individual and collective features Experimental details 150 unknown and unidentifiable interacting 60’ per experimental session individuals 10’ of standardized training with the tool 15 Experimental sessions of 10 randomized and the task subjects 5‘ for the sociodemographic 3 Task Modality (i.e. cognitive constraints) data collection 15 several sessions 45’ of virtual interaction by text messages 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 6
  • 7. Summary Framework Introduction Starting Point Interface Description Experimental Framework Parameters & Explored Dimension Small Group Dynamics Experiment Blank - Topic - Voting Modality Interaction Environment Communication environment Community Private Mood Choice Recipient Choice 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 7
  • 8. Summary Framework Introduction Starting Point Interface Description Experimental Framework Parameters & Explored Dimension Small Group Dynamics Experiment Blank - Topic - Voting Modality Radar Environment Affinity Space (Private Radar) Each individual has his icon at the center of the radar, and uses the radar to set up his affinity network during all the interaction Each individual can move only his icon, monitoring the positions of the others. Room Space The distance between the icons affects the contrast of the textual messages (Public Radar) displayed in the community 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 8
  • 9. Summary Framework Introduction Starting Point Interface Description Experimental Framework Parameters & Explored Dimensions Small Group Dynamics Experiment Blank - Topic - Voting Modality Order Parameters Formalization t Wij Probability of interaction Pij = t t Centrality Degree ct = (W t )2 i ii t Wi. N Wijt #Sjk (i) t Activity at = Betweenness Degree bt = i t i #Sjk t j=1,i=j j,k N,j⇥=k Considered dimensions Communicative Dimension Quality of the Interaction GM. Messages globally sent, both in the CPosM. Messages with positive mood community and private in community CM. Messages sent in community CNegM. Messages with negative mood PM. Messages sent in private in community CNulM. Neutral messages in Spatial Dimension community PUB Radar. (x,y) are the coordinates of PPosM. Messages with positive mood the subject within the public radar in private PRI Radar. (x,y) are the coordinates of PNegM. Messages with negative mood the subject within the private radar in private PNulM. Neutral messages in private 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 9
  • 10. Summary Framework Introduction Starting Point Interface Description Experimental Framework Parameters & Explored Dimensions Small Group Dynamics Experiment Blank - Topic - Voting Modality Affinity The common task along all the three modality it was to modify constantly the Space affinity space for the entire duration of the experiment, depending on the degree of perceived affinity toward others Blank Modality Topic Modality Voting Modality The subjects could interact freely, We asked to the subjects to talk The subjects discuss and choose The experimental task asked to about a specific topic, in particular their own preference through three the subjects simply to represent about animals experimentation, voting sessions, trying to belong to themselves during the interaction negotiating their opinion the second cluster of majority 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 10
  • 11. Summary Framework Introduction Starting Point Interface Description Experimental Framework Parameters & Explored Dimensions Small Group Dynamics Experiment Blank - Topic - Voting Modality Focusing on Voting modality The subjects interacting First vote into a minority game. Color (15’) The condition to satisfy has been to belong to the second cluster of majority in the final voting. Voting rules Second vote Each subject had to select the color, shape Shape (30’) and the acronym they preferred The vote preferences were expressed using the apposite voting card Only one preference (vote) can be expressed Third vote After the voting phase, winners were be Acronym (45’) announced by the responsible of experiment 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 11
  • 12. Summary Voting Game Strategies Results Starting Point Comparison Between Modality Experimental Framework Affinity Strategies Assesment Small Group Dynamics Experiment Conclusion 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 Normalized Frequency Normalized Frequency Normalized Frequency 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 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 Normalized Frequency 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 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 12
  • 13. Summary Voting Game Strategies Results Starting Point Comparison Between Modality Experimental Framework Affinity Strategies Assesment Small Group Dynamics Experiment Conclusion Blank - Topic -Voting: Centrality degree in community comparison Centrality Degree Centrality Degree Centrality Degree Blank−Exp 05 : Public Messages Topic−Exp 01 : Public Messages Voting−Exp 01 : Global Messages 0.025 0.025 0.025 0.02 Weighted Centrality Degree of the agent Weighted Centrality Degree of the agent Weighted Centrality Degree of the agent 0.02 0.02 0.015 0.015 0.015 0.01 0.01 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 Blank - Topic -Voting: Centrality degree in private comparison 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 Weighted Centrality Degree of the agent Weighted Centrality Degree of the agent Weighted Centrality Degree of the agent 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 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 13
  • 14. Summary Voting Game Strategies Results Starting Point Comparison Between Modality Experimental Framework Affinity Strategies Assesment Small Group Dynamics Experiment Conclusion Blank - Topic - Voting Anova for Activity: Mean Differences Blank vs Topic Blank vs Voting Topic vs 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** -107.1** **: p. < .01, *: p. < .05 (Bonferroni test for ANOVA) The Activity mean differences refers to a different usage of the environment, depending on the task required to the subjetcs in interaction. 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 14
  • 15. Summary Voting Game Strategies Results Starting Point Comparison Between Modality Experimental Framework Affinity Strategies Assesment Small Group Dynamics Experiment Conclusion Blank - Topic - Voting Anova for Centrality Degree: Mean Differences Blank vs Topic Blank vs Voting Topic vs Voting Observables 45’ 45’ 45’ Centrality CposM .017** - .017** Centrality CneuM .025** - .021** Centrality CnegM .025* - - Centrality PM .14* - - Centrality PposM .14** - -.18** Centrality PnegM .079* .077* - **: p. < .01, *: p. < .05 (Bonferroni test for ANOVA) The Centrality degree provide us an overview on the system and on the mean state of the subjects in interaction. The mean differences regard the mood of the messages and the private communication. 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 15
  • 16. Summary Voting Game Strategies Results Starting Point Comparison Between Modality Experimental Framework Affinity Strategies Assesment Small Group Dynamics Experiment Conclusion Affinity recipes: linear regression Betweenness in r2 = 0,686 Blank Modality 150 P OS 450 P OS 450 B(i) = 1 (CM )Act + 2 (CM )Cent + 3 (CM )Betw Betweenness in r2 = 0,330 Topic Modality 300 N eg 150 B(i) = 1 (P RIRad )Act + 2 (CM )Betw Betweenness in r2 = 0,431 Voting Modality 450 150 N eg 450 B(i) = 1 (CM )Cent + 2 (P U BRad )Betw + 3 (PM )Act 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 16
  • 17. Summary Voting Game Strategies Results Starting Point Comparison Between Modality Experimental Framework Affinity Strategies Assesment Small Group Dynamics Experiment Conclusion Strategies in Voting modality The subjects evolve and negotiate effectively an effective strategy to face with the (frustrated) task All the participants are able to belong in the third vote to a cluster with an high probability of victory (e.g. size 2-4) The voting strategy used by the subjects approximate always the best strategy Group structure The average time needed to establish a group structure is about 15’ in community communication, for all the tasks. The private communication never reached a stationary state Different levels of analysis show different structures Affinity network The final affinity space depends on the task, as so as the strategy used by the subjects to assess their affinity with others The affinity network is affected both from communicative and non- communicative factors 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 17
  • 18. Thanks for the attention Selected bibliography Bagnoli, F., Carletti, T., Fanelli, D., Guarino, A., Guazzini, A. (2007). “Modeling mutual affinity in opinion dynamics", Phys. Rev. E, 76, 066105. DOI: 10.1103/PhysRevE. 76.066105 Bagnoli, F., Carletti, T., Fanelli, D., Guarino, A., Guazzini, A. (2008). “Meet, Discuss and Trust each other: large versus small groups”, proceedings WIVACE 2008 (12 pag). Guazzini, A., Liò, P., Bagnoli, F., Passarella, A., Conti, M. (2010) “Cognitive network dynamics in chatlines”, Procedia Computer Science, Volume 1, Issue 1, May 2010, Pages 2349-2356. ICCS 2010. DOI:10.1016/j.procs.2010.04.265 Guazzini, A., Vilone, D., Bagnoli, F., Carletti, T., Lauro-Grotto, R. (2012) “Cognitive network structure: an experimental study”, Vol. 15, No. 6, Advances in Complex Systems. DOI: 10.1142/S0219525912500841 Guazzini, A., Cini, A., Lauro-Grotto, R., Bagnoli, F. (2012) “Virtual small group dynamics: a quantitative experimental framework”, Vol.1 Iss.2, pp 10-17, in Journal of Review of Psychology Frontier (RPF) 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 18
  • 19. Summary Voting Game Strategies Results Starting Point Comparison Between Modality Experimental Framework Affinity Strategies Assesment Small Group Dynamics Experiment Conclusion Blank - Topic - Voting Anova for Betweeness Degree: Mean Differences Blank vs Topic Blank vs Voting Topic vs 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 (Bonferroni test for ANOVA) The Betweenness degree mean differences depending on the tasks required to the subjects in interaction give us information concerning the topology of the network considered 03 - 07 September 2012 A.Cini, A.Guazzini CODYM 2012 - ECCS 2012 - Bruxelles - Belgium 19

Editor's Notes

  • #2: \n
  • #3: We&apos;ll present you an experiment about the dynamics of a small group, specifically a framework designed to analyze the communications, the relationships and the dynamics occurring in a small group of people in virtual interaction.\nOur intent is to investigate how people build their personal representation about the relationship structure. We&apos;ll present first the results of a minority voting game, then a comparison among three different modalities, characterizied by three different tasks and finally three linear regression equations, one for each modality, to summarize the strategies followed by the subjects to build their Affinity spaces.\n
  • #4: We focus on a small size group. In psychology, the small group is a special social dimension, with a fusion of features of dyadic relationship and collective behaviors. Social dynamics and opinion dynamics often treat larger systems, formed by many elements. The relations among them are quite simple to modelize. On the contrary the dynamics emerging in a small group of people appear to be more complex exhibiting oscillations, shift etc. We can say that these systems are never at equilibrium.\nOur intent is to provide some suggestions to model the dynamics occurred in this social space, trying to take some insight from the theory of physical field. The first who translate this concept from physic to psychology was Lewin, with the &quot;field theory&quot;. The behavior of the people not depend exclusively on the characteristics of the individual within the group, but also on the configuration and the internal movement at a given time. \nThis seems to indicate that the events that occur are based on the principle of temporal causality, according to which what happens before influence what happens after, and on the dynamics of the system, which includes the elements involved and their mutual relations.\n\n
  • #5: We took inspiration from the concept of physical field, trying to extend it to the psychological domain. In particular, we focussed on the memory of the elements interacting in the system. It is very important in the dynamics of opinions that the elements preserve the memory of the interactions. In the physical domain this is represented as the inertia of the elements, in a psychological field this may be represented by a matrix of affinities, which takes account of previous interactions and influences the opinion modifying the relationships with others.\n
  • #6: We consider the small group as a complex network, where the subjects are considered as nodes. In this way it is possible to observe the evolution of the group structure, and considering at the same time the state of the elements. We extended some concepts and parameters derived from the social network analysis to define the evolution of the system along the all different sessions.\n
  • #7: The experiments were held in a computer lab.\nThe framework that we have designed consistes in a chatroom as virtual place of interaction, displayed on every computer of every participant. \nIt allowed anonymous interactions and the standardization of the information available to the individuals.\nThe communication through the chat room allowed also to control and isolate some communicative factors that influence social interaction, taking into account for this study only the frequencies of the sent and received messages and the mood characterizing the textual messages, and analyzing it by means of the social network analysis theory.\n\nWe have selected a sample of 150 subjects,divided into 15 groups o f 10 people\n\n\n
  • #8: Let me to introduce you the interface where the interactions took place\n\nThe chat room was divided into two separate spaces, one for public communications, labelled community, where everyone could interact with every others, and one for peer to peer communications, labelled private, where everyone can exchange textual messages only with another person at once. \nThe subjects can select the addressee of the message. The subjects can accompany the textual messages with some information about their mood. Moreover, to permit an interaction closer to the real social experience, we added two-dimensional spaces, manipulable by the subjects.\n
  • #9: In the affinity space, or private radar, the subjects can change the positions of the others&amp;#x2019; icon, moving near him icon, fixed at the centero of the radar, the icon of the subject felt with a greater affinity, and move away the others. \n\nWe assume that the distance reflects the relative affinity among people\n\nIn the room space, or public radar, shared by all participants, a subject can change his position, dragging and dropping his icon within this space. The distance to the other subject affects the contrast of the textual messages visualized in the community, to simulate the loudness variation of a spoken verbal exchange.\n\nFollowing the logic: the farther away is an individual on the radar, the dimmer his message, analogously to what happens whit sound and distance.\n\n\n
  • #10: All the events occurring within the experimental environment are recorded in a log file that collects all the information available about the dynamics of observable messages. \nWe have extrapolated a series of temporal matrices W whose elements are the number of exchanged messages or the vicinity among icons in the radars.\nWe have defined the equation of probability of interaction, that describes the probabilty of the occurrence of an event at time t.\nThe activity is the average of the events produced in any dimensions by the subject i and directed to the subject j over time,\nThe centrality degree, a measure that indicates the number of the nodes/subjects linked to the node i at instant t\nand 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 describing the network were computed.\n\nTrought this parameters we analyzed 11 different dimensions, 3 related to communicative dimension, 6 related to the quality of interaction and 2 for the two-dimensional spaces\n\n
  • #11: In order to investigate how different tasks affect the dynamics and the final affinity space, we designed three different modality of interaction.\n\nThe common task in all the different modalities was to configure the private radar basing on the perceived feeling of affinity with others.\n\nWe labelled &amp;#x201C;Blank Modality&amp;#x201D; the control task where the first five small groups interacted. In this modality the subjects can interact freely, without any topic constraint.\nThe second experimental condition was labelled &amp;#x201C;Topic Modality&amp;#x201D;.5 small groups interacted under the constraint of talking about a specific topic, in particular about animal experimentation. The goal of this argument was that of strongly polarize the group, leading the subjects towards two opposite opinions.\n\nThe remaining 5 small groups interacted in the last experimental session, called &amp;#x201C;Voting Modality&amp;#x201D;.\n
  • #12: In this case, the subjects played the role of a team of advertisers, discussing about three different features, that togheter go to form a logo, and choosing for each feature their own preferences, expressed through three different phases of voting, one every 15 minutes of discussion.\n\n\nAfter any voting phases, the experimenter announced the results of the voting.\nThe winners of this game were those who belonged in the last vote to the second largest cluster.\n\n\n
  • #13: As a first step, we analyzed the results of the strategies of vote. \n\nThe graphs on the top shows a comparison between a simulated random process of cluster size distribution and the experimental data.\nOn the x axis we have the clusters size, on the y axis the normalized frequencies. the dotted lines indicate the distributions generated by a random process, the continuous lines show the trend of the experimental data\n\nAs we see all the participants are able to take part in the third vote to a cluster with an high probability of victory. \n\nFollowing the trend of the black line and the dotted blu line, is it possible to observe that the subjects strategies seem to approximate the distribution of the probability of victory of the clusters size in the case of a random process of vote, but making a correction on it , probably due to the strategies discussion and strategies sharing.\n\nThe graph below show the trend of the clusters size relative to the voting preferences.\nThe different colors of lines identify the different experiments\nIt&amp;#x2019;s interesting to observe how the size of the clusters decrease during the three votes, up to the closest size to the probability of winning the game in the last vote.\n\nDuring the first two votes the subjects apparently adopt other kind of strategies, 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.\n
  • #14: We presented now a comparison between the blank, topic and voting modality. First of all, we explored the evolution of the trend of the centrality degree regarding the two general communicative dimension; the public communication and the private communication.\n\nIn the graph above are shown the graphs relate to the measure of Centrality Degree in the community side of the chat for the three different experimental tasks. \nThe color of the line identifies a different subject. \nAs we see, the groups tend in the first third of each experiment towards an order state, giving us a first indication about the structure of the network, a full-connected network, regardless to the task required.\n\nThe centrality degree in the private side, reported in the graph at the bottom clearly shows an evolution different from that shown in community space. \nHere the trends are highly unstable and it never reach an equilibrium state.\n
  • #15: The table shows the mean significative differences among the 3 conditions resulting for the ANOVA test for the Activity at the end of any session. \n\nThe data suggest that the subjects seem to interact in Voting Modality and in the Blank Modality in similar manner, with the exception of the parameter that indicates the amount of the manipulation of the Affinity Space (Activity in private radar) \n\nThe Topic modality appears to be the condition that more differs from the two others, where the subjects seem to use more the neutral mood messages\n\n
  • #16: Also in this table the blank and the voting modality differ significatively only for one dimension. Specifically, the data suggest that the subject in voting modality less interact with private negative messages.\n\nAnother interesting suggestion emerges from the comparison between topic and voting modalities regarding the private communication. In voting modality are exchanged more messages with positive mood in private communication with respect to the topic modality\n\nMoreover,Blank and Topic modality show many significative differences in the exchange of mood characterized messages\n\n
  • #17: We propose three linear regression equations, the best one for each experimental condition.\nThe term on the left is ever the betweenness degree in the affinity space, and on the right we have the temporal parameters related to the dimension analyzed. \n\nWe consider the betweenness degree of a subject i in the affinity network defined by the entire group as the average degree of affinity perceived by the group towards him\nTherefore, the regression equations can be seen as the cognitive strategies through which the subjects have built their own Affinty space\n \nIn Blank modality with the regression equation we can explain around the 70% of variance of data\nIt&apos;s interesting to note that the subjects consider also non-communicative factors, related to the spatial dimensions, to determine their affinity space, as we can see in the topic and the voting equations. \n
  • #18: In summary, the data of the voting modality show that the subjects in virtual interaction effectively succeed in fulfilling the experimental requests.\nIn all the sessions the subjects enact the strategy most likely to win, forming only small clusters composed by one, two or three individuals.\nThis suggests that the subjects are able to organize themselves in brief time in a context of small group virtual interaction.\n\nMoreover, a comparison among the three conditions proposed show that if on one hand we have seen that the three modalities show similar trends with regard to the parameters of centrality in public and private messages, on the other hand, the modalities show many signifcative differences when we change the networks analyzed especially if we consider also the mood that accompanies the messages.\n\nThe affinity among individuals appears to be sensitive to different aspects related to the task.\nThe subjects assess the affinity in different ways, depending on the nature of the task. \n\nConcluding, the results show that in the blank modality it is possible to forecast the final affinity between any two subjects, while this is not possible in more structured tasks. The interpretation of this result is that, in the absence of a specific task, people tends to structure their affinity according with the communicative space , while for structured tasks other dimensions become more important.\n
  • #19: \n
  • #20: The data presented in the table suggest that the Blank and Voting modalities show a greater average degree of betweenness with respect to the Topic modality for messages with positive mood. \n\nThe Betweenness for the community with a negative mood seem to well distinguish the blank modality.\n\nThe Betweenness for the community with a neutral mood appears to be significative different between Topic and Voting modality. \n\nThe average degree of Betweenness in the network of messages in the community with negative mood seems to differ significantly only for the Blank modality than the other 2 conditions, which means that in a context of free interaction the subjects tend to be involved in conversations with negative mood.\n\nFocusing on the peer to peer communication, the data suggest that the subjects in voting modality are involved in more conversations in the network of interaction with positive mood with respect to the others two experimental modalies. Furthermore, in the voting modality the subjects are involved more in conversations with neutral mood than in Topic modality.\n\n\n