Using Importances in Group Preference Aggregation to Block Strategic Manipulation

This paper clarifies, how a preference aggregation problem can be solved using the prioritized aggregation operators (PAO), where, a given group of candidates should be aggregated based upon their satisfaction for a collection of ranked places. The comparison results show that the proposed method can accurate aggregate a preference ranking system with less computation and without the need to solve any mathematical model. Also, a metasearch application shows the usefulness of applying the PAO for a preference aggregation. © 2010 Wiley Periodicals, Inc.

(1) A domain of preferences allows for topological aggregation for each number of people if and only if this domain of preferences is contractible. (2) The combination of continuity and the Pareto principle implies the existence of a unique manipulator. (3) Arrow’s theorem can be translated into the previous statement. All of these results are obtained via algebraic topology. This paper introduces some of the tools developed in topology and applies them upon the problem of preference aggregation.

In his recent article, “Rousseau on Agenda-Setting and Majority Rule” (2003), Ethan Putterman examines how the democratic principle of popular majority rule might be reconciled with agenda-setting by legislative experts through an analysis of Rousseau's political theory. He argues that Rousseau accomplishes this reconciliation through a novel separation of powers between the legislative and the executive powers where the sovereign people delegates the exclusive power to initiate laws to the executive. Putterman thereby identifies as a solution to the problem of democratic self-legislation what Rousseau sees as the most important danger to it. At issue is not merely the correct interpretation of Rousseau's theory, for Putterman's argument raises far-reaching questions concerning the compatibility of democratic principles and institutions. After demonstrating that Putterman is incorrect that the sovereign people in Rousseau's state delegate the power of legislative initiative, I examine how Rousseau anticipates and addresses a related question central to contemporary democratic and social choice theory: the problem of preference aggregation through voting in the absence of agenda-setting institutions.

Information retrieval on RDF data benefits greatly from additional provenance information attached to the individual pieces of information. Provenance information such as origin of data, certainty, and temporal information on RDF statements can be used to rank search results according to one of those dimensions. In this paper, we consider the problem of aggregating provenance information from different dimensions in order to obtain a joint ranking over all dimensions. We relate this to the problem of preference aggregation in social choice theory and translate different solutions for preference aggregation to the problem of aggregating provenance rankings. By exploiting the ranking orderings on the provenance dimensions, we characterize three different approaches for aggregating preferences, namely the lexicographical rule, the Borda rule and the plurality rule, in our framework of provenance aggregation.

Group Recommendation (GR) is the task of suggesting relevant items/events for a group of users in online systems, whose major challenge is to aggregate the preferences of group members to infer the decision of a group. Prior group recommendation methods applied predefined static strategies for preference aggregation. However, these static strategies are insufficient to model the complicated decision making process of a group, especially for occasional groups which are formed adhoc. Compared to conventional individual recommendation task, GR is rather dynamic and each group member may contribute differently to the final group decision. Recent works argue that group members should have non-uniform weights in forming the decision of a group, and try to utilize a standard attention mechanism to aggregate the preferences of group members, but they do not model the interaction behavior among group members, and the decision making process is largely unexplored.In this work, we study GR in a more general scenario, that is Occasional Group Recommendation (OGR), and focus on solving the preference aggregation problem and the data sparsity issue of group-item interactions. Instead of exploring new heuristic or vanilla attention-based mechanism, we propose a new social self-attention based aggregation strategy by directly modeling the interactions among group members, namely Group Self-Attention (GroupSA). In GroupSA, we treat the group decision making process as multiple voting processes, and develop a stacked social self-attention network to simulate how a group consensus is reached. To overcome the data sparsity issue, we resort to the relatively abundant user-item and user-user interaction data, and enhance the representation of users by two types of aggregation methods. In the training process, we further propose a joint training method to learn the user/item embeddings in the group-item recommendation task and the user-item recommendation task simultaneously. Finally, we conduct extensive experiments on two real-world datasets. The experimental results demonstrate the superiority of our proposed GroupSA method compared to several state-of-the-art methods in terms of HR and NDCG.

We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for public expenditure without an exogenously available budget, such as participatory budgeting or voluntary tax programs, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents with linear utility functions over projects report the amount of their contribution, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism—the Nash product rule—which picks the distribution that maximizes the product of the agents’ utilities. This rule is Pareto efficient and incentivizes agents to contribute their entire budget while spending each agent’s contribution only on projects the agent finds acceptable.

Many areas of study, such as information retrieval, collaborative filtering, and social choice face the preference aggregation problem, in which multiple preferences over objects must be combined into a consensus ranking. Preferences over items can be expressed in a variety of forms, which makes the aggregation problem difficult. In this work we formulate a flexible probabilistic model over pairwise comparisons that can accommodate all these forms. Inference in the model is very fast, making it applicable to problems with hundreds of thousands of preferences. Experiments on benchmark datasets demonstrate superior performance to existing methods

This paper seeks to prove that under a large class of group decision rules some sincere voting situations will be unstable because of strategic manipulation by single individuals. The concept of stability used is weaker than the stability concepts figuring in many earlier contributions in this area, insofar as under the concept used here any individual, while disrupting a given voting situation, considers the possibility of retaliation by other individuals. DUMMETT AND FARQUHARSON [2], Murakami [7], Farquharson [3], Sen [14], Gibbard [4], Satterthwaite [13], and Pattanaik [10, 11, and 12] have discussed various aspects of the problem of stability in voting. The general conclusion which emerges from these writings seems to be that stability of all possible sincere voting situations (which implies the absence of strategic distortion of preferences by voters) is an extremely rare feature of democratic group decision procedures. However, the notion of stability or equilibrium underlying many of these contributions is a simple one and does not take into account several phenomena usually associated with strategic voting such as the possibility of counter-coalitions when a coalition (of one or more individuals) threatens to disrupt a voting situation. The purpose of this paper is twofold. First, it introduces a less demanding notion of stability which takes into account the possibility of formation of countercoalitions when an individual seeks to influence the outcome in his own favor by strategic manipulations in voting. Secondly, using this very weak notion of stability, it is shown that, while under the changed definition the possibility of having unstable sincere voting situations because of strategic voting by single individuals is somewhat reduced, invulnerability of all possible sincere voting situations to voting maneuvres of single individuals still remains a very rare property among democratic group decision rules based on pairwise comparisons. We lay down the basic notation and some preliminary definitions in Section 1. In Section 2 we introduce a notion of stability taking into account the possibility of counter-coalitions. Using this very weak definition of stability, in Section 3 we show that under most democratic group decision rules based on pairwise comparisons, there is the danger of having unstable sincere voting situations owing to strategic manipulations by single individuals. We conclude in Section 4.

We consider the problem of group decision making where the selection process is based upon a group preference function, obtained by an aggregation of the participating agents individual preference functions. We describe some methods for formulating the group preference from the individual preference functions. We note the possibility of the individual agents strategically manipulating the information they provide, so as to further their own goal of getting their most preferred alternative selected by the group. With this in mind, we suggest ways of modifying the formulation of the group decision functions to discourage strategic manipulation by the participating agents.

How can several individuals’ probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events—the agenda—is a sigma -algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma -algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we unify our results with existing results on binary judgment aggregation and Arrovian preference aggregation. We show that the same kinds of axioms (independence and consensus preservation) have radically different implications for different aggregation problems: linearity for probability aggregation and dictatorship for binary judgment or preference aggregation.

We consider a problem that can arise in group decision-making when the selection process is based upon a group preference function obtained by an aggregation of the individual preference functions of the group members. We observe the possibility of the individual agents strategically manipulating the information they provide so as to further their own goal of getting their most preferred alternative selected by the group. With this in mind we suggest ways of modifying the formulation of the group decision functions to discourage strategic manipulation by the participating agents.

Preference aggregation and judgment aggregation are two basic research models of group decision making. And preference aggregation has been deeply studied in social choice theory. However, researches of social choice theory gradually focus on judgment aggregation which appears recently. Judgment aggregation focuses on how to aggregate many consistent logical formulas into one, from the perspective of logic. We try to start with judgment aggregation model based on logic and then explore different solutions to problem of judgment aggregation.

Extensive research on judicial politics has documented disparities in adjudication and biases in judging. Yet, lacking statistical methods to infer individual preferences from group decisions, existing studies have focused on courts publishing individual judges’ opinions, leaving a gap in understanding collegial courts that report only collective and unanimous (‘per curiam’) panel decisions. We introduce a statistical methodology to identify the most fitting decision-theoretic models for such collective decisions, infer judges’ individual preferences, and quantify the inconsistency in the courts’ decisions. This methodology is applicable in various small group decision-making contexts where group assignments are repeated and exogenous. Applying it to the Swiss appellate court for asylum appeals, where decisions are made in three-judge panels, we find that in 45 per cent of cases, the chair-as-dictator rule applies (rather than majority rule). Although judges’ preferences vary strongly with partisanship, the partially collective decision making of the panel moderates this heterogeneity.

Multi criteria decision making (MCDM) and group decision making (GDM) are two well practiced approaches to solve decision making problems. Group decision making combines opinions from Decision makers (DMs) into a coherent group decision. The aim of this paper is to develop a new fuzzy group decision making algorithm and apply it to a real-world groundwater development problem to select the most preferred alternative. Five decision makers (DMs) are selected to express their judgments about relative importance of 3 criteria (water pumped, cost, and risk) and have given their preferences as ordinal preferences, utility values, fuzzy preference relations and multiplicative preference relations. Decision makers' opinions are aggregated based on a fuzzy group decision making. Ordered weighted averaging (OWA) operator has been used to aggregate decision makers' opinions. Consensus measure is also defined to evaluate convergence between group and individual opinions. The outcomes of the proposed algorithm show that proposed fuzzy group decision making process is a relevant approach to aggregate the individual expert's opinion and is a desirable tool to reach consensus among DMs.

Group decision-making, in which a collective decision needs to be derived from individual agents’ preferences has been an active area of research. In group decisionmaking, autonomous agents need some procedures or mechanisms that can collect preference information from them and make a decision; or some protocols that enable them to be involved in the decision process, to interact with each other and to jointly make a collective decision. Examples include preference aggregation mechanisms, negotiation protocols, voting procedures, and auctions. This thesis studies the problem of agent-based group decision-making in various problem settings, proposing several efficient approaches to support multiple agents in reaching efficient and fair collective decisions overmultiple issues. The research work in this thesis can be divided into two parts, addressing the agent-based group decision-making problem in circumstances in which there is, respectively, complete and incomplete information available. The first part of this thesis focuses on preference aggregation in combinatorial domains, provided all agents’ preferences. Structured preferences Conditional Preference Network (CP-nets) and its variant Trade-off enhanced CP-nets (TCP-nets) are used as formal models for representing the agents’ preferences in group decision-making. Before going into the problem of making a group decision from a collection of CP-nets or TCP-nets, the problem of individual preference reasoning is studied and a computationally efficient heuristic algorithm for dominance testing in CP-nets, which forms the basis for many group decision-making mechanisms, is introduced. Subsequently, we consider the group decision-making problem with multiple agents’ CP-nets and TCP-nets. As the space of possible outcomes in combinatorial domains has a size exponential in the number of variables, computational complexity in group decision-making will be one of the issues that need to be addressed. Two computationally efficient approaches are proposed in order to support agent-based group decisionmaking in combinatorial domains with different decision criteria: (i) an approach that converts the qualitative preferences derived from CP-nets or TCP-nets into numerical penalty scoring functions, and then searches for an optimal collective decision based on the individual penalty scores; and (ii) an approach that focuses on combinatorial vote and computes the winners (i.e., winning alternatives) from a collection of CP-nets according to Majority voting rule. The second part of this thesis is concerned with the disadvantage of disclosing preference information in group decision-making and considers the incomplete information setting. Two negotiation approaches are presented in order to support agent-based group decision-making in, respectively, combinatorial domains and in domains with multiple continuous issues. Firstly, a negotiation protocol in combinatorial domains is proposed, which enables agents to distributively make decisions and leads them to Pareto-optimal agreements under incomplete information setting. Then for the domains with multiple continuous issues, a cooperative mediated negotiation approach is proposed to support the agents searching for joint utility gains and reaching an efficient and fair agreement. For every approach introduced in this thesis, experiments are carried out and the results are presented and analysed in order to provide insights into the performance of these approaches.