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Group Decision-Making for Collaborative Educational Games.
Conference Paper · January 1998
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Proceedings of
CRIWG'98
•
Fourth International Workshop on Groupware
Quarto Seminario Internacional sobre Sistemas Cooperativos
Cuarto Taller Internacional en Sistemas Cooperativos
September 9-11, 1998
Arma~ao de Buzios, Rio de Janeiro, Brasil
GROUP DECISION-MAKING FOR
COLLABORATIVE EDUCATIONAL GAMES
Giannina Nunez
[email protected]
Ulises Aguero
[email protected]
Cesar Olivares
[email protected]
Centro de Investigaciones en Computacion
Instituto Tecnologico de Costa Rica
Abstract
Human beings live in a dynamic world. We confront numerous
situations that demand decisions at the personal level.
However, in a globalized world, the performance of groups has
more impact than that of the individuals. The presence of
plausibility-driven
group
decision-making
tools
in
collaborative educational games results in the following
advantages: increased game dynamics, better group awareness,
respect for different opinions and improved critical thinking.
In this context, the purpose of this paper is to report on the
main partial results of an ongoing project that intends to
develop collaborative educational games as tools to improve
the quality of the learning process in the presence of
globalization issues. The focus is on the use of consensusbuilding techniques in a game's group decision-making
activities.
1 INTRODUCTION
Human beings live in a dynamic world. We confront numerous situations that demand
decisions at the personal level. However, in a globalized world, the performance of groups
has more impact than that of the individuals. As a consequence, effective group decision
making techniques that take full advantage of technological advances must be systematically
infused into society (see [DeKr60] [Jani72], [John81], [Mart89], [Mart92], and [Mert80] for
discussions about the role of individuals and groups in society).
In the presence of such clear need for building group awareness, modem education must
certainly lead the way to reach that objective. The effort ought to start with children and
develop towards higher levels of education, so to produce a solid foundation from where to
grow. The power of networks in general, and the Internet in particular, must be fully
exploited to create effective educational tools for group decision-making. In addition, many
long standing educational techniques to develop group dynamics need to be reworked to take
into account the new collaboration technologies (see [CaZa71] and [CiVi66]).
In this context, the purpose of this paper is to report on the main partial results of an ongoing
project that intends to develop collaborative educational games as tools to improve the
143
J
i
J
quality of the learning process in the presence of globalization issues. The focus will be on
the use of consensus-building techniques in a game's group decision making activities. More
specifically, the paper bas the following objectives:
I
1. Show the importance of collaborative educational games for modern globalized
education.
2. Analyze the role of group decision-making in collaborative educational games.
J
3. Discuss consensus-building approaches to group decision making, including a significant
voting scheme that improves the effectiveness of the games.
j
To complete the objectives, the paper covers the following topics:
j
Team Work and Education. In this respect, it is interesting to note the strong relationship
between group dynamics techniques and modern education. From this perspective, education
uses the psychological and sociological strengths of group dynamics to form self-sufficient
individuals that are capable of surviving in society and, at the same time, be integral part of
groups [CiVi66].
Collaborative Educational Games. These games represent valuable tools for group-aware
education. This because collaborative educational games (a) are entertaining and based on
experience-driven heuristic learning, (b) encourage collaboration and (c) serve as laboratories
for experimenting with conflict resolution approaches.
The Theory of Plausibility. In the games, conflict resolution is rooted on consensus-building
arguments, so that decisions represent the group better. This approach uses the reasoning
principles of the theory of plausibility and a flexible voting scheme.
Application. Finally, the paper describes the general nature of the design of a collaborative
educational game to support the area of equivalent fractions.
2 GROUP WORK AND EDUCATION
It is quite common to find comparisons between the so-called traditional and modern
approaches to education [CiVi66]. Modem education considers individuals as intelligent
organisms that perform in a social environment. For these individuals, learning is active
problem-solving and not just memorization. Experience leaves in an individual a guide for
action in future situations; therefore, a person needs to discover how to learn, how to
experiment, how to act in groups and how to make decisions. In our societies, evidence
evolves and so must decisions. As a result, children must learn principles, not details, so that
they can adapt to evolving circumstances and decisions.
Correspondingly, a group exhibits the following characteristics in group dynamics
[CaZa71][CiVi66]:
1. A distinguishable association between two or more individuals.
2. Group conscience: the members consider themselves a whole group; there is a collective
perception of unit, a conscientious mutual identification.
3. A sense of participation with common goals and ideals.
4. Reciprocal dependency on the satisfaction of needs; the group members need to help each
other achieve the common goals that motivated the team formation.
144
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5. The members have means to communicate among them.
6. Ability to act as whole.
7. The group has an internal structure, where roles are well-established.
In this context, the following are eight basic principles that can guide the dynamics of team
work [CiVi66]:
1. Environment: The environment must contribute to improve participation, spontaneity
and cooperation among all group members.
2. Reduction of intimidation: The reduction of personal confrontation and intimidation
among group members improves productivity.
3. Distributed leadership: All members must have the opportunity to fully develop their
potential and initiatives to improve team capabilities.
4. Goal definition: All members should participate in the team goals definition to increase
collective conscience.
5. Flexibility: The group must allow goal reformulation to adapt to changing circumstances.
6. Consensus: The group must establish a free and spontaneous communication in order to
reach decisions by means of mutual agreements among all group members.
7. Process understanding: Group members must fully understand the rules for interaction
and collaboration in order to increase the possibilities of reaching the common goals.
8. Continuous evaluation: The group needs frequent feedback about its progress in reaching
the team goals.
Many of these principles may be satisfied in the design of educational games based on
collaborative consensus-building decision-making schemes. To achieve this educational
goal, the use of computers and networks becomes a great asset when combined with the wellestablished discipline of group dynamics. In this respect, Computer Supported Collaborative
Leaming (CSCL) is the term commonly used to refer to the integration of computers,
networks and collaborative learning [SIGCU92], that is, the integration of Computer
Supported Cooperative Work (CSCW) and group dynamics in education.
3 COLLABORATIVE EDUCATIONAL GAMES
For the purposes of this paper, a collaborative educational game has the following
characteristics: 1
1. It is based on rules and takes place in an entertaining environment-therefore, it is a
game.
2. Seeks the construction of knowledge-therefore, it is educational.
3. It is restricted to the realm of computer networks and includes software components for
players to participate and collaborate even when they are physically distant from each
other-therefore, it is collaborative.
Collaborative games do not intend to replace conventional activities; on the contrary they should be
part of a series of integrated means to learn.
1
145
4. The different proposed solutions are discussed with the help of consensus-building tools,
including threaded discussions, decision graphs and voting. All these are based on the
Theory of Plausibility (see below).
Figure I shows a sketch of the collaboration interface of a game on equivalent fractions.
PLAY ..\ND VERSION CONTROL
VOTING
PLAYERS
TOOLS
CON~'EN~'US-BUILDING DrnC-'USSIONS
Figure 1 : Work areas for a collaborative game.
The sketch shows several areas. Some of these areas are visible to all players and others are
local to a player. The following is the general functionality of each area:
Play area: the main activity takes place here. In particular, in this area is where the players
register their answers and manipulate objects. It also includes a version-control area.
Players: it is a global area where the participants are identified and information about them
can be requested.
Tools: it is a set of collaboration and object-manipulation tools available to the players.
Voting: it is where the players cast their votes, using white and blue balls to express
agreement and disagreement, respectively (see the section on voting below). The voting
process results are accounted for here, establishing a plausibility state for a given issue or
proposed solution.
Discussion: here is where consensus-building discussions take place. These discussions may
be private or public, using group decision-making support tools designed with plausibility
criteria-i.e., decision graphs, discussion forums and voting facilities.
l
J
l
4 PLAUSIBILITY-DRIVEN DECISION-MAKING
The Theory of Plausibility was first introduced as a basis for explaining the way computer
architecture designers make decisions when determining the features of a machine[Ague87].
However, it has been used in the general area of group decision making, even at the
commercial level.2
The theory of plausibility for group decision-making is based on two fundamental objects of
study: plausible issues and plausibility statements.
A decision is organized in terms of issues. During a step of a decision-making process, an
issue may be in any of the plausibility states acceptable, satisfactory, doubtful,
unsatisfactory, or undetermined, depending upon the evidence at hand.
2 For example, Virtua!Meetings™ is a commercial Costa Rican product based on the theory of
plausibility, developed by CREADISA in 1993, to support group decision-making.
146
J
I
A plausibility statement is the structure used to make claims about the plausibility of a
decision.
Issues that qualify to be in the
ace table lausib · state.
to be
in the sat.isfacto,,,
pla11S1bili%y state.
Issues that qualify t-0 be in the
wuleurmined pla11S1bili%y state
Issues that qualify to be in the
doubt
state
Issues
to be
in the uns,tiefacto,,,
plausibihty state.
Figure 2: Regions of the plausibility space.
During a design process, the plausibility of an issue may change from one decision step to
another. As a consequence, an issue C may be in one of five plausibility states:
1. Acceptable: there is no evidence against C's plausibility.
2. Satisfactory: there is significant evidence in favor of and no evidence against C's
plausibility.
3. Doubtful: there is evidence against C 's plausibility.
4. Unsatisfactory: there is significant evidence against C's plausibility.
5. Undetermined: it is unknown whether or not there is evidence against C's plausibility.
This is the initial state of every new issue.
The evidence in the above definitions may be any combination of the following three kinds:
•
Precise and formal, based on two-valued deduction theories.
•
Approximate (and formal), based on heuristic methods founded on less precise logic
than two-valued logic.
•
Experimental, based on experimental methods such as simulation and emulation.
Plausibility statements are intended to model claims about a decision in order to enhance a
decision maker's confidence in it.
,
I
r
A plausibility statement may establish the plausibility (state) of an issue as being acceptable,
satisfactory, doubtful or unsatisfactory.
Plausibility statements are fundamental entities in the theory of plausibility. They are used to
establish an issue's plausibility state for purposes such as: evaluating an existing decision;
driving the development of new decisions; determining the advantages and disadvantages of
one decision with respect to another; and supporting the plausibility of decisions. In any
case, the use of conventional features such as anonymity and retraction enhances de decision
process.
147
Based on the five states of the plausibility of an issue, some verifiable laws ofp lausibility
can be specified (see Figure 2):
1. If issue C qualifies to be in the satisfactory plausibility state, then C qualifies to be in the
acceptable plausibility state.
2. If C qualifies to be in the acceptable plausibility state then C does not qualify to be in the
doubtful plausibility state.
3. If C does not qualify to be in the doubtful plausibility state and C does not qualify to be
in the undetermined plausibility state, then C qualifies to be the acceptable state.
4. If C does not qualify to be in the doubtful plausibility state, then C does not necessarily
qualify to be in the satisfactory state.
5. If C does not qualify to be in the satisfactory plausibility state, then C does not
necessarily qualify to be in the doubtful state.
6. If C qualifies to be in the acceptable plausibility state, then C does not necessarily
qualify to be in the satisfactory plausibility state.
7. If C qualifies to be in the undetermined plausibility state, then C does not qualify to be
in any other state.
A plausibility-driven voting model generates, for the decision maker, more flexible voting
options. As a consequence, the decision maker may explain his or her position better. In
fact, he may express consent and disagreement at the same time for a given issue.
5 A PLAUSIBILITY-DRIVEN VOTING SCHEME [0LIV96]
In a group decision-making situation, there are decision makers and issues. As explained
before, the plausibility state of an issue can be defined in terms of the evidence in favor of
and against the issue, as established by the group. In a voting scheme, it is possible to gather
that evidence by creating a variation of the Group Valance Model [HoK194).
In a voting activity, issues frequently take the form of alternatives. The group evaluation is
based on the evaluation of each individual and on the influence or weight that the individual
has on the overall decision.
When considering an issue, a decision maker should pay attention to both positive and
negative evidence. The evidence in favor of or against an issue is represented in terms of a
degree of approval and a degree of disapproval. The plausibility (or acceptability) of an
issue is calculated by combining the evidence expressed by each individual.
Voting Principles
The voting scheme is based on five basic principles that represent high-level specifications or
restrictions:
•
1. Each decision maker may express both approval and disapproval, even at the same time.
2. Approval and disapproval may be expressed in different degrees.
3. Decision makers may have different influence levels on the decision.
j
148
4. The degree of approval of the group is calculated by combining the degrees of approval
of all members, adjusted with respect to their influence levels. Corresponding
considerations apply to the degree of disapproval.
5. Issues are placed in plausibility states according to their assigned degrees of approval and
disapproval.
Voting Norms
Derived from the principles, the voting scheme includes more specific norms to structure the
plausibility-driven voting process, as follows:
1. Each decision maker is assigned a number of white balls and blue balls.
2. The number of white and blue balls assigned to a decision maker represents the influence
level of the decision maker--i.e., his power within the group.
3. The degree of approval of a given issue o by a decision maker dis the number of white
balls d assigns too. The degree of disapproval of a given issue o by a decision maker dis
the number of blue balls d assigns too.
4. The degree of group approval of o is the algebraic sum of the individual degrees of
approval, and the degree ofgroup disapproval of o is the algebraic sum of the individual
degrees of disapproval.
5. The voting scheme includes the definition of an approval mark (mJ, a minimum approval
mark (uJ, a disapproval mark (m,.) and a minimum disapproval mark (11i,). Ola must be
between 1 and the total number of white balls assigned to the decision makers. Ua must
be between 1 and m •. m,. must be between 1 and the total number of blue balls assigned to
the decision makers. 11i, must be between 1 and m,._
6. An issue that as been exposed to a voting process qualifies for a plausibility state
according to the following definitions (see Figure 2):
•
Satisfactory: degree of approval greater than or equal to the approval mark and
degree of disapproval less than the minimum disapproval mark.
•
Acceptable: degree of approval greater than or equal to the minimum approval mark
and degree of disapproval less than the minimum disapproval mark.
•
Doubtful: degree of disapproval greater than or equal to the minimum disapproval
mark.
•
Unsatisfactory: degree of disapproval greater than the disapproval mark.
•
Undetermined: degree of approval less than the minimum approval mark and degree
of disapproval less than the minimum disapproval mark.
Voting Policies
A policy is a set of restrictions to administer the voting process. The following are the main
types of policies:
1. The distribution of influence in the group.
149
2. The possibility of decision makers of establishing different degrees of approval (and
disapproval) for competing alternatives.
3. The possibility of decision makers providing both positive and negative evidence for a
given issue.
4. The consensus required for the approval or disapproval of an issue.
Influence distribution policies
Balanced: All decision makers have the same influence--expressed in the number of balls
received.
Unbalanced: The distribution of balls is not the same for all decision makers.
Expressivity policies
Expressivity refers to the possibility for decision makers to vote with different degrees of
approval and disapproval for competing alternatives. The following are two examples:
1. A single approval policy limits decision makers to express approval for no more than one
alternative.
2. A linear approval policy limits the decision makers to assign the same number of
approval (white) balls to all the alternatives with a non-zero degree of approval.
Evaluation policies
The following are examples of evaluation policies:
1. Unidimensional: a decision maker may express either approval or disapproval for a given
alternative, but not both..
2. Multidimensional: a decision maker may express both approval and disapproval for a
given alternative.
Consensus policies.
Consensus refers to the degrees of approval and disapproval required and tolerated when
selecting one of the competing alternatives. ln general, consensus policies are expressed in
terms of the values assigned to the approval and disapproval marks and minimum marks.
The following are some examples:
I. Fixed: the approval mark and its minimum are chosen based on the total number of white
balls distributed among the decision makers.
2. Relative: the approval mark and its minimum are chosen based on the total number of
white balls deposited by the decision makers.
3. Medium consensus: the approval mark is at least half the number of accountable white
balls--i.e., distributed or deposited. Similarly, the minimum approval mark is at least one
third the accountable white balls.
4. Low consensus: the approval mark is at least two thirds the number of accountable white
balls; the minimum approval mark is at least one.
150
6 EDUCATIONAL GAMES AND GROUP DECISION-MAKING
The types of multiplayer educational games that we are researching emphasize problems that
allow for different correct solutions because they are better suited to discussions. We are not
concerned so much about the strategies players use to find solutions, but on the evaluation of
the proposed solutions by the group of players themselves. As part of the games, we want
players to criticize and search for consensus on the plausibility of the solutions.
Players will have at least three different group decision-making tools available in their search
for consensus: a decision graph tool, discussion forums and voting faci lities.
r
Decision graph tool. This is a visual tool for the construction of decision graphs-and trees
in particular. The solutions proposed by the different players or teams of players become,
automatically, part of a predefined decision tree. The solutions represent leaves of the tree
and have plausibility-driven evaluation forums (i.e., specialized threaded discussions)
associated with them (see Figure 3).
Fractions
I
No Name
[] P-OR
r
Groupl
[]P-OR
I
Solutionl
Solution2 Solutionl
Solution2
□
Cl
(!]
CD
I====
Solution3
Ci1
I====
Figure 3: A decision graph for the fractions game
In the graph's nodes, specific icons represent plausibility states of the solutions; through laws
of plausibility-that define the behavior of AND and OR-the plausibility states are
automatically propagated from the leaves to higher levels. The states of the terminal nodes
are determined through either evaluation forums or voting processes.
Any team may create their own decision graphs to help synthesize their proposed solutions.
The construction may be done collaboratively in real-time.
Plausibility-driven threaded discussion forums. These are general-purpose forums where
annotations to main entries can be labeled as annotations against or in favor of the entry.
Evaluation forums-mentioned above-are specializations of these forums. Through an
automatic analysis of the annotations, the plausibility logic engine is able to provide feedback
to the players about the plausibility state of the forum entries (see Figure 4).
151
:§)
0
ULISES Mon Jul 27 16:28:31 1998
General Entry
ffl ESTRE Mon Jul 27 16:34:01 1998
General annotation
PJ IBARRANT Mon Jul 27 16:38:42 1998
Annotation In Favor Of
&J
LCAMPOS Mon Jul 27 16:40:13 1998
Annotation Against
Figure 4: An annotated entry in a forum.
Voting facilities. In the collaborative games, plausibility-driven voting is associated with
solutions that, in tum, correspond to nodes in the automatically generated decision tree.
Players will typically decide to vote on a proposed solution when they are not able to reach
consensus in the evaluation forums. Players may also decide to vote on any general entry of
a discussion forum. In order to vote, white and blue balls are assigned to each player based
on predetermined game parameters.
7 AN APPLICATION
The example is a game to experiment and play with the concept of equivalent fractions. It has
been inspired on the work of [DeVa96][DuLe96][CaLe96][Quin89].
The game's general objective is to form a specified fraction inside a number of different
pictures, using the parts provided. Only proper fractions are considered--i.e., those with the
numerator less than the denominator.
Educational Objectives
The following are specific educational objectives of this game:
•
Identify equivalent fractions.
•
Derive the concept of equivalent fractions.
•
Experiment with fractions in general.
•
Develop group conscience through plausibility-able tools.
•
Experience the effectiveness of collaborative educational material through computers.
•
Complement the conventional classroom activities related to a difficult topic such as
fractions.
Game Guidelines
The following are the basic game guidelines:
1. Each participant must place one of the pieces provided on each of the pictures.
2. The game is played in rounds. During his or her turn, a player has exclusive access to the
game area (see Figure 1).
152
3. The parts that form a fraction inside a picture do not have to be positioned side-by-side
(see Figures 5 and 6)
4. All parts used to form a fraction must be of equal size.
5. The fraction that must be formed on each picture has a numerator greater than or equal to
one (see Figures 5 and 6).
6. The fraction that must be formed is selected by the software automatically.
7. Each completed round generates one new version (see Figure 1). The software keeps
track of all versions so that players may start discussions and voting processes on any
vers10n.
8. Players discuss about the plausibility of the proposed solutions, registering evidence in
favor of and against the solutions in the corresponding decision graph. The evidence is
expressed in natural language and labeled by the player as evidence in favor of or against
a proposed solution. According to the evidence provided and the definitions of the
various plausibility states, the software gives feedback about the plausibility of the
solutions.
9. Players may start voting processes to solve conflicts that the general discussions did not
clear. The voting results are calculated automatically by the software, providing the
corresponding feedback to the players about the plausibility of the solutions.
I 0. Once the players have ended the discussions and the voting processes, they may request
the software to check the proposed solutions automatically.
Figure 5: Forming one half.
~E-.1
□
■
[] ■
■ CB
Figure 6: Forming three quarters.
8 IMPLKMENTATION ISSUES
The types of games that have been characterized in this paper are better suited for real-time
collaboration because of their inherent dynamics. Players must be able to manipulate and
153
visualize objects concurrently with the best possible response time. We are already
developing a set of programming tools for the management of real-time collaboration. The
tools are based on the UDP/IP protocol in order to overcome some of the overhead associated
with TCP/IP.
With respect to plausibility issues, the logic manipulations necessary to provide useful
feedback should be transparent to the players. Here, interface and human-machine
interaction design decisions will be of primary importance. These facilities are being
implemented as a set of programming tools.
The implementation of our first prototype will be based primarily on the T .120 standard for
real-time collaboration, complemented with the above-mentioned programming tools. The
prototype will be able to run on any UDP/IP network, including Internet.
9 CONCLUSIONS
The presence of plausibility-driven group decision-making tools in collaborative educational
games results in the following advantages:
Increased Game Dynamics. Games becoIIJ.e more interesting and challenging for the players
because the areas of activity are not limited to the game itself.
Better Group Awareness. Plausibility arguments, game rules and frequent player interaction
drive players to improve their awareness about the important role that each individual plays
in the outcome of the group's performance as a whole.
Respect for Different Opinions. The presence of decision-making activities as integral parts
of the game promotes each player's recognition that their own opinions are not always
common sense for the rest of the group members.
Improved Critical Thinking. Plausibility-driven discussions and voting require that the
players assume clear positions about their degree of agreement and disagreement on different
issues. This implies an increased quality of the thinking process.
The collaborative educational games project is now at the application design and
development stage in order to produce a working prototype.
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