WP2
Main.WP2 History
Hide minor edits - Show changes to output
Changed lines 87-126 from:
to:
of judgment aggregation problems using three values, thus providing a more suitable framework.
'''References'''
[Arrow51] K. Arrow. Social Choice and Individual Values. Wiley, NY, 1951/1963.
[BF04] S. Brams and P. Fishburn. Voting procedures. In K. Arrow, A. Sen, and K. Suzumura (eds.), Handbook of Social Choice and Welfare, chapter 4. Elsevier, 2004.
[Caminada06] M.W.A. Caminada. On the issue of reinstatement in argumentation. In 10th European Conference, JELIA 2006, LNAI 4160, pp.111-123, 2006.
[CDKLM07] S. Coste-Marquis, C. Devred, S. Konieczny, M.-C. Lagasquie-Schiex, and P. Marquis. On the merging of Dung’s argumentation systems. Artificial Intelligence, 171: 730–753, 2007.
[CELM07] Y. Chevaleyre, U. Endriss, J. Lang, and N. Maudet. A short introduction to computational social choice. Proc. SOFSEM-2007, Springer-Verlag, 2007.
[CG09] M.W.A. Caminada and D.M. Gabbay. A logical account of formal argumentation. Studia Logica, 93(2-3): 109-145, 2009.
[CP11] M.W.A. Caminada and G. Pigozzi. On judgment aggregation in abstract argumentation. JAAMAS, 22: 64-102, 2011.
[CPP11] M. Caminada, G. Pigozzi, and M. Podlaszewski. Manipulation in group argument evaluation. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 121-126, 2011.
[DH10] E. Dokow and R. Holzman. Aggregation of binary evaluations with abstentions. Journal of Economic Theory, 145(2): 544-561, 2010.
[DMW12] P.E. Dunne, P. Marquis, M. Wooldridge. Argument Aggregation: Basic Axioms and Complexity Results Proceedings of the 4th International Conference on Computational Models of Argument (COMMA'12), Vienna, p. 129-140, 2012.
[Gibbard73] A. Gibbard. Manipulation of voting schemes. Econometrica, 41:587-602, 1973.
[KG06] S. Konieczny and E. Grégoire. Logic-based approaches to information fusion. Information Fusion, 7: 4–18, 2006.
[KP02] S. Konieczny and R. Pino Pérez. Merging information under constraints: a qualitative framework. Journal of Logic and Computation, 12(5): 773-808, 2002.
[LP09] C. List and C. Puppe. Judgment aggregation: A survey. In Oxford Handbook of Rational and Social Choice. Oxford University Press (New York), 2009.
[LP10] C. List and B. Polak. Introduction to judgment aggregation. Journal of Economic Theory, 145(2): 441-466, 2010.
[RL08] I. Rahwan and K. Larson. Welfare properties of argumentation-based semantics. In Proc. of AAAI 2008, pp. 150-155, 2008.
[RT10] I. Rahwan and F. Tohmé. Collective argument evaluation as judgment aggregation. In Proc. of AAMAS 2010, pp. 417–424, 2010.
[Satterthwaite75] M. Satterthwaite. Strategyproofness and Arrow’s conditions. Journal of Economic Theory, 10: 187-217, 1975.
[TBS08] F.A. Tohmé, G. A. Bodanza, and G. R. Simari. Aggregation of attack relations: A social-choice theoretical analysis of defeasibility criteria. In Proc. of FoIKS, 8-23, 2008.
'''References'''
[Arrow51] K. Arrow. Social Choice and Individual Values. Wiley, NY, 1951/1963.
[BF04] S. Brams and P. Fishburn. Voting procedures. In K. Arrow, A. Sen, and K. Suzumura (eds.), Handbook of Social Choice and Welfare, chapter 4. Elsevier, 2004.
[Caminada06] M.W.A. Caminada. On the issue of reinstatement in argumentation. In 10th European Conference, JELIA 2006, LNAI 4160, pp.111-123, 2006.
[CDKLM07] S. Coste-Marquis, C. Devred, S. Konieczny, M.-C. Lagasquie-Schiex, and P. Marquis. On the merging of Dung’s argumentation systems. Artificial Intelligence, 171: 730–753, 2007.
[CELM07] Y. Chevaleyre, U. Endriss, J. Lang, and N. Maudet. A short introduction to computational social choice. Proc. SOFSEM-2007, Springer-Verlag, 2007.
[CG09] M.W.A. Caminada and D.M. Gabbay. A logical account of formal argumentation. Studia Logica, 93(2-3): 109-145, 2009.
[CP11] M.W.A. Caminada and G. Pigozzi. On judgment aggregation in abstract argumentation. JAAMAS, 22: 64-102, 2011.
[CPP11] M. Caminada, G. Pigozzi, and M. Podlaszewski. Manipulation in group argument evaluation. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 121-126, 2011.
[DH10] E. Dokow and R. Holzman. Aggregation of binary evaluations with abstentions. Journal of Economic Theory, 145(2): 544-561, 2010.
[DMW12] P.E. Dunne, P. Marquis, M. Wooldridge. Argument Aggregation: Basic Axioms and Complexity Results Proceedings of the 4th International Conference on Computational Models of Argument (COMMA'12), Vienna, p. 129-140, 2012.
[Gibbard73] A. Gibbard. Manipulation of voting schemes. Econometrica, 41:587-602, 1973.
[KG06] S. Konieczny and E. Grégoire. Logic-based approaches to information fusion. Information Fusion, 7: 4–18, 2006.
[KP02] S. Konieczny and R. Pino Pérez. Merging information under constraints: a qualitative framework. Journal of Logic and Computation, 12(5): 773-808, 2002.
[LP09] C. List and C. Puppe. Judgment aggregation: A survey. In Oxford Handbook of Rational and Social Choice. Oxford University Press (New York), 2009.
[LP10] C. List and B. Polak. Introduction to judgment aggregation. Journal of Economic Theory, 145(2): 441-466, 2010.
[RL08] I. Rahwan and K. Larson. Welfare properties of argumentation-based semantics. In Proc. of AAAI 2008, pp. 150-155, 2008.
[RT10] I. Rahwan and F. Tohmé. Collective argument evaluation as judgment aggregation. In Proc. of AAMAS 2010, pp. 417–424, 2010.
[Satterthwaite75] M. Satterthwaite. Strategyproofness and Arrow’s conditions. Journal of Economic Theory, 10: 187-217, 1975.
[TBS08] F.A. Tohmé, G. A. Bodanza, and G. R. Simari. Aggregation of attack relations: A social-choice theoretical analysis of defeasibility criteria. In Proc. of FoIKS, 8-23, 2008.
Changed line 34 from:
-> ! Subtask 2.1. Axiomatic characterization of arguments aggregation procedures
to:
-> '''Subtask 2.1. Axiomatic characterization of arguments aggregation procedures'''
Changed line 50 from:
to:
-> '''Subtask 2.2. Definition of specific aggregation procedures'''
Changed line 61 from:
to:
-> '''Subtask 2.3. Properties of aggregation procedures'''
Changed line 75 from:
to:
-> '''Subtask 2.4. Aggregating arguments vs. aggregating judgments'''
Changed line 12 from:
to:
'''Background.''' The problem of how to aggregate individual argumentation systems into a collective one is a
Changed line 30 from:
to:
'''Challenges/Subtasks.''' As we have seen in the background section, the study of the aggregation of individual
Changed line 34 from:
! Subtask 2.1. Axiomatic characterization of arguments aggregation procedures
to:
-> ! Subtask 2.1. Axiomatic characterization of arguments aggregation procedures
Changed lines 1-7 from:
10 min: Présentation des membres (chacun dit deux mots sur ce sur quoi il travaille/souhaite travailler pour le WP2)
2 exposés (25 minutes chacun + 5 min questions): Patricia Everaere (état de l'art sur les prop. "classiques" attendues de l'agreg de jugement, et de la fusion)
Srdjan Vesic (travail sur la séparabilité dans l’agrégation de jugements)
30 min: Discussion
to:
'''Aim.''' The aim of this WP is to study how to aggregate different argumentation systems. Before designing
deliberation protocols aiming at exchanging arguments between agents, we need to be able to say if the result
of a deliberation is satisfying from a social point of view. In order to achieve this, we will rely on tools from
social choice theory and from logical aggregation. The main research question of this WP is to study how to
define an aggregation system that best represents a set of argument systems coming from different agents.
The problem is challenging because agents may have different sets of arguments to start with, or different
opinions as to what constitutes a contradiction between some of these arguments. Furthermore,
argumentation is a reasoning model which typically allows conflicting “viewpoints” even if the agents agree
on the underlying “background” theory: this means that aggregation of viewpoints may be necessary at
different stages.
""Background."" The problem of how to aggregate individual argumentation systems into a collective one is a
novel research question. There is some initial work, particularly from the members of this project
[CDKLM07, CP11, CPP11]. Specifically, Coste-Marquis et al. [CDKLM07] have put forward the first
proposal addressing the merging of argumentation systems, where the individual argumentation frameworks
may be different. Conflicts between argumentation frameworks are solved using merging techniques [KP02].
On the other hand, the case of the aggregation of different viewpoints on a given argumentation framework
has been investigated by Caminada and Pigozzi [CP11]. Three aggregation procedures suitable for small
groups where agents wish to reach a collective position that is compatible with their individual views were
proposed. Welfare properties and strategic issues of these operators have also been studied [CPP11]. The
natural framework for studying the aggregation of individual argumentation systems is social choice. The
study of the aggregation of individual preferences, and the properties that aggregation rules may satisfy can
be used as a theoretical reference to the aggregation of individual attack relations [TBS08]. When preference
relations over individual positions are considered, welfare properties of collective argument evaluation (like
Pareto optimality) can also be explored, as done in [RL08]. There is also a line of work building on the
similarity between judgment aggregation and argumentation aggregation [RT10]. Recently, Marquis and
colleagues have investigated argument aggregation under an axiomatic perspective, and studied preliminary
complexity results [DMW12].
""Challenges/Subtasks."" As we have seen in the background section, the study of the aggregation of individual
argumentation frameworks into a collective one is promising but still in its infancy. Several steps need to be
undertaken in order to provide the field with a solid ground.
! Subtask 2.1. Axiomatic characterization of arguments aggregation procedures
The first issue to tackle is to define a set of desirable properties that one may wish an arguments aggregation
procedure to satisfy, e.g. anonymity (i.e. all individuals count the same), unanimity (i.e. if all agents agree on
the evaluation of one argument, the group position on that argument should reflect the unanimous view), and
collective rationality (i.e. the collective outcome must be a permissible evaluation of the argumentation
system). These are some standard properties employed in aggregation theories like social choice [Arrow51],
belief merging [KP02, KG06] and judgment aggregation [LP09, LP10]. However, existing axioms may not
simply be imported in the new framework. Unanimity, for example, is not a trivial axiom in arguments
aggregation: arguments are connected by attack relations, and the evaluation of one argument affects the
evaluation of arguments attacked by it. And it may happen that, even though there is a unanimous opinion
on the status of one argument, such view cannot be preserved at the group level [CP11]. Thus, the
aggregation of argumentation systems may call for specific axioms that are not common to other disciplines.
Once a set of axioms suitable for the aggregation of argumentation systems is put forward, the next quest is
for possibility and impossibility results to cast a light on which axioms are mutually consistent and which are
not.
! Subtask 2.2. Definition of specific aggregation procedures
Given a profile of individual argumentation systems, there exist several ways to aggregate them into a group
argumentation system [BF04]. The choice among different procedures depends - among other things - on the
axioms that we want to be satisfied, on the particular properties we wish for the aggregation procedure, but
also on the decision context. For example, anonymity is an intuitive desirable axiom, but when the agents
participating to the decision have different competences, one may require a rule that takes this information
into account. As far as it concerns the decision contexts, some require a majoritarian approach whereas
others call for an egalitarian approach, when aiming at equally distributing the individual satisfaction seems
to be more appropriate. One of the challenges of this WP will then be to propose a whole range of
aggregation procedures.
! Subtask 2.3. Properties of aggregation procedures
In addition to the definition of several aggregation rules, we need to study what are the properties that we
expect from these procedures. The aim here is to define what kind of properties one could expect from the
aggregation of several argumentation systems. This is necessary to be able to distinguish between interesting
aggregation procedures and the ones with bad behaviours, but also to classify them according to the specific
decision contexts and to their respective behaviours. Examples are social welfare properties like Pareto
optimality, and properties of the aggregation procedure, like its sensibility to manipulation. When a rule is
manipulable, an agent (upon knowing the other participants’ votes) may cast an insincere input in order to
obtain a social outcome that is better for him compared to the one he had obtained, had he voted sincerely.
Clearly, a strategy-proof procedure is desirable, but unfortunately very unlikely [Gibbard73,
Satterthwaite75]. But as the recent findings of computational social choice show [CELM07], even if an
aggregation procedure is manipulable, its complexity may be so high that manipulation is practically
difficult.
! Subtask 2.4. Aggregating arguments vs. aggregating judgments
Another key issue is to clarify the relation between argumentation aggregation, voting procedures and
judgment aggregation on the one hand, and belief merging on the other hand. The question of whether it is
possible to embed the aggregation of argumentation systems into the judgment aggregation framework
[LP10] seems particularly urgent, as already pointed out by [RT10, CP11]. The analogy (at least when the
agents share the same argumentation system) is striking. Once this relation is clarified, results obtained in
judgment aggregation may eventually be reformulated for the argumentation aggregation case (e.g. results
that relate to the agendas and to the conditions that the aggregation rules need to satisfy in order to guarantee
consistent group positions). But there are also differences between argumentation aggregation and judgment
aggregation, most notably the fact that the underlying logic of judgment aggregation is usually a classical
two-value propositional logic. For argument labelling [Caminada06, CG09], three values can be taken (in,
out, undec). Recently, [DH10] have studied aggregation of non-binary evaluations, allowing for an extension
of judgment aggregation problems using three values, thus providing a more suitable framework.
deliberation protocols aiming at exchanging arguments between agents, we need to be able to say if the result
of a deliberation is satisfying from a social point of view. In order to achieve this, we will rely on tools from
social choice theory and from logical aggregation. The main research question of this WP is to study how to
define an aggregation system that best represents a set of argument systems coming from different agents.
The problem is challenging because agents may have different sets of arguments to start with, or different
opinions as to what constitutes a contradiction between some of these arguments. Furthermore,
argumentation is a reasoning model which typically allows conflicting “viewpoints” even if the agents agree
on the underlying “background” theory: this means that aggregation of viewpoints may be necessary at
different stages.
""Background."" The problem of how to aggregate individual argumentation systems into a collective one is a
novel research question. There is some initial work, particularly from the members of this project
[CDKLM07, CP11, CPP11]. Specifically, Coste-Marquis et al. [CDKLM07] have put forward the first
proposal addressing the merging of argumentation systems, where the individual argumentation frameworks
may be different. Conflicts between argumentation frameworks are solved using merging techniques [KP02].
On the other hand, the case of the aggregation of different viewpoints on a given argumentation framework
has been investigated by Caminada and Pigozzi [CP11]. Three aggregation procedures suitable for small
groups where agents wish to reach a collective position that is compatible with their individual views were
proposed. Welfare properties and strategic issues of these operators have also been studied [CPP11]. The
natural framework for studying the aggregation of individual argumentation systems is social choice. The
study of the aggregation of individual preferences, and the properties that aggregation rules may satisfy can
be used as a theoretical reference to the aggregation of individual attack relations [TBS08]. When preference
relations over individual positions are considered, welfare properties of collective argument evaluation (like
Pareto optimality) can also be explored, as done in [RL08]. There is also a line of work building on the
similarity between judgment aggregation and argumentation aggregation [RT10]. Recently, Marquis and
colleagues have investigated argument aggregation under an axiomatic perspective, and studied preliminary
complexity results [DMW12].
""Challenges/Subtasks."" As we have seen in the background section, the study of the aggregation of individual
argumentation frameworks into a collective one is promising but still in its infancy. Several steps need to be
undertaken in order to provide the field with a solid ground.
! Subtask 2.1. Axiomatic characterization of arguments aggregation procedures
The first issue to tackle is to define a set of desirable properties that one may wish an arguments aggregation
procedure to satisfy, e.g. anonymity (i.e. all individuals count the same), unanimity (i.e. if all agents agree on
the evaluation of one argument, the group position on that argument should reflect the unanimous view), and
collective rationality (i.e. the collective outcome must be a permissible evaluation of the argumentation
system). These are some standard properties employed in aggregation theories like social choice [Arrow51],
belief merging [KP02, KG06] and judgment aggregation [LP09, LP10]. However, existing axioms may not
simply be imported in the new framework. Unanimity, for example, is not a trivial axiom in arguments
aggregation: arguments are connected by attack relations, and the evaluation of one argument affects the
evaluation of arguments attacked by it. And it may happen that, even though there is a unanimous opinion
on the status of one argument, such view cannot be preserved at the group level [CP11]. Thus, the
aggregation of argumentation systems may call for specific axioms that are not common to other disciplines.
Once a set of axioms suitable for the aggregation of argumentation systems is put forward, the next quest is
for possibility and impossibility results to cast a light on which axioms are mutually consistent and which are
not.
! Subtask 2.2. Definition of specific aggregation procedures
Given a profile of individual argumentation systems, there exist several ways to aggregate them into a group
argumentation system [BF04]. The choice among different procedures depends - among other things - on the
axioms that we want to be satisfied, on the particular properties we wish for the aggregation procedure, but
also on the decision context. For example, anonymity is an intuitive desirable axiom, but when the agents
participating to the decision have different competences, one may require a rule that takes this information
into account. As far as it concerns the decision contexts, some require a majoritarian approach whereas
others call for an egalitarian approach, when aiming at equally distributing the individual satisfaction seems
to be more appropriate. One of the challenges of this WP will then be to propose a whole range of
aggregation procedures.
! Subtask 2.3. Properties of aggregation procedures
In addition to the definition of several aggregation rules, we need to study what are the properties that we
expect from these procedures. The aim here is to define what kind of properties one could expect from the
aggregation of several argumentation systems. This is necessary to be able to distinguish between interesting
aggregation procedures and the ones with bad behaviours, but also to classify them according to the specific
decision contexts and to their respective behaviours. Examples are social welfare properties like Pareto
optimality, and properties of the aggregation procedure, like its sensibility to manipulation. When a rule is
manipulable, an agent (upon knowing the other participants’ votes) may cast an insincere input in order to
obtain a social outcome that is better for him compared to the one he had obtained, had he voted sincerely.
Clearly, a strategy-proof procedure is desirable, but unfortunately very unlikely [Gibbard73,
Satterthwaite75]. But as the recent findings of computational social choice show [CELM07], even if an
aggregation procedure is manipulable, its complexity may be so high that manipulation is practically
difficult.
! Subtask 2.4. Aggregating arguments vs. aggregating judgments
Another key issue is to clarify the relation between argumentation aggregation, voting procedures and
judgment aggregation on the one hand, and belief merging on the other hand. The question of whether it is
possible to embed the aggregation of argumentation systems into the judgment aggregation framework
[LP10] seems particularly urgent, as already pointed out by [RT10, CP11]. The analogy (at least when the
agents share the same argumentation system) is striking. Once this relation is clarified, results obtained in
judgment aggregation may eventually be reformulated for the argumentation aggregation case (e.g. results
that relate to the agendas and to the conditions that the aggregation rules need to satisfy in order to guarantee
consistent group positions). But there are also differences between argumentation aggregation and judgment
aggregation, most notably the fact that the underlying logic of judgment aggregation is usually a classical
two-value propositional logic. For argument labelling [Caminada06, CG09], three values can be taken (in,
out, undec). Recently, [DH10] have studied aggregation of non-binary evaluations, allowing for an extension
of judgment aggregation problems using three values, thus providing a more suitable framework.
Added lines 1-7:
15-20 minutes: Présentation générale du WP2
10 min: Présentation des membres (chacun dit deux mots sur ce sur quoi il travaille/souhaite travailler pour le WP2)
2 exposés (25 minutes chacun + 5 min questions): Patricia Everaere (état de l'art sur les prop. "classiques" attendues de l'agreg de jugement, et de la fusion)
Srdjan Vesic (travail sur la séparabilité dans l’agrégation de jugements)
30 min: Discussion
10 min: Présentation des membres (chacun dit deux mots sur ce sur quoi il travaille/souhaite travailler pour le WP2)
2 exposés (25 minutes chacun + 5 min questions): Patricia Everaere (état de l'art sur les prop. "classiques" attendues de l'agreg de jugement, et de la fusion)
Srdjan Vesic (travail sur la séparabilité dans l’agrégation de jugements)
30 min: Discussion