A note on Murakami’s theorems and incomplete social choice without the Pareto principle

In Arrovian social choice theory assuming the independence of irrelevant alternatives, Murakami (1968) proved two theorems about complete and transitive collective choice rules that satisfy strict non-imposition (citizens’ sovereignty), one being a dichotomy theorem about Paretian or anti-Paretian rules and the other a dictator-or-inverse-dictator impossibility theorem without the Pareto principle. It has been claimed in the later literature that a theorem of Malawski and Zhou (1994) is a generalization of Murakami’s dichotomy theorem and that Wilson’s (1972) impossibility theorem is stronger than Murakami’s impossibility theorem, both by virtue of replacing Murakami’s assumption of strict non-imposition with the assumptions of non-imposition and non-nullness. In this note, we first point out that these claims are incorrect: non-imposition and non-nullness are together equivalent to strict non-imposition for all transitive collective choice rules. We then generalize Murakami’s dichotomy and impossibility theorems to the setting of incomplete social preference. We prove that if one drops completeness from Murakami’s assumptions, his remaining assumptions imply (i) that a collective choice rule is either Paretian, anti-Paretian, or dis-Paretian (unanimous individual preference implies noncomparability) and (ii) that adding proposed constraints on noncomparability, such as the regularity axiom of Eliaz and Ok (2006), restores Murakami’s dictator-or-inverse-dictator result

Policy-making and policy assessments with partially ordered alternatives

The present work collects three essays on social choice and decision-making in the presence of multiple objectives and severe informational limitations. When feasible alternatives must be ordered according to their performance under various criteria, it is typically necessary to make use of a specific functional relation and assume the implied rates of substitution between scores in different criteria. In the special case of collective choice and voting, rather than having proper rates of substitution, each individually preferred ordering of the alternatives is usually weighted according to its frequency in the population. Both decision frameworks imply the availability of extensive information about such functional relation and the proper weights of each criterion or must acknowledge a vast and arbitrary discretion to those in charge of resolving the decision process. The alternative approach herein discussed consists in applying the Pareto criterion to identify Pareto-superior alternatives in each pairwise comparison, a procedure that easily produces an incomplete ordering. Then, applying a tool of Order Theory, a complete ordering is identified from the linear extensions of the partially ordered set derived from the Pareto criterion. The claim is that this method highlights conflicts in value judgements and in incomparable criteria, allowing to search for a conflict-mitigating solution that doesn\u2019t make assumptions on the reciprocal importance of criteria or judgements. The method is actually a combination of existing but unrelated approaches in Social Choice Theory and in Order Theory and provides outcomes with interesting properties. The essays present, respectively, an axiomatic discussion of the properties of this approach and two applications to policy issues

Computational aspects of voting: a literature survey

Preference aggregation is a topic of study in different fields such as philosophy, mathematics, economics and political science. Recently, computational aspects of preference aggregation have gained especial attention and “computational politics” has emerged as a marked line of research in computer science with a clear concentration on voting protocols. The field of voting systems, rooted in social choice theory, has expanded notably in both depth and breadth in the last few decades. A significant amount of this growth comes from studies concerning the computational aspects of voting systems. This thesis comprehensively reviews the work on voting systems (from a computing perspective) by listing, classifying and comparing the results obtained by different researchers in the field. This survey covers a wide range of new and historical results yet provides a profound commentary on related work as individual studies and in relation to other related work and to the field in general. The deliverables serve as an overview where students and novice researchers in the field can start and also as a depository that can be referred to when searching for specific results. A comprehensive literature survey of the computational aspects of voting is a task that has not been undertaken yet and is initially realized here. Part of this research was dedicated to creating a web-depository that contains material and references related to the topic based on the survey. The purpose was to create a dynamic version of the survey that can be updated with latest findings and as an online practical reference

Proceedings of the IJCAI-09 Workshop on Nonmonotonic Reasoning, Action and Change

Copyright in each article is held by the authors. Please contact the authors directly for permission to reprint or use this material in any form for any purpose.The biennial workshop on Nonmonotonic Reasoning, Action and Change (NRAC) has an active and loyal community. Since its inception in 1995, the workshop has been held seven times in conjunction with IJCAI, and has experienced growing success. We hope to build on this success again this eighth year with an interesting and fruitful day of discussion. The areas of reasoning about action, non-monotonic reasoning and belief revision are among the most active research areas in Knowledge Representation, with rich inter-connections and practical applications including robotics, agentsystems, commonsense reasoning and the semantic web. This workshop provides a unique opportunity for researchers from all three fields to be brought together at a single forum with the prime objectives of communicating important recent advances in each field and the exchange of ideas. As these fundamental areas mature it is vital that researchers maintain a dialog through which they can cooperatively explore common links. The goal of this workshop is to work against the natural tendency of such rapidly advancing fields to drift apart into isolated islands of specialization. This year, we have accepted ten papers authored by a diverse international community. Each paper has been subject to careful peer review on the basis of innovation, significance and relevance to NRAC. The high quality selection of work could not have been achieved without the invaluable help of the international Program Committee. A highlight of the workshop will be our invited speaker Professor Hector Geffner from ICREA and UPF in Barcelona, Spain, discussing representation and inference in modern planning. Hector Geffner is a world leader in planning, reasoning, and knowledge representation; in addition to his many important publications, he is a Fellow of the AAAI, an associate editor of the Journal of Artificial Intelligence Research and won an ACM Distinguished Dissertation Award in 1990

Social Choice for Partial Preferences Using Imputation

Within the field of multiagent systems, the area of computational social choice considers the problems arising when decisions must be made collectively by a group of agents. Usually such systems collect a ranking of the alternatives from each member of the group in turn, and aggregate these individual rankings to arrive at a collective decision. However, when there are many alternatives to consider, individual agents may be unwilling, or unable, to rank all of them, leading to decisions that must be made on the basis of incomplete information. While earlier approaches attempt to work with the provided rankings by making assumptions about the nature of the missing information, this can lead to undesirable outcomes when the assumptions do not hold, and is ill-suited to certain problem domains. In this thesis, we propose a new approach that uses machine learning algorithms (both conventional and purpose-built) to generate plausible completions of each agent’s rankings on the basis of the partial rankings the agent provided (imputations), in a way that reflects the agents’ true preferences. We show that the combination of existing social choice functions with certain classes of imputation algorithms, which forms the core of our proposed solution, is equivalent to a form of social choice. Our system then undergoes an extensive empirical validation under 40 different test conditions, involving more than 50,000 group decision problems generated from real-world electoral data, and is found to outperform existing competitors significantly, leading to better group decisions overall. Detailed empirical findings are also used to characterize the behaviour of the system, and illustrate the circumstances in which it is most advantageous. A general testbed for comparing solutions using real-world and artificial data (Prefmine) is then described, in conjunction with results that justify its design decisions. We move on to propose a new machine learning algorithm intended specifically to learn and impute the preferences of agents, and validate its effectiveness. This Markov-Tree approach is demonstrated to be superior to imputation using conventional machine learning, and has a simple interpretation that characterizes the problems on which it will perform well. Later chapters contain an axiomatic validation of both of our new approaches, as well as techniques for mitigating their manipulability. The thesis concludes with a discussion of the applicability of its contributions, both for multiagent systems and for settings involving human elections. In all, we reveal an interesting connection between machine learning and computational social choice, and introduce a testbed which facilitates future research efforts on computational social choice for partial preferences, by allowing empirical comparisons between competing approaches to be conducted easily, accurately, and quickly. Perhaps most importantly, we offer an important and effective new direction for enabling group decision making when preferences are not completely specified, using imputation methods

Aggregating partially ordered preferences

Abstract. Preferences are not always expressible via complete linear orders: sometimes it is more natural to allow for the presence of incomparable outcomes. This may hold both in the agents ’ preference ordering and in the social order. In this paper we consider this scenario and we study what properties it may have. In particular, we show that, despite the added expressivity and ability to resolve conflicts provided by incomparability, classical impossibility results (such as Arrow’s theorem, Muller-Satterthwaite’s theorem, and Gibbard-Satterthwaite’s theorem) still hold. We also prove some possibility results, generalizing Sen’s theorem for majority voting. To prove these results, we define new notions of unanimity, monotonicity, dictator, triple-wise value-restriction, and strategy-proofness, which are suitable and natural generalizations of the classical ones for complete orders.

Aggregating partially ordered preferences

none4Preferences are not always expressible via complete linear orders: some- times it is more natural to allow for the presence of incomparable outcomes. This may hold both in the agents' preference ordering and in the social order. In this paper we consider this scenario and we study what properties it may have. In par- ticular, we show that, despite the added expressivity and ability to resolve con icts provided by incomparability, classical impossibility results (such as Arrow's theorem, Muller-Satterthwaite's theorem, and Gibbard-Satterthwaite's theorem) still hold. We also prove some possibility results, generalizing Sen's theorem for majority voting. To prove these results, we dene new notions of unanimity, monotonicity, dictator, triple-wise value-restriction, and strategy-proofness, which are suitable and natural generalizations of the classical ones for complete orders.mixedMARIA SILVIA PINI; F. ROSSI; KRISTEN BRENT VENABLE; TOBY WALSHPini, MARIA SILVIA; Rossi, Francesca; KRISTEN BRENT, Venable; Toby, Wals