Application of prioritized aggregation operators in preference voting

We consider the problem of preference aggregation in group decision making. The role of the collaborative imperative used by the group in determining the form of the aggregation function is noted. We focus on one collaborative imperative, called the primal, deriving from participant autonomy, an agent doesn't have to accept a decision by the group it doesn't like. We showed that t-norms and more generally the class of uninorms having zero fixation provide appropriate aggregation operators to implement this primal collaborative imperative. We then discuss the possibility of an agent using a strategic manipulation of its preference information to get its preferred alternative. A mechanism based upon the use of an importance weighting is then suggested for modifying the construction of the group decision function to defend against strategic manipulation.

(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.

In this paper, we investigate the uncertain linguistic multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Motivated by the idea of prioritized aggregation operators (R. R. Yager, Prioritized aggregation operators, Int. J. Approximate Reasoning48 (2008) 263–274.), we develop some prioritized aggregation operators for aggregating uncertain linguistic information, and then apply them to develops some models for uncertain linguistic multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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.

Prioritized aggregation operators

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.

Prioritized multi-criteria decision making based on preference relations

This paper introduces the ordered weighted average inflation (OWAI). The OWAI operator aggregates the information of a set of inflations and provides a range of scenarios from the minimum and the maximum inflation. The advantage of this approach is that it can provide a flexible inflation formula that can be adapted to the specific characteristics of the enterprise, region, state or country. Therefore, the novelty of this operator is that experts can forecast the information and provide optimistic or pessimistic results of the expected average inflation according to the knowledge, aptitude or expectations for the whole country or an event that represents a specific sector, market or industry. The paper develops several extensions by using the induced, heavy and prioritized aggregation operators. The work studies the applicability of the operator to the analysis of Mexican inflation by developing some aggregation systems that consider the average inflation of Mexico.

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

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.

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.

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Politics. Please check back later for the full article.Narrowly understood, social choice theory is a specialized branch of applied logic and mathematics that analyzes abstract objects called preference aggregation functions, social welfare functions, and social choice functions. But more broadly, social choice theory identifies, analyzes, and evaluates rules that may be used to make collective decisions. So understood, social choice is a subfield of the social sciences that examines what may be called “voting rules” of various sorts. While social choice theory typically assumes a finite set of alternatives over which voter preferences are unrestricted, the spatial model of social choice assumes that policy alternatives can be represented by points in a space of one or more dimensions, and that voters have preferences that are plausibly shaped by this spatial structure.Social choice theory has considerable relevance for the study of legislative (as well as electoral) institutions. The concepts and tools of social choice theory make possible formal descriptions of legislative institutions such as bicameralism, parliamentary voting procedures, effects of decision rules (e.g., supramajority vs. simple majority rule and executive veto rules), sincere vs. strategic voting by legislators, agenda control, and other parliamentary maneuvers. Spatial models of social choice further enrich this analysis and raise additional questions regarding policy stability and change. Spatial models are used increasingly to guide empirical research on legislative institutions and processes.

Voting systems have a great impact on the results of contests or elections. Simple methods are actually used, whereas they do not provide most accurate results. For example, in the Eurovision Song Contest, the winner may not be the most preferred candidate. Condorcet criterion, which consists in preserving most of the individual votes in the final ranking, seems intuitively the most relevant. In this paper, we propose a new ranking method founded on Condorcet voting count principle which minimizes the number of pairwise inversions of the individual preferences. We propose a two-step method: computing the cycles among vote preferences and removing a minimal set of pairwise preferences to erase all the cycles and turn the votes into a partial order as close as possible to a total order. Finally, we evaluate the impact of our ranking procedure on the last 30 Eurovision Song Contests.

PurposeThis study examined the waiting times to board an attraction at a theme park (Tokyo DisneySea in Japan) using a simulation based on measured values. Park visitors often complain that waiting times are too long; guests (Disney's term for park visitors) must stand in long, slow-moving queues outdoors in all weather, enduring heat, cold, rain and wind. This can undermine their health and reduce customer satisfaction. To date, no research has offered a scientific approach to solve the problem in the context of theme park queues.Design/methodology/approachThe attraction examined two queues: a short waiting queue for guests with priority entry tickets and a long waiting queue for guests without priority entry tickets. The total number of guests with priority entry tickets remained a constant value, as in the current system; however, the author designed the number as a monotonically increasing function to reduce the waiting times for nonpriority entry. It was impractical to analyze queues or try to explain proposed wait time reduction methods using theories and mathematical models alone. Therefore, the author used a simulation study based on real data to demonstrate the proposed method of this study.FindingsThe simulation results indicated that the proposed method significantly decreased guests' waiting times in the nonpriority entry queue, without changing the number of guests in both priority and nonpriority entry queues.Research limitations/implicationsSimple queues can be analyzed using theoretical calculations, but complicated queue systems require simulation methods. Therefore, this paper cannot provide a theoretical basis for the method.Practical implicationsThe proposed method offers benefits to managers of any event or location seeking to manage queue times and not just theme parks (e.g. exhibitions, concerts, etc.). Advance tickets are equivalent to priority entry tickets, so applying the proposed method can shorten waiting times on the day of the event.Originality/valueThis study has important practical implications for queues management, and the proposed approach is a unique system that reduces waiting times, thus increasing customer satisfaction. The proposed method can be applied to similar types of priority entry systems.