Binary Preference Research Articles

A Novel Class of Unfolding Models for Binary Preference Data

Abstract We develop a new class of spatial voting models for binary preference data that can accommodate both monotonic and non-monotonic response functions, and are more flexible than alternative “unfolding” models previously introduced in the literature. We then use these models to estimate revealed preferences for legislators in the U.S. House of Representatives and justices on the U.S. Supreme Court. The results from these applications indicate that the new models provide superior complexity-adjusted performance to various alternatives and that the additional flexibility leads to preferences’ estimates that more closely match the perceived ideological positions of legislators and justices.

Preferences, risk neutrality and risk-sensitive MDPs

Preferences, risk neutrality and risk-sensitive MDPs

Hybrid Active and Passive Cable Contour Shielding of Magnetic Fields of Double-Circuit Overhead Power Lines

The purpose of the work is to design a hybrid screen designed to reduce the level of the magnetic field generated by double-circuit overhead power lines, to increase the efficiency of shielding the original magnetic field in residential buildings, to the level of sanitary standards and to reduce the sensitivity of the system to changes in system parameters. To achieve this goal, the structure of a hybrid screen was determined, consisting of a double contour active and a cable contour passive part. The developed hybrid screen is characterized by increased efficiency in reducing the magnetic field of industrial frequency. Designing a hybrid screen comes down to solving a minimax vector optimization problem, in which the vector objective function is calculated based on solution to Maxwell's equations in a quasi-stationary approximation using the COMSOL Multiphysics software package. The solution to the minimax vector optimization problem is calculated based on multi-particle swarm optimization algorithms from Pareto-optimal solutions taking into account binary preference relations. During the design of the hybrid screen, the coordinates of the spatial location of the two compensation windings, as well as the magnitude of the currents and its phases in the windings of the active screen, were calculated. The important results are theoretical and experimental studies on the effectiveness of the designed hybrid magnetic field shield generated by double-circuit overhead power lines. The significance of the results obtained lies in the fact that practical recommendations are given for a reasonable choice of the spatial arrangement of two shielding windings of a robust system of hybrid shielding of the magnetic field generated by double-circuit overhead power lines.

Optimization and Beyond

This paper will be concerned with hard choices—that is, choice situations where an agent cannot make a rationally justified choice. Specifically, this paper asks: if an agent cannot optimize in a given situation, are they facing a hard choice? A pair of claims are defended in light of this question. First, situations where an agent cannot optimize because of incompleteness of the binary preference or value relation constitute a hard choice. Second, situations where agents cannot optimize because the binary preference or value relation violates acyclicity do not constitute a hard choice.

Ranking-Based Color Constancy With Limited Training Samples.

Computational color constancy is an important component of Image Signal Processors (ISP) for white balancing in many imaging devices. Recently, deep convolutional neural networks (CNN) have been introduced for color constancy. They achieve prominent performance improvements comparing with those statistics or shallow learning-based methods. However, the need for a large number of training samples, a high computational cost and a huge model size make CNN-based methods unsuitable for deployment on low-resource ISPs for real-time applications. In order to overcome these limitations and to achieve comparable performance to CNN-based methods, an efficient method is defined for selecting the optimal simple statistics-based method (SM) for each image. To this end, we propose a novel ranking-based color constancy method (RCC) that formulates the selection of the optimal SM method as a label ranking problem. RCC designs a specific ranking loss function, and uses a low rank constraint to control the model complexity and a grouped sparse constraint for feature selection. Finally, we apply the RCC model to predict the order of the candidate SM methods for a test image, and then estimate its illumination using the predicted optimal SM method (or fusing the results estimated by the top k SM methods). Comprehensive experiment results show that the proposed RCC outperforms nearly all the shallow learning-based methods and achieves comparable performance to (sometimes even better performance than) deep CNN-based methods with only 1/2000 of the model size and training time. RCC also shows good robustness to limited training samples and good generalization crossing cameras. Furthermore, to remove the dependence on the ground truth illumination, we extend RCC to obtain a novel ranking-based method without ground truth illumination (RCC_NO) that learns the ranking model using simple partial binary preference annotations provided by untrained annotators rather than experts. RCC_NO also achieves better performance than the SM methods and most shallow learning-based methods with low costs of sample collection and illumination measurement.

Hybrid Active-Passive Shielding of Magnetic Field of Overhead Power Lines with Triangular Phase Conductors Arrangements

The aim of the work is to design a robust hybrid active-passive magnetic field shielding system created by overhead power lines with a triangular arrangement of phase wires, designed to increase the shielding efficiency of the initial magnetic field in residential premises to the level of sanitary standards and reduce the system's sensitivity to changes in system parameters. To achieve this goal, the following tasks were solved: the structure of a hybrid system of active-passive shielding was developed, and the synthesis of a system consisting of a double-circuit active and multi-circuit passive parts was performed. The synthesis of the system is reduced to solving a vector game, in which the vector payoff is calculated based on the solutions of the Maxwell equations in the quasi-stationary approximation using the COMSOL Multiphysics software. The solution of a multicriteria game is found on the basis of algorithms for optimizing a multi-swarm of particles from Pareto optimal solutions, taking into account binary preference relations. The most important results are theoretical and experimental studies of the effectiveness of the synthesized hybrid active-passive shielding system for the magnetic field created by overhead power lines with a triangular arrangement of phase wires in the shielding zone. The significance of the results obtained lies in the fact that in the course of designing a hybrid active and multiloop passive screens, the parameters of passive and active screens were calculated; as well as practical recommendations are given on the reasonable choice of the spatial arrangement of a multi-loop passive shield and two shielding windings of a robust system of hybrid shielding of the magnetic field created by overhead power lines with a triangular arrangement of phase wires.

To eat, or not to eat: a phantom decoy affects information-gathering behavior by a free-ranging mammalian herbivore.

When foraging, making appropriate food choices is crucial to an animal's fitness. Classic foraging ecology theories assume animals choose food of greatest benefit based on their absolute value across multiple dimensions. Consequently, poorer options are considered irrelevant alternatives that should not influence decision-making among better options. But heuristic studies demonstrate that irrelevant alternatives (termed decoys) can influence the decisions of some animals, indicating they use a relative rather than absolute evaluation system. Our aim was to test whether a decoy influenced the decision-making process-that is, information-gathering and food choice-of a free-ranging mammalian herbivore. We tested swamp wallabies, Wallabia bicolor, comparing their behavior toward, and choice of, two available food options over time in the absence or presence of the decoy. We used a phantom decoy-unavailable option-and ran two trials in different locations and seasons. Binary preferences (decoy absent) for the two available food options differed between trials. Irrespective of this difference, across both trials the presence of the decoy resulted in animals more likely to overtly investigate available food options. But, the decoy only shifted food choice, weakly, in one trial. Our results indicate that the decoy influenced the information-gathering behavior during decision-making, providing the first evidence that decoys can affect decision-making process of free-ranging mammalian herbivores in an ecologically realistic context. It is premature to say these findings confirm the use of relative evaluation systems. Whether the foraging outcome is more strongly affected by other decoys, food dimensions, or ecological contexts, is yet to be determined.

Optimization of spatial arrangement of magnetic field sensors of closed loop system of overhead power lines magnetic field active silencing

Aim. Development of a method for optimization of spatial arrangement and angular position of magnetic field sensors of a closed system to ensure maximum efficiency of active silencing canceling of the magnetic field generated by overhead power lines. Methodology. Spatial arrangement and angular position of magnetic field sensors of closed loop system of overhead power lines magnetic field active silencing determined based on binary preference relations of local objective for multi-objective minimax optimization problem, in whith the vector objective function calculated based on Biot–Savart law. The solution of this vector minimax optimization problem calculated based on nonlinear Archimedes algorithm of multi-swarm multi-agent optimization. Results. Results of simulation and experimental research of optimal spatial arrangement and angular position of magnetic field sensors of a closed system to ensure maximum efficiency of active silencing of the magnetic field generated by overhead power lines with a barrel-type arrangement of wires. Originality. The method for optimization of spatial arrangement and angular position of magnetic field sensors of a closed system to ensure maximum efficiency of active shielding of the magnetic field generated by overhead power lines is developed. Practical value. An important practical problem optimization of spatial arrangement and angular position of magnetic field sensors of a closed system to ensure maximum efficiency of active silencing of the magnetic field generated by overhead power lines has been solved.

An interactive ACO enriched with an eclectic multi-criteria ordinal classifier to address many-objective optimisation problems

Despite the vast research on many-objective optimisation problems, the presence of many objective functions is still a challenge worthy of further study. A way to treat this kind of problem is to incorporate the preferences of the decision maker (DM) into the optimisation process. In this paper, we introduce an interactive ant colony optimisation combined with an ordinal classification method in which classes are described by characteristic profiles. Through several interactions, the DM is supposed to identify some representative solutions of the classes ‘satisfactory’ and ‘dissatisfactory,’ which are used to initialise an ordinal classifier that increases the selective pressure by discriminating in favour of the ‘satisfactory’ class. This method can work with any either asymmetric or symmetric binary preference relation, a feature that confers a very wide generality. As another advantage, the interaction with the DM has minimal cognitive demands, which is an advisable feature for any approach based on interaction. Although the preference model is quite general, the proposal was tested using an eclectic model which combines compensatory preferences, veto conditions, and interval numbers to handle imprecise values; those preferences are aggregated in an asymmetric preference relation. Our approach performs particularly well in 10-objective problems according to the standards in the state-of-the-art literature. Numerical results and tests for statistical significance on the DTLZ and WFG test suites support this claim.

International trade with binary preferences and heterogeneous productivity

This study constructs a trade model between a developed and a developing country with binary preferences and heterogeneous productivity, finding that firm selection brings four new results with the possibility of arbitrage. First, we observe a price reversal, such that the price in the developed (high-income) country is lower than that in the developing (low-income) country. Second, we demonstrate the existence of export-only firms in the developing country due to the significant cross-country price differential; additionally, some firms in the developed country do not export despite having the ability. Third, the selection effect of domestic supply is stronger in the small country when trade is more liberalized. Finally, a higher degree of heterogeneity simultaneously enlarges the gains from trade in the developed country and losses from trade in the developing country.

The method of multi-objective parametric design of magnetic field active canceling robust system for residential multy-story buildings closed to double-circuit overhead power lines

Aim. Development the method of multi-objective parametric design for robust system of active canceling of magnetic field based on binary preference relations of local objective for multi-objective minimax optimization problem. Methodology. Spatial location coordinates of the compensating winding and the current in the shielding winding were determined during the preference-based multi-objective parametric design of systems of active canceling based on solution of the vector minimax optimization, in whith the vector objective function calculated based on Biot-Savart's law. The solution of this vector minimax optimization problem calculated based on nonlinear Archimedes algorithm. Components of Jacobi matrix and Hesse matrix calculated based on multi-swarm multi-agent optimization. Results. Theoretically and experimentally confirmed the effectiveness of reducing the level of the magnetic field in residential multy-storey old building of a double-circuit overhead power transmission lines with a barrel-type arrangement of wires by means of active shielding with two compensation winding. Originality. The method of multi-objective parametric design for robust system of active canceling of magnetic field based on binary preference relations of local objective for multi-objective minimax optimization problem is developed. Practical value. It is shown the possibility to reduce the level of magnetic field in residential multy-storey old building closed to double-circuit overhead power transmission lines with a barrel-type arrangement of wires by means of system of active canceling with two canceling winding to a level safe for the population with an induction of 0.5 μT.

Прогнозирование потенциально возможных неисправностей технической системы на основе нечетких графов и нечетких когнитивных карт

The development of a hierarchical step-by-step procedure for forecasting potential faults of a technical system based on fuzzy graphs and fuzzy cognitive maps is considered. Mathematically, this is based on the notion of a fuzzy binary preference relation. A fuzzy binary relation is always built on some set of objects. Since there are connections between objects and the consideration is conducted essentially at the level of a fuzzy graph, the connections between objects are described by the degree of affiliation and interpreted as «fault of object oi generates fault of object oj ». Next, it is necessary to allocate a hierarchy on this fuzzy graph, which will allow you to determine all possible scenarios for the occurrence of faults and the sequence of diagnostic measures. All problems of fault detection and localization, fault tolerance can be solved at the level of a fuzzy undirected graph, but obtaining an oriented graph additionally provides a fundamental opportunity for causal analysis of the occurrence and spread of faults in a technical system, their ranking by degree of importance, the influence of control actions on the behavior of the system.

Narrowing the Pareto set on the basis of fuzzy information about the ratio of ODA preferences

A multi-criteria choice model is considered, which includes a set of possible options, a numerical vector criterion and a fuzzy binary preference relation of the decision-maker person (DPR). The task of multi-criteria selection is to choose one or more "best" options from the Pareto set, that is, to narrow this set taking into account the information about the preference ratio of the DPR. Narrowing is carried out according to the axiomatic approach. The paper considers the algorithm for narrowing the Pareto set based on an arbitrary finite set of "quanta" of fuzzy information about the preference ratio of the DPR. Accordingly, an algorithm is proposed that allows, on the basis of an arbitrary set of clear information, to construct an estimate from above for an unknown set of options to be chosen, that is, to narrow the Pareto set. The purpose of this paper is to extend this algorithm to the case of a fuzzy preference relation, where the DPR assigns different degrees of certainty to its reasoning. In the fuzzy case under consideration, the set of options to be chosen and the top estimate constructed for it are also fuzzy. In the first section of the article, the statement of the problem of multi-criteria selection is presented and the basic axioms are formulated. The second chapter is devoted to the description of the reduction of this task to the geometric problem of constructing a fuzzy double cone. In the third section, a generalization of the algorithm is given, which makes it possible to construct the generators of a fuzzy double cone. Based on these constituents, a new vector criterion is constructed, the Pareto set with respect to which is the desired narrowing of the original Pareto set. An illustrative example is considered in the fourth chapter.

Independent natural extension for choice functions

We introduce an independence notion for choice functions, which we call ‘epistemic independence’ following the work by De Cooman et al. [17] for lower previsions, and study it in a multivariate setting. This work is a continuation of earlier work of one of the authors [29], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [11]. We obtain the many-to-one independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less expressive imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [28], which De Bock and De Cooman [2] have called S-independence. We show that neither is more general than the other.

Exposing some points of interest about non-exposed points of desirability

We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) gave an axiomatisation of binary preferences—on horse lotteries, rather than on gambles—that also leads to a unique representation in terms of sets of probability mass functions. To reach this goal, they use two devices, which we will call ‘SSK–Archimedeanity’ and ‘SSK–extension’. In this paper, we will make the arguments of Seidenfeld et al. (1995) explicit in the language of gambles, and show how their ideas imply even convexity and allow for conservative reasoning with evenly convex sets of desirable gambles, by deriving an equivalence between the SSK–Archimedean natural extension, the SSK–extension, and the evenly convex natural extension.

A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes

Skew-Gaussian Processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also represent asymmetric distributions. In a recent contribution, we showed that SkewGP and probit likelihood are conjugate, which allows us to compute the exact posterior for non-parametric binary classification and preference learning. In this paper, we generalize previous results and we prove that SkewGP is conjugate with both the normal and affine probit likelihood, and more in general, with their product. This allows us to (i) handle classification, preference, numeric and ordinal regression, and mixed problems in a unified framework; (ii) derive closed-form expression for the corresponding posterior distributions. We show empirically that the proposed framework based on SkewGP provides better performance than Gaussian processes in active learning and Bayesian (constrained) optimization. These two tasks are fundamental for design of experiments and in Data Science.

A model of discrete choice based on reinforcement learning under short-term memory

A family of models of individual discrete choice are constructed by means of statistical averaging of choices made by a subject in a reinforcement learning process, where the subject has a short, k-term memory span. The choice probabilities in these models combine in a non-trivial, non-linear way the initial learning bias and the experience gained through learning. The properties of such models are discussed and, in particular, it is shown that probabilities deviate from Luce’s Choice Axiom. Moreover, it is shown that the latter property is recovered as the memory span increases.Two different applications in utility theory are considered. In the first, we use the discrete choice model to generate a binary preference (weak stochastic order) relation on simple lotteries. We show that the relation violate the transitivity and independence axioms of expected utility theory. Furthermore, we establish the dependence of the preferences on frames, with risk aversion for gains, and risk seeking for losses. Based on these findings, we consider a parametric model of choice based on the probability maximization principle, as a model for deviations from the expected utility principle. To illustrate the approach, we apply this model to the classical problem of demand for insurance.

Modelling epistemic irrelevance with choice functions

We consider coherent choice functions under the recent axiomatisation proposed by De Bock and de Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning to define a notion of irrelevance, and we obtain the irrelevant natural extension in this framework: the least informative choice function that satisfies a given irrelevance assessment.

ACTIVE SHIELDING OF EXTERNAL MAGNETIC FIELD OF BUILT-IN TRANSFORMER SUBSTATIONS

This paper deals with the mitigation of low-frequency magnetic field of build-in transformer substations down to the reference level 0.5 μT in nearby living spaces. To meet the reference level, we substantiate the actuality of the usage of active shielding methods having higher efficiency, comparably to metal consuming passive shielding. We show that the optimization of parameters and localization of compensation coils is the main goal of the synthesis of the active shielding system. The solution of synthesis problem is based on the developed 3D numerical model by using particles multiswarm optimization algorithms from Pareto-optimal solutions set taking into account binary preference relations. This allows justifying the usage of simple active shielding system for magnetic field mitigation down to the reference level in living spaces, located near build-in transformer substations (2×400 kVA, 6/0.4 kV). The synthesized active shielding system has two plane compensation coils installed near the ceiling (wall) of the substation room. The area of each coil is less than 10 m2 and the number of ampere-turns is less than 30. We show that the efficiency of the active shielding system is 6 when it electric power consumption is less than 100 W. This allows mitigating the magnetic field down to 0.5 μT in 40 m2 living space located on top or side from the substation. The application of synthesized active shielding system (subject to the positive results of experimental studies of their full-scale physical models) allows solving the actual and socially significant problem of the health protection of tenants of residential buildings with build-in transformer substations from the negative effects of power frequency magnetic field.

Active Shielding of External Magnetic Field of Built-In Transformer Substations

This paper deals with the mitigation of low-frequency magnetic field of build-in transformer substations down to the reference level 0.5 μT in nearby living spaces. To meet the reference level, we substantiate the actuality of the usage of active shielding methods having higher efficiency, comparably to metal consuming passive shielding. We show that the optimization of parameters and localization of compensation coils is the main goal of the synthesis of the active shielding system. The solution of synthesis problem is based on the developed 3D numerical model by using particles multiswarm optimization algorithms from Pareto-optimal solutions set taking into account binary preference relations. This allows justifying the usage of simple active shielding system for magnetic field mitigation down to the reference level in living spaces, located near build-in transformer substations (2×400 kVA, 6/0.4 kV). The synthesized active shielding system has two plane compensation coils installed near the ceiling (wall) of the substation room. The area of each coil is less than 10 m2 and the number of ampere-turns is less than 30. We show that the efficiency of the active shielding system is 6 when it electric power consumption is less than 100 W. This allows mitigating the magnetic field down to 0.5 μT in 40 m2 living space located on top or side from the substation. The application of synthesized active shielding system (subject to the positive results of experimental studies of their full-scale physical models) allows solving the actual and socially significant problem of the health protection of tenants of residential buildings with build-in transformer substations from the negative effects of power frequency magnetic field.