A canonical theory of dynamic decision-making

Decision-making behavior is studied in many very different fields, from medicine and eco- nomics to psychology and neuroscience, with major contributions from mathematics and statistics, computer science, AI, and other technical disciplines. However the conceptual- ization of what decision-making is and methods for studying it vary greatly and this has resulted in fragmentation of the field. A theory that can accommodate various perspectives may facilitate interdisciplinary working. We present such a theory in which decision-making is articulated as a set of canonical functions that are sufficiently general to accommodate diverse viewpoints, yet sufficiently precise that they can be instantiated in different ways for specific theoretical or practical purposes. The canons cover the whole decision cycle, from the framing of a decision based on the goals, beliefs, and background knowledge of the decision-maker to the formulation of decision options, establishing preferences over them, and making commitments. Commitments can lead to the initiation of new decisions and any step in the cycle can incorporate reasoning about previous decisions and the rationales for them, and lead to revising or abandoning existing commitments. The theory situates decision-making with respect to other high-level cognitive capabilities like problem solving, planning, and collaborative decision-making. The canonical approach is assessed in three domains: cognitive and neuropsychology, artificial intelligence, and decision engineering

Collective decision-making with goals

Des agents devant prendre une décision collective sont souvent motivés par des buts individuels. Dans ces situations, deux aspects clés doivent être abordés : sélectionner une alternative gagnante à partir des voix des agents et s'assurer que les agents ne manipulent pas le résultat. Cette thèse étudie l'agrégation et la dimension stratégique des décisions collectives lorsque les agents utilisent un langage représenté de manière compacte. Nous étudions des langages de type logique : de la logique propositionnelle aux CP-nets généralisés, en passant par la logique temporelle linéaire (LTL). Notre principale contribution est l'introduction d'un cadre de vote sur les buts, dans lequel les agents soumettent des buts individuels exprimés comme des formules de la logique propositionnelle. Les fonctions d'agrégation classiques issues du vote, de l'agrégation de jugements et de la fusion de croyances sont adaptées et étudiées de manière axiomatique et computationnelle. Les propriétés axiomatiques connues dans la littérature sur la théorie du choix social sont généralisées à ce nouveau type d'entrée, ainsi que les problèmes de complexité visant à déterminer le résultat du vote. Une autre contribution importante est l'étude de l'agrégation des CP-nets généralisés, c'est-à-dire des CP-nets où la précondition de l'énoncé de préférence est une formule propositionnelle. Nous utilisons différents agrégateurs pour obtenir un classement collectif des résultats possibles. Grâce à cette thèse, deux axes de recherche sont ainsi reliés : l'agrégation des CP-nets classiques et la généralisation des CP-nets à des préconditions incomplètes. Nous contribuons également à l'étude du comportement stratégique dans des contextes de prise de décision collective et de théorie des jeux. Le cadre du vote basé sur les buts est de nouveau étudié sous l'hypothèse que les agents peuvent décider de mentir sur leur but s'ils obtiennent ainsi un meilleur résultat. L'accent est mis sur trois règles de vote majoritaires qui se révèlent manipulables. Par conséquent, nous étudions des restrictions à la fois sur le langage des buts et sur les stratégies des agents en vue d'obtenir des résultats de votes non manipulables. Nous présentons par ailleurs une extension stratégique d'un modèle récent de diffusion d'opinion sur des réseaux d'influence. Dans les jeux d'influence définis ici, les agents ont comme but des formules en LTL et ils peuvent choisir d'utiliser leur pouvoir d'influence pour s'assurer que leur but est atteint. Des solutions classiques telles que la stratégie gagnante sont étudiées pour les jeux d'influence, en relation avec la structure du réseau et les buts des agents. Enfin, nous introduisons une nouvelle classe de concurrent game structures (CGS) dans laquelle les agents peuvent avoir un contrôle partagé sur un ensemble de variables propositionnelles. De telles structures sont utilisées pour interpréter des formules de logique temporelle en temps alternés (ATL), grâce auxquelles on peut exprimer l'existence d'une stratégie gagnante pour un agent dans un jeu itéré (comme les jeux d'influence mentionnés ci-dessus). Le résultat principal montre qu'un CGS avec contrôle partagé peut être représenté comme un CGS avec contrôle exclusif. En conclusion, cette thèse contribue au domaine de la prise de décision collective en introduisant un nouveau cadre de vote basé sur des buts propositionnels. Elle présente une étude de l'agrégation des CP-nets généralisés et une extension d'un cadre de diffusion d'opinion avec des agents rationnels qui utilisent leur pouvoir d'influence. Une réduction du contrôle partagé à un contrôle exclusif dans les CGS pour l'interprétation des logiques du raisonnement stratégique est également proposée. Par le biais de langages logiques divers, les agents peuvent ainsi exprimer buts et préférences sur la décision à prendre, et les propriétés souhaitées pour le processus de décision peuvent en être garanties.Agents having to take a collective decision are often motivated by individual goals. In such scenarios, two key aspects need to be addressed. The first is defining how to select a winning alternative from the expressions of the agents. The second is making sure that agents will not manipulate the outcome. Agents should also be able to state their goals in a way that is expressive, yet not too burdensome. This dissertation studies the aggregation and the strategic component of multi-agent collective decisions where the agents use a compactly represented language. The languages we study are all related to logic: from propositional logic, to generalized CP-nets and linear temporal logic (LTL). Our main contribution is the introduction of the framework of goal-based voting, where agents submit individual goals expressed as formulas of propositional logic. Classical aggregation functions from voting, judgment aggregation, and belief merging are adapted to this setting and studied axiomatically and computationally. Desirable axiomatic properties known in the literature of social choice theory are generalized to this new type of propositional input, as well as the standard complexity problems aimed at determining the result. Another important contribution is the study of the aggregation of generalized CP-nets coming from multiple agents, i.e., CP-nets where the precondition of the preference statement is a propositional formula. We use different aggregators to obtain a collective ordering of the possible outcomes. Thanks to this thesis, two lines of research are thus bridged: the one on the aggregation of complete CP-nets, and the one on the generalization of CP-nets to incomplete preconditions. We also contribute to the study of strategic behavior in both collective decision-making and game-theoretic settings. The framework of goal-based voting is studied again under the assumption that agents can now decide to submit an untruthful goal if by doing so they can get a better outcome. The focus is on three majoritarian voting rules which are found to be manipulable. Therefore, we study restrictions on both the language of the goals and on the strategies allowed to the agents to discover islands of strategy-proofness. We also present a game-theoretic extension of a recent model of opinion diffusion over networks of influence. In the influence games defined here, agents hold goals expressed as formulas of LTL and they can choose whether to use their influence power to make sure that their goal is satisfied. Classical solution concepts such as weak dominance and winning strategy are studied for influence games, in relation to the structure of the network and the goals of the agents. Finally, we introduce a novel class of concurrent game structures (CGS) in which agents can have shared control over a set of propositional variables. Such structures are used for the interpretation of formulas of alternating-time temporal logic, thanks to which we can express the existence of a winning strategy for an agent in a repeated game (as, for instance, the influence games mentioned above). The main result shows by means of a clever construction that a CGS with shared control can be represented as a CGS with exclusive control. In conclusion, this thesis provides a valuable contribution to the field of collective decision-making by introducing a novel framework of voting based on individual propositional goals, it studies for the first time the aggregation of generalized CP-nets, it extends a framework of opinion diffusion by modelling rational agents who use their influence power as they see fit, and it provides a reduction of shared to exclusive control in CGS for the interpretation of logics of strategic reasoning. By using different logical languages, agents can thus express their goals and preferences over the decision to be taken, and desirable properties of the decision process can be ensured

Dynamically rational judgment aggregation

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators

Ordering based decision making: a survey

Decision making is the crucial step in many real applications such as organization management, financial planning, products evaluation and recommendation. Rational decision making is to select an alternative from a set of different ones which has the best utility (i.e., maximally satisfies given criteria, objectives, or preferences). In many cases, decision making is to order alternatives and select one or a few among the top of the ranking. Orderings provide a natural and effective way for representing indeterminate situations which are pervasive in commonsense reasoning. Ordering based decision making is then to find the suitable method for evaluating candidates or ranking alternatives based on provided ordinal information and criteria, and this in many cases is to rank alternatives based on qualitative ordering information. In this paper, we discuss the importance and research aspects of ordering based decision making, and review the existing ordering based decision making theories and methods along with some future research directions

An Introduction to Mechanized Reasoning

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We introduce mechanized reasoning to economists in three ways. First, we introduce mechanized reasoning in general, describing both the techniques and their successful applications. Second, we explain how mechanized reasoning has been applied to economic problems, concentrating on the two domains that have attracted the most attention: social choice theory and auction theory. Finally, we present a detailed example of mechanized reasoning in practice by means of a proof of Vickrey's familiar theorem on second-price auctions

Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNN) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as its relationship to current developments in neural-symbolic computing.Comment: Updated version, draft of accepted IJCAI2020 Survey Pape