The Small Group Dynamics A minority voting game experiment A. Cini(1) and A. Guazzini(1,2) 1) CSDC, University of Florence, via S. Marta 3, I-50139 Firenze, Italy. 2) Department of Psychology, University of Florence,Via di San Salvi 12, 50100, Firenze, Italy. Summer Solstice 2012 - Arcidosso - Italy 26 - 29 June 2012
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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.
The main goal of the present work is the characterization of how a small group of people builds and structures their communication network and the related affinities, during a short virtual group interaction, and what differences can be revealed by comparing different conditions.
We show how our experimental framework captures some fundamental aspects of the subject’s behaviour in a small group virtual dynamics.
We present here the results of a minority game situation
(Voting modality), in which there is no winning strategy for reaching consensus
in the majority of participants, and we confront the outcome of
this experiments with that of similar set-ups without
any task (Blank modality) and a majority game (Topic modality)
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.
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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.
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
Standardized Colour Voting Distribution of the clusters size : First (Colour) Voting
Size of the Cluster
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Exp1Exp2Exp3Exp4Exp5Cumulate
1 2 3 4 5 6 7 8 9 100
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Standardized Shape Voting Distribution of the clusters size : Second (Shape) Voting
Size of the Cluster
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Exp1Exp2Exp3Exp4Exp5Cumulate
1 2 3 4 5 6 7 8 9 100
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Standardized Acronym Voting Distribution of the clusters size : Third (Acronym) Voting
Size of the Cluster
Nor
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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.
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Voting ModalityExperimental vs Random Generated Data
First Vote (Color) Comparison between Experimental and Random generated data
Size of the Cluster
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Size distribution (Random)Win Probability (Random)Size distribution (Experimental)Win Probability (Experimental)
1 2 3 4 5 6 7 8 9 100
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Second Vote (Shape) Comparison between Experimental and Random generated data
Size of the Cluster
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Size distribution (Random)Win Probability (Random)Size distribution (Experimental)Win Probability (Experimental)
1 2 3 4 5 6 7 8 9 100
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Third Vote (Acronym) Comparison between Experimental and Random generated data
Size of the Cluster
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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.
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Order Parameters TrendPublic Messages Centrality Degree
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.
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Order Parameters TrendPrivate Messages Centrality Degree
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
Mean Diff. Topic Mean Diff. Voting Mean Diff. Voting
Observables 45’ 45’ 45’Activity GM 81.7* -107.1**Activity CM 73.8* -95.7**
Activity CposM 106.3** -127.4**
Activity CneuM -46.8* 44.1*
Activity PM 7.8* -11.3**
Activity PposM 5.2** -7.6**
Activity PRIRADAR -20.1**
**: p. < .01, *: p. < .05 (Test Bonferroni for ANOVA)
The data suggest that there is significant differences between the Topic modality and, respectively, the Blank modality and the Voting modality. The data also suggest that the only observable significantly different between the Blank modality and the
Voting modality regards the activity in the private radar (i.e. the average number of movements made by the subjects in their own private radar)
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.
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Correlations in Different SessionPrivate Radar Betweenness Centrality Degree
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.
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Betweenness Affinity Space in Blank ModalityAffinity assessment strategy regression model
r. Adj r. St. Err Sum of SquaresModel ResidualSum of Squares
Model Residual F
0,843 0,686 0,02 0,085 0,035 27.727**
Predictor Beta t
Betweenness Degree in Community Positive Messages (45’) 0,574 7.004**
Centrality Degree in Community Positive Messages (45’) 0,248 2.623**
Activity in Community Messages (15’) 0,303 3.190**
Betweenness Degree in Public Radar (15’) 0,189 2.309*
B(i) = β1(CposM )45
�
Betw + β2(CposM )45
�
Cent + β3(CM )15�
Act + β4(PUBRad)15�
Betw
The value of Betweenness in private radar, interpreted as a measure of affinity, depends on the frequency with which the subject is involved and he is crucial in conversations with
positive mood, how many messages with positive mood are exchanged in the community space at the end of the session, on the activity in first 15’ in the community space and on the
structural importance for the conformation of the group defined in the public radar.
Betweenness Affinity Space in Voting ModalityAffinity assessment strategy regression model
B(i) = β1(CM )45�
Cent + β2(PUBRad)15�
Betw + β3(PNegM )45
�
Act
The Betweenness degree in the affinity space depends on the number of the messages with positive mood sended and received by a subject at the end of the session, on the structural importance for the conformation of the group defined in the public radar in
the first 15’ of interaction and on the activity on the production of messages with negative mood in the private space at the end of the session
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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.