Ranking of Weighted Majority Rules

We study the uncertain dichotomous choice model. In this model a set of decision makers is required to select one of two alternatives, say ‘support’ or ‘reject’ a certain proposal. Applications of this model are relevant to many areas, such as political science, economics, business and management. The purpose of this paper is to estimate and compare the probabilities that different decision rules may be optimal. We consider the expert rule, the majority rule and a few in-between rules. The information on the decisional skills is incomplete, and these skills arise from an exponential distribution. It turns out that the probability that the expert rule is optimal far exceeds the probability that the majority rule is optimal, especially as the number of the decision makers becomes large.

The paper introduces the concept of polar decision rules and establishes that majority rules are polar rules. We identify second best rules and penultimate rules in cases that majority rules are optimal or the most inferior, respectively. We especially specify the almost expert rule and the almost majority rule as the secondary rules of the expert and majority rules, respectively.

This paper aims to find a suitable decision rule for a binary composite hypothesis-testing problem with a partial or coarse prior distribution. To alleviate the negative impact of the information uncertainty, a constraint is considered that the maximum conditional risk cannot be greater than a predefined value. Therefore, the objective of this paper becomes to find the optimal decision rule to minimize the Bayes risk under the constraint. By applying the Lagrange duality, the constrained optimization problem is transformed to an unconstrained optimization problem. In doing so, the restricted Bayesian decision rule is obtained as a classical Bayesian decision rule corresponding to a modified prior distribution. Based on this transformation, the optimal restricted Bayesian decision rule is analyzed and the corresponding algorithm is developed. Furthermore, the relation between the Bayes risk and the predefined value of the constraint is also discussed. The Bayes risk obtained via the restricted Bayesian decision rule is a strictly decreasing and convex function of the constraint on the maximum conditional risk. Finally, the numerical results including a detection example are presented and agree with the theoretical results.

In this paper, uniformly consistent estimation (learnability) of decision rules for pattern classification under a family of probability measures is investigated. In particular, it is shown that uniform boundedness of the metric entropy of the class of decision rules is both necessary and sufficient for learnability under each of two conditions: (i) the family of probability measures is totally bounded, with respect to the total variation metric, and (ii) the family of probability measures contains an interior point, when equipped with the same metric. In particular, this shows that insofar as uniform consistency is concerned, when the family of distributions contains a total variation neighborhood, nothing is gained by this knowledge about the distribution. Then two sufficient conditions for learnability are presented. Specifically, it is shown that learnability with respect to each of a finite collection of families of probability measures implies learnability with respect to their union; also, learnability with respect to each of a finite number of measures implies learnability with respect to the convex hull of the corresponding families of uniformly absolutely continuous probability measures.

Asymptotic analysis of statistical decision rules in econometrics

Problem statement: one of the important problems in modern intelligent robots, equipped with the Central nervous system (CNS), is the problem of forming images based on the analysis of sensory data. To solve this problem, it is necessary to build a classification model, on the basis of which, by logical analysis of the found regularities, the objects considered in the CNS can be attributed to a class. Purpose of research: mathematical formulation of the problem of forming images in the Central nervous system robot, analysis of the decisive rules for assigning images to a particular class of images and the construction of simple logical-probabilistic and logical-linguistic classification algorithms. Results: the mathematical formulation of the problem of forming images in the Central nervous system robot is formulated. In this problem statement, a set of images in the form of ordered sets with elements in the form of logical variables that take the value 0 or 1 is formed based on logical and mathematical analysis of sensory data about the robot’s selection environment. Each element of such sets is characterized by a set of features (attributes), whose values can be numeric, logical, or symbolic. Then these sets are compared in pairs with similar sets of reference images stored in the CNS database, and using the decision rules, the presented images are assigned to a particular class of images. Algorithms for constructing decision rules are analyzed and logical-probabilistic and logical-linguistic algorithms for implementing decision rules for image classification are obtained. Practical significance: The proposed principles of image formation in the CNS robot as a result of the analysis of sensory data characterized by a set of attributes with a certain degree of confidence, which can be set in the form of probability values or membership functions, and the resulting logical-probabilistic and logical-linguistic algorithms for their classification can be used in intelligent robots when processing incomplete and not completely reliable information.

Using tools for modelling and solving agricultural problems under risk

This work investigates the robustness of optimal decision rules under a changing size of a decision group where the competence of one member is outstanding while the others possess an identical competence. More specifically, we focus on the expert rule, the almost expert rule and the tie-breaking chairperson rule. We first establish criteria for the optimality of each of these rules and then use it to investigate their robustness. Robustness is an important property of decision rules, especially when cost of adjustment to a new rule is high. Our findings are that the expert rule and the chairperson rule are robust while the almost expert rule is not.

We have observed that some recent results cast serious doubts uponthe applicability of majority rule as a device for forming a group-willout of individual wills. On the other hand, majority rule has manyproperties to recommend it. Especially, the decisiveness propertyshould please anyone interested in efficiency considerations. How-ever, when it comes to the second major criterion, consistency, major-ity rule with pairwise comparison of alternatives often leads to diffi-culties. Indeed, we have seen that there is typically no core or Con-dorcet winner when the policy space is multidimensional real space.And when there is no core, the situation looks grim indeed for major-ity rule: literally any outcome may become the majority winner. Somerelief of this very strong result is provided by the fact that no majoritycycles can go through the outcomes that belong to the M2 bargainingset. This finding, of course, solves the problem facing majority rule onlyinsofar as a method can be devised by which the M2 bargaining set out-comes can be determined in a reliable way. Here, thus, we are con-fronted with the sincerity problem. The absence of the core can lead to chaotic trajectories of votingoutcomes in multidimensional space. However, there are ways of over-coming the difficulties if a sufficient amount of flexibility is allowedin institutional design. If we consider the various nonequilibrium solu-tion concepts, and the minimax set in particular, we can always designa decision rule which (under mild restrictions) makes the vote-maximiz-ing outcome trajectory enter the solution set. The flexibility needed isgreat, indeed: the decision rule, λ-majority, must be alterable for eachvoting situation. The determination of the winner in a pair-wise comparison of alter-natives is not the main source of the difficulties surrounding majorityrule. As a matter of fact, the method of building the agenda is the mostcrucial part of the problem of cyclical majorities. In multicandidatecontests the occurrence of cyclical majorities has motivated the studyof other.decision procedures in addition to the majority comparisonof alternatives. The most recent proposal, approval voting, is morestrategyproof than its competitors in the class of single-ballot, non-ranked voting systems. At the moment the relationships betweenapproval voting and majority rule are not clear. It seems that furtherstudy of the interrelationships of these procedures is called for. Thefeatures in which approval voting is superior to majority comparisonof pairs of alternatives, however, are not, strictly speaking, procedural,but are external to the method of making collective decisions.

Previous research has indicated sex differences in style of interaction for members in small groups. It was assumed that some of these sex differences could be attributed to demand characteristics in relation to specific topics discussed by group members in earlier investigations. The purpose of the present study was to investigate the relative importance of two such demand characteristics, decision rule (consensus rule vs. majority rule), and decision consequence (high vs. low consequences), in addition to the sex composition of the group membership. Adherence to the group decision was also studied. On a topic previously rated as important, 16 four-person groups of males and the same number of female groups met and deliberated on a decision regarding an academic policy. Later these undergraduate students indicated their preference on the decision topic. The results showed male—female differences not accounted for by decision rule, decision consequence, or group decision post-test change. Explanation of the sex differences was offered in terms of varying academic aspiration levels and incongruency with attained academic achievement. The results also lend partial support for the importance of some operating demand characteristics, as yet unidentified.

The purpose of economic decision rules is to guide decision makers who have competing goals or are uncertain about how their goals can be fulfilled. This chapter discusses the assumptions underlying major decision rules such as expected utility maximization, discounting of future events, maximin, and various types of efficiency criteria including cost effectiveness and Pareto efficiency. All of these decision rules impose restrictions on the information to be taken into account, and since these restrictions are value laden, so are the decision rules. However, in the process of applying decision rules, the value assumptions are often put out of sight instead of being brought forward and discussed.

CCTV inspections are frequently used to diagnose defects in underground sewer pipes. A model for classification of sewer pipe defects in video frames and a corresponding five-phase training method are proposed. The model is based on deep convolutional neural network with a sigmoid output layer and information-extreme decision rules. The training method includes augmentation, feature extractor training resemblant of a Siamese network with triplet mining and softmax, computation of binary code for each class, training with joint binary cross-entropy loss using binary codes for each class as label and optimization of a hyper-spherical container for each class in Hamming space based on information criterion. Information criterion, expressed in the paper as logarithmic function of accuracy characteristics, provides a robust and reliable model for the most difficult case in the statistical sense. Results of a simulation with the optimal model on a dataset provided by Ace Pipe Cleaning, Inc confirm the efficiency of the proposed model and method and their suitability for practical usage.

This focus issue of Physiological Measurement follows the 38th Annual International Computing in Cardiology (CinC) Conference, hosted in Hangzhou, China in September 2011 by Zhejiang University. Each year, the NIH-sponsored PhysioNet resource (http://physionet.org/) runs an open competition lasting several months, aimed at encouraging the development of solutions to an unsolved or poorly solved problem in biomedicine, in most cases making use of relevant clinical and experimental data provided freely by PhysioNet. Participants in these annual challenges discuss their diverse approaches to the Challenge problems during dedicated scientific sessions at CinC. The topics of these PhysioNet/CinC Challenges range from physiologic signal processing and analysis to forecasting and modelling clinically important events and processes.

The paper explores the effectiveness of the major decision rules commonly applied to the selection of investment alternatives. The rules are applied to a continual stream of simulated investments, as they arise period by period throughout the planning horizon. Thus the dynamics of investing now rather than later, with capital rationing, are taken into account. The practitioners' preference for the payback period is examined for a typical series of simulated investments, and the returns are compared against the returns of the more academically acceptable discounting decision rules. Particular attention is devoted to the benefits of each of the decision rules with reference to both risk and average returns.

In this paper we present a new approach to handling incomplete information and classifier complexity reduction. We describe a method, called D 3 RJ, that performs data decomposition and decision rule joining to avoid the necessity of reasoning with missing attribute values. In the consequence more complex reasoning process is needed than in the case of known algorithms for induction of decision rules. The original incomplete data table is decomposed into sub-tables without missing values. Next, methods for induction of decision rules are applied to these sets. Finally, an algorithm for decision rule joining is used to obtain the final rule set from partial rule sets. Using D3RJ method it is possible to obtain smaller set of rules and next better classification accuracy than classic decision rule induction methods. We provide an empirical evaluation of the D3RJ method accuracy and model size on data with missing values of natural origin.