Majority-rule-based preference aggregation on multi-attribute domains with CP-nets

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.

The increased water demand and the increased capital construction costs of water resource development projects force engineers and water planners to utilize efficiently the existing and proposed water resources systems. Hence, it is considered necessary to find the optimum real time operating rules for systems of multiple reservoirs.Stochastic dynamic programming (SDP) has been used as the tool for deriving the real time operating rules for a system of multiple reservoirs, in preference to simulation analysis and linear programming. This is because the operation of the storages is considered as a sequential decision problem and dynamic programming is well suited to handle sequential, multi-period type decision problems. Further, the stochastic nature of streamflow is considered explicitly through a multivariate distribution for streamflow. The method theoretically produces the global optimum solution.The computational difficulties in terms of computer time and memory space have prohibited the realistic application of this method to systems of multiple reservoirs in the past. In this study, two methods have been introduced to reduce the computational difficulties of the method, thus making SDP more attractive to use in the derivation of the real time operating rules for a system of multiple reservoirs.The first method, the assumption of cross correlation of streamflow, reduces the number of states in the SDP method which reduces computer time and memory space. Further, it reduces the number of conditional probability estimates of streamflow which are used in recursive relation of the SDP algorithm. The second method, the “corridor” approach, reduces computer time involved in the SDP method by eliminating the computation of infeasible and/or inferior (suboptimal) solutions. These two methods have resulted in significant savings in the computer effort of the SDP method.The conditional probabilities of streamflow are computed by considering the hypervolume under the conditional probability density function between the integration limits using the computationally efficient Gaussian Legendre quadrature method. The conditional probability density function is derived from the historical streamflow data.Real time operating rules are expressed as a function of the storage volume(s) at the beginning of the current time interval and the forecast inflow into the storage(s) during the current time interval.The Melbourne water supply system is used as the example. The derived operating rules have been tested by operating a simulation model and the conclusion is made that the SDP method is a satisfactory technique for objectively deriving real time operating rules for a system of multiple reservoirs.Finally, a combined stochastic dynamic programming – statistical disaggregation approach is introduced to determine the real time operating rules for a system of multiple reservoirs where operational data are available. Releases from individual storages are a function of the total system storage volume and inflow. The method uses SDP to determine the release rules from the equivalent single reservoir of the multiple reservoir system; these releases are then disaggregated to individual releases using the statistical release disaggregation model whose parameters are derived from the historical operational data. The approach was used to derive real time operating rules for the Melbourne water supply system and the operating rules were validated using a simulation model of the system.

Computational social choice is a new interdisciplinary research area at the intersection of social choice theory and computer science that studies computational aspects of social choice mechanisms as well as applications of social choice ideas in the design and analysis of computing systems. Research on computational social choice now encompasses a variety of topics, including the algorithmic aspects of voting rules, computational barriers to strategic behaviour, collective decision-making in multi-agent systems, preference elicitation and communication issues in voting, fair division, computational aspects of weighted voting games, collective decision-making in combinatorial domains, logic-based formalisms for social choice problems, belief and judgement aggregation, and social software. The aim of this special issue is to build on the spectacular success of two workshops on computational social choice (COMSOC’06, Amsterdam and COMSOC’08, Liverpool), and provide a forum for reseachers in the area to present their ideas on a variety of topics. This special issue is composed of nine research articles and a short note that span a fairly wide range of issues, including voting, mechanism design, judgment aggregation, and fairness, and a similarly wide range of techniques, such as logic, experiments, and computational complexity. The paper by Agotnes, van der Hoek and Wooldridge defines a new modal logic for representing and reasoning about preference and judgment aggregation. The authors show that their logic can be used to express a variety of concepts and results from the social choice domain, including majority voting, the discursive paradox, Arrow’s theorem and Condorcet’s paradox. Baharad, Goldberger, Koppel and Nitzan propose a maximum likelihood estimation-based approach for aggregating voters’ opinions over several issues. They argue that their method is vastly superior to simple majority voting, and use both analytical and empirical evaluation to support their argument. Balan, Richards and Luke deal with the problem of selecting a sequence of actions when the actions have multiple beneficiaries. Their goal is to select the actions according to a lexicographic fairness criterion. The explore the complexity of this problem for both finite and infinite sequences of actions and present both algorithms and intractability results for this problem. The paper by Caminada and Pigozzi applies argumentation theory to judgment aggregation, and proposes aggregation operators satisfying not only the usual property of collective rationality, but another highly desirable property,

The University of Padua conducted a survey to elicit the preferences of its students for new services that the university, the city and local authorities could offer to improve student life before, during and after graduation. In this paper, we present the statistical methodology for ranking services according to students' preferences and discuss the resulting ranks of the services grouped in 10 thematic areas. We conclude that the preference elicitation method and the rank estimation method adopted in our research are appropriate for within- university prioritisation of student services.

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.

In the last decade the Netherlands has experienced an economic recession. Now, in 2017, the economy is picking up again. This growth does not only come with advantages because economic growth demands more from the transport system. Congestion is increasing again, the capacity of the train system is now insufficient during peak hours, and the world faces environmental challenges that are partly due to emissions caused by travellers. These negative effects worsen as travellers make rational choices, which could be undesirable from a system, or social welfare, perspective. For example, car drivers do often not choose public transport options, because it costs them more effort; however, if they choose public transport options, then the system improves since congestion and emissions will reduce. Or another example, if travellers choose to avoid peak hours, they might not arrive at their desired time, but then they do not contribute to peak hour congestion or crowding. In addition, the capacity of the transport system is more effectively used if travellers spread out over the day. Passenger transport pricing can be an incentive for travellers to change their choices, and can therefore be used to mitigate congestion, emissions, and other undesirable effects. Passenger transport pricing is the umbrella term for measures that make passengers pay for their travels. Traditional pricing measures are for example: fuel excise taxes, public transport fares, and periodical registration fees for vehicles. More innovative measures are cordon charges (e.g., in London, Stockholm, and Singapore), special tolling lanes, and peak avoidance projects. When such an innovative measure has different prices for times of the day, and for different locations (i.e., it is time- and space-differentiated), travellers’ choices related to route, mode and departure time can be influenced. By changing these choices, the overall performance of the transport system can improve. Travellers have differences regarding time valuation, preferred departure or arrival times, and car ownership. Therefore, a measure can become even more effective if it also allows to differentiate amongst characteristics of travellers. However, innovative pricing measures have not been implemented widely across the globe, despite their potential to reduce congestion and emissions. This is primarily due to lack of public and political support. The Netherlands has experienced decades of political discourse and many failed proposals. Low public support did not contribute to (political) agreement either, because it has always fuelled the discussion with dissenting opinions. In the process of designing policies and making decisions, strategic planning models usually estimate (or forecast) the effects of the policy. The preferences of travellers and the transport system are captured by mathematical equations. Such models are always a simplified representation of reality. To apply them to asses pricing measures, they should capture the underlying mechanisms that are important for transport pricing as realistic as possible. This dissertation identifies disadvantages of current strategic network models for passenger transport pricing and provides methodological advances to resolve them. This is done with a holistic approach that combines game theory, discrete choice analysis, traffic flow theory, and tranport economics into one modelling framework. This framework has many sub-models and provides a toolbox for analysts to determine the effects of innovative pricing schemes. The basic principle for each tool is to make them realistic (so that the results are credible for decision makers), and computationally efficient. The latter means that many different pricing schemes can be computed within reasonable time. By providing the methodological advances, that are briefly discussed in the next sections, this dissertation aims to improve public and political support. For example, the preferences of multiple stakeholders can be considered, the possible conflicts between them can be identified, and solutions based on concepts that aim to resolve these conflicts can be computed.

El artículo estudia la Paradoja de Condorcet aplicada al funcionamiento del Cabildo Cantonal de Cuenca – Ecuador. La votación realizada al interior de un espacio político obedece a la regla de mayorías aún cuando su decisión involucre el normal desenvolvimiento organizacional. Los hallazgos determinan que por varios años las tarifas de agua potable no fueron modificadas pese a que ETAPA- EP presentaba necesidades de dinero y veía comprometida su operación. Se reconoce la Paradoja de Condorcet cuando las preferencias de los votantes son cíclicas aún a pesar de que la preferencia individual sea contraria a la grupal. El estudio presenta análisis de tipo histórico - cualitativo. Palabras clave: Empresa de agua, gobierno local, decisiones sociales, economía, política, fijación de tarifas. URL: http://revistas.uta.edu.ec/erevista/index.php/bcoyu/article/view/719

The variability in responses generated by Large Language Models (LLMs) like OpenAI’s GPT-4 poses challenges in ensuring consistent accuracy on medical knowledge assessments, such as the United States Medical Licensing Exam (USMLE). This study introduces a novel multi-agent framework—referred to as a "Council of AIs"—to enhance LLM performance through collaborative decision-making. The Council consists of multiple GPT-4 instances that iteratively discuss and reach consensus on answers facilitated by a designated "Facilitator AI." This methodology was applied to 325 USMLE questions across Step 1, Step 2 Clinical Knowledge (CK), and Step 3 exams. The Council achieved consensus responses that were correct 97%, 93%, and 94% of the time for Step 1, Step 2CK, and Step 3, respectively, outperforming single-instance GPT-4 models. In cases where there wasn’t an initial unanimous response, the Council of AI deliberations achieved a consensus that was the correct answer 83% of the time. For questions that required deliberation, the Council corrected over half (53%) of responses that majority vote had gotten incorrect. At the end of deliberation, the Council often corrected majority responses that were initially incorrect: the odds of a majority voting response changing from incorrect to correct were 5 (95% CI: 1.1, 22.8) times higher than the odds of changing from correct to incorrect after discussion. We additionally characterized the semantic entropy of the response space for each question and found that deliberations impact entropy of the response space and steadily decrease it, consistently reaching an entropy of zero in all instances. This study showed that in a Council model response variability—often viewed as a limitation—could be leveraged as a strength, enabling adaptive reasoning and collaborative refinement of answers. These findings suggest new paradigms for AI implementation and reveal diversity of responses as a strength in collective decision-making even in medical question scenarios where there is a single correct response.Author SummaryIn our study, we explored how collaboration among multiple artificial intelligence (AI) systems could improve accuracy on medical licensing exams. While individual AI models like GPT-4 often produce varying answers to the same question—a challenge known as "response variability"—we designed a "Council of AIs" to turn this variability into a strength. The Council consists of several AI models working together, discussing their answers through an iterative process until they reach consensus.When tested on 325 medical exam questions, the Council achieved 97%, 93%, and 94% accuracy on the Step 1, Step 2CK, and Step 3, respectively. This improvement was most notable when answers required debate: in cases where initial responses disagreed, the collaborative process corrected errors 83% of the time. Our findings suggest that collective decision-making— even among AIs—can enhance accuracy and AI collaboration can potentially lead to more trustworthy tools for healthcare, where accuracy is critical. By demonstrating that diverse AI perspectives can refine answers, we challenge the notion that consistency alone defines a "good" AI. Instead, embracing variability through teamwork might unlock new possibilities for AI in medicine and beyond. This approach could inspire future systems where AIs and humans collaborate (e.g. on Councils with both humans and AIs), combining strengths to solve complex problems. While technical challenges remain, our work highlights a promising path toward more robust, adaptable AI solutions.

We introduce three different approaches for decision making under uncertainty, if (I) there is only partial (both cardinal and ordinal) information on an agent’s preferences and (II) the uncertainty about the states of nature is described by a credal set. Particularly, (I) is modeled by a pair of relations, one specifying the partial rank order of the alternatives and the other modeling partial information on the strength of preference. Our first approach relies on criteria that construct complete rankings of the acts based on generalized expectation intervals. Subsequently, we introduce different concepts of global admissibility that construct partial orders by comparing all acts simultaneously. Finally, we define criteria induced by suitable binary relations on the set of acts and, therefore, can be understood as concepts of local admissibility. Whenever suitable, we provide linear programming based algorithms for checking optimality/admissibility of acts.

In mobility markets – especially vehicle for hire markets – drivers offer individual transportation by car to customers. Drivers individually decide where to go to pick up customers to increase their own utilization (probability of carrying a customer) and utility (profit). The utility drivers retrieve from customers comprises both costs of driving to another location and the revenue from carrying a customer and is thus not shared between different drivers. In this thesis, I present the Vehicle for Hire Problem (VFHP) as a generalization of the Kolkata Paise Restaurant Problem (KPRP) to evaluate different strategies for drivers in vehicle for hire markets. The KPRP is a multi-round game model presented by Chakrabarti et al. (2009) in which daily laborers constitute agents and restaurants constitute resources. All agents decide simultaneously, but independently where to eat. Every restaurant can cater only one agent and agents cannot divert to other resources if their first choice is overcrowded. The number of agents equals the number of resources. Also, there is a ranking of restaurants all agents agree upon, and no two resources yield the same utility. The VFHP relaxes assumptions on capacity and utility: Resources (customers) are grouped in districts, agents (drivers) can redirect to other resources in the same district. As the distance between agent and resource reduces the agent’s utility and the location is not identical for all agents, the utility of a given resource is not identical for all agents. To study the impact of the different assumptions, I build four different model variants: Individual Preferences (IP) replaces the shared utility of the KPRP with uniformly distributed utilities per agent. The Mixed Preferences (MP) model variant uses the utility assumption of the VFHP, but the capacity of all districts remains 1. The Individual Preferences with Multiple Customers per District (IPMC) model variant groups customers in districts, and uses the uniform utilities introduced in the IP model variant. Mixed Preferences and Multiple Customers per District (MPMC) implements all assumptions of the VHFP. In this thesis, I study different strategies for the KPRP and all variants of the VFHP to build a foundation for an incentive scheme for dynamic matching in mobility markets. The strategies comprise history-dependent and utility-dependent strategies. In history-dependent strategies, agents incorporate their previous decisions and the utilization of resources in previous iterations in their decision. Agents adapting utility-dependent strategies choose the resource offering the highest utility with a given probability. Keywords: vehicle for hire markets; distributed decision making; agent-based modelling; congestion game; limited rationality

This paper investigates the connections between two state of the art classifiers: decision forests (DFs, including decision jungles) and convolutional neural networks (CNNs). Decision forests are computationally efficient thanks to their conditional computation property (computation is confined to only a small region of the tree, the nodes along a single branch). CNNs achieve state of the art accuracy, thanks to their representation learning capabilities. We present a systematic analysis of how to fuse conditional computation with representation learning and achieve a continuum of hybrid models with different ratios of accuracy vs. efficiency. We call this new family of hybrid models conditional networks. Conditional networks can be thought of as: i) decision trees augmented with data transformation operators, or ii) CNNs, with block-diagonal sparse weight matrices, and explicit data routing functions. Experimental validation is performed on the common task of image classification on both the CIFAR and Imagenet datasets. Compared to state of the art CNNs, our hybrid models yield the same accuracy with a fraction of the compute cost and much smaller number of parameters.

We consider the problem of processing similarity queries over a set of top-k rankings where the query ranking and the similarity threshold are provided at query time. Spear- man's Footrule distance is used to compute the similarity between rankings, considering how well rankings agree on the positions (ranks) of ranked items (i.e., the L1 distance). This setup allows the application of metric index structures such as M- or BK-trees and, alternatively, enables the use of traditional inverted indices for retrieving rankings that overlap (in items) with the query. Although both techniques are reasonable, they come with individual drawbacks for our specific problem. In this paper, we propose a hybrid index- ing strategy, which blends inverted indices and metric space indexing, resulting in a structure that resembles both in- dexing methods with tunable emphasis on one or the other. To find the sweet spot, we propose an assumption-lean but highly accurate (empirically validated) cost model through theoretical analysis. We further present optimizations to the inverted index component, for early termination and mini- mizing bookkeeping. The performance of the proposed al- gorithms, hybrid variants, and competitors is studied in a comprehensive evaluation using real-world benchmark data consisting of Web-search-result rankings and entity rankings based on Wikipedia.

Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow's theorem and Condorcet's paradox--which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation--including classical preference aggregation. As a case study we present a logical study of, including a formal proof of, the neutrality lemma, the main ingredient in a well-known proof of Arrow's theorem.

OF THE DISSERTATION Adaptive OFDM Radar for Target Detection and Tracking by Satyabrata Sen Doctor of Philosophy in Electrical Engineering Washington University in St. Louis, December 2010 Research Advisor: Dr. Arye Nehorai We develop algorithms to detect and track targets by employing a wideband orthogonal frequency division multiplexing (OFDM) radar signal. The frequency diversity of the OFDM signal improves the sensing performance since the scattering centers of a target resonate variably at different frequencies. In addition, being a wideband signal, OFDM improves the range resolution and provides spectral efficiency. We first design the spectrum of the OFDM signal to improve the radar’s wideband ambiguity function. Our designed waveform enhances the range resolution and motivates us to use adaptive OFDM waveform in specific problems, such as the detection and tracking of targets. We develop methods for detecting a moving target in the presence of multipath, which exist, for example, in urban environments. We exploit the multipath reflections by utilizing different Doppler shifts. We analytically evaluate the asymptotic performance of the detector and adaptively design the OFDM waveform, by maximizing the noncentrality-parameter expression, to further improve the detection performance. ii Next, we transform the detection problem into the task of a sparse-signal estimation by making use of the sparsity of multiple paths. We propose an efficient sparse-recovery algorithm by employing a collection of multiple small Dantzig selectors, and analytically compute the reconstruction performance in terms of the `1-constrained minimal singular value. We solve a constrained multi-objective optimization algorithm to design the OFDM waveform and infer that the resultant signal-energy distribution is in proportion to the distribution of the target energy across different subcarriers. Then, we develop tracking methods for both a single and multiple targets. We propose a tracking method for a low-grazing angle target by realistically modeling different physical and statistical effects, such as the meteorological conditions in the troposphere, curved surface of the earth, and roughness of the sea-surface. To further enhance the tracking performance, we integrate a maximum mutual information based waveform design technique into the tracker. To track multiple targets, we exploit the inherent sparsity on the delay-Doppler plane to develop an computationally efficient procedure. For computational efficiency, we use more prior information to dynamically partition a small portion of the delay-Doppler plane. We utilize the block-sparsity property to propose a block version of the CoSaMP algorithm in the tracking filter.

This paper presents an all-direct domain decomposition approach for large-scale structural analysis. The proposed approach achieves computational robustness and efficiency by enforcing the compatibility of the displacement field across the subdomain boundaries via local Lagrange multipliers and augmented Lagrangian formulation (ALF). The proposed domain decomposition approach was compared to the existing FETI approach in terms of the computational time and memory usage. The parallel implementation of the proposed algorithm was described in detail. Finally, a preliminary validation was attempted for the proposed approach, and the numerical results of two- and three-dimensional problems were compared to those obtained through a dual-primal FETI approach. The results indicate an improvement in the performance as a result of the implementing the proposed approach.