大型群体决策问题中的简单多数规则（3个评选对象场合）

一个群体决策问题取决于两个因素,一个是群体决策的规则,另一个是投票。当选定群体决策规则时,一个群体决策问题由投票完全决定,此时,群体决策问题与投票之间一一对应。简单多数规则是个简单且被广泛采用的群体决策规则,但它有缺陷,我们可举出些群体决策问题使用简单多数规则没法从投票得到最后群体决策的结果。这里我们将给出一个简单多数规则的有趣性质,即在3个评选对象场合,使用简单多数规则没法从投票得到最后群体决策结果的n个评选人的群体决策问题的个数与所有n个评选人的群体决策问题的个数之比当评选人个数n趋向无穷时趋于零,这说明3个评选对象的大型群体决策场合,简单多数规则的缺陷不严重。     

Continuos social decision procedures

Classical social decision procedures are supposed to map lists of preference orderings into binary relations which describe society ‘preferences’. But when there are infinitely many alternatives the resulting plethora of possible preference orderings make it impossible to differentiate ‘nearby’ preference relations. If the preference information used to make social decisions is imperfect, society may wish to implement a continuous social decision procedure (SDP) so that nearby preference configurations will map into nearby social preference relations. It is shown here that a continuity requirement can severely restrict the admissible behavior of a social decision procedure. Furthermore, a characterization of continuous SDPs is presented which facilitates the examination of such procedures and their relation to various voting mechanisms.     

Improved bounds for the randomized decision tree Complexity of recursive majority

We consider the randomized decision tree complexity of the recursive 3‐majority function. We prove a lower bound of for the two‐sided‐error randomized decision tree complexity of evaluating height h formulae with error . This improves the lower bound of given by Jayram, Kumar, and Sivakumar (STOC'03), and the one of given by Leonardos (ICALP'13). Second, we improve the upper bound by giving a new zero‐error randomized decision tree algorithm that has complexity at most . The previous best known algorithm achieved complexity . The new lower bound follows from a better analysis of the base case of the recursion of Jayram et al. The new algorithm uses a novel “interleaving” of two recursive algorithms. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 612–638, 2016     

Eliciting Electre Tri category limits for a group of decision makers

Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.     

Condorcet Winners for Public Goods

In this work, we consider a public facility allocation problem decided through a voting process under the majority rule. A location of the public facility is a majority rule winner if there is no other location in the network where more than half of the voters would have been closer to than the majority rule winner. We develop fast algorithms for interesting cases with nice combinatorial structures. We show that the computing problem and the decision problem in the general case, where the number of public facilities is more than one and is considered part of the input size, are all NP-hard. Finally, we discuss majority rule decision making for related models.     

多数满意偏好规则的充分必要条件

研究基于满意选择的群体决策的一个基本数学理论问题. 给出并证明了群体在方案集上的任一群体满意偏好映射是多数满意偏好规则的充分必要条件.     

The Condorcet criterion and committee selection

Recent studies have evaluated election procedures on their propensity to select committees that meet a Condorcet criterion. The Condorcet criterion has been defined to use majority agreement from voters' preferences to compare the selected committee to all other committees. This study uses a different definition of the Condorcet criterion as defined on committees. The focus of the new definition is on candidates. That is, we consider majority agreement on each candidate in the selected committee as compared to each candidate not in the selected committee.This new definition of the Condorcet criterion allows for the existence of majority cycles on candidates within the selected committee. However, no candidate in the non-selected group is able to defeat any candidate in the selected committee by majority rule. Of particular interest is the likelihood that a committee meeting this Condorcet criterion exists. Attention is also given to the likelihood that various simple voting procedures will select a committee meeting this Condorcet criterion when one does exist.     

多数满意陪审团定理的极大和极小概率

证明了在群体中,当各个体正确判断方案满意性的概率越分散,由多数满意规则确定的相应群体正确判断方案满意性的概率将越大.根据这一结果得到：在所有的个体正确判断方案满意性的平均概率相同的情况下,由多数满意陪审团定理决定的群体正确判断方案满意性的极大概率和极小概率的表达式.     

Weighted multiple majority games with unions: Generating functions and applications to the European Union

An a priori system of unions or coalition structure is a partition of a finite set of players into disjoint coalitions which have made a prior commitment to cooperate in playing a game. This paper provides “ready-to-apply” procedures based on generating functions that are easily implementable to compute coalitional power indices in weighted multiple majority games. As an application of the proposed procedures, we calculate and compare coalitional power indices under the decision rules prescribed by the Treaty of Nice and the new rules proposed by the Council of the European Union.     

一种Vague偏好群体决策方法

采用 Vague集理论来描述和处理不确定信息或含糊信息 ,比采用模糊集理论描述和处理不确定信息或含糊信息在很多情况下更贴近客观现实 .在诸学者对模糊群体决策研究的基础上 ,提出一种 Vague群体决策方法 ,采用 Vague值作为决策者对备选方案的评估值 ,通过对决策者的各备选方案偏好值的集结 ,最后根据集结值的效用值对备选方案排序 ,进行决策 .     

Approaches to multistage one-shot decision making

In this research, multistage one-shot decision making under uncertainty is studied. In such a decision problem, a decision maker has one and only one chance to make a decision at each stage with possibilistic information. Based on the one-shot decision theory, approaches to multistage one-shot decision making are proposed. In the proposed approach, a decision maker chooses one state amongst all the states according to his/her attitude about satisfaction and possibility at each stage. The payoff at each stage is associated with the focus points at the succeeding stages. Based on the selected states (focus points), the sequence of optimal decisions is determined by dynamic programming. The proposed method is a fundamental alternative for multistage decision making under uncertainty because it is scenario-based instead of lottery-based as in the other existing methods. The one-shot optimal stopping problem is analyzed where a decision maker has only one chance to determine stopping or continuing at each stage. The theoretical results have been obtained.     

Aggregation and disaggregation in Markov decision models for inventory control

In this paper the possibility is investigated of using aggregation in the action space for some Markov decision processes of inventory control type. For the standard (s, S) inventory control model the policy improvement procedure can be executed in a very efficient way, therefore, aggregation in the action space is not of much use. However, in situations where the decisions have some aftereffect and, hence, the old decision has to be incorporated in the state, it might be rewarding to aggregate actions. Some variants for aggregation and disaggregation are formulated and analyzed. Numerical evidence is presented.     

On the empirical Bayes approach to multiple decision problems with sequential components

The empirical Bayes approach to multiple decision problems with a sequential decision problem as the component is studied. An empirical Bayesm-truncated sequential decision procedure is exhibited for general multiple decision problems. With a sequential component, an empirical Bayes sequential decision procedure selects both a stopping rule function and a terminal decision rule function for use in the component. Asymptotic results are presented for the convergence of the Bayes risk of the empirical Bayes sequential decision procedure.     

A fuzzy solution to a majority voting game

In the Fiorina-Plott majority voting game experiment several puzzling phenomena were discovered: (1) In the experiment series where the payoffs were small in general, the predictive performance of the core was markedly worse than in the high payoff series. (2) The core outcome was found to be defeatable by another proposal. (3) Some of the majority winning social outcomes were Pareto-suboptimal. (4) Even when there was no theoretical equilibrium point, there was a clear clustering of outcomes. The paper outlines a fuzzy decision making procedure which seems to be capable of explaining all the puzzling features (1)–(4). In the absence of data on membership functions the explanation provided is of non-predictive nature; it renders the observed outcomes plausible without precisely predicting each one of them.     

Designing information structures for quadratic decision problems

This paper investigates the problem of unconstrained optimization when there is only partial information on the random parameters in the objective function. The relation between the optimization performance and the available information is established. The best information structure design with fixed rank is described. The designing procedure is set up in such a way that successive information augmentation or deletion can be considered. The procedure can also be extended to multiperson decision problems.     

多数满意规则的一般陪审团概率及其极限

对于在一陪审团(群体)中,每一个决策者正确判断方案的满意性都具有各自不同概率的情况,建立了陪审团(群体)正确判断方案满意性概率的一般形式的定理.同时,证明了该陪审团(群体)正确判断方案满意性的概率,将随着参与决策者人数的增加趋于它的极限1.     

Dimension of complete simple games with minimum

Weighted majority games have the property that players are totally ordered by the desirability relation (introduced by Isbell in [J.R. Isbell, A class of majority games, Quarterly Journal of Mathematics, 7 (1956) 183–187]) because weights induce it. Games for which this relation is total are called complete simple games. Taylor and Zwicker proved in [A.D. Taylor, W.S. Zwicker, Weighted voting, multicameral representation, and power, Games and Economic Behavior 5 (1993) 170–181] that every simple game (or monotonic finite hypergraph) can be represented by an intersection of weighted majority games and consider the dimension of a game as the needed minimum number of them to get it. They provide the existence of non-complete simple games of every dimension and left open the problem for complete simple games.     

Utility efficiency and its approximation

Summary We assume a multi-attribute decision making problem under uncertainty with partial information on the decision maker's preferences, by a vector utility function with two components and imprecision over their scaling constants. We propose an approximation set whose determination may be easier than the one of the utility efficient set and we consider an interactive procedure which uses such approximation to decision aid. We study some nesting and convergence properties based on the interactive reduction of the approximation set. Finally, we illustrate the procedure with a numerical example.     

Supporting Learning in Evolving Dynamic Environments

In dynamic decision environments such as direct sales, customer support, and electronically mediated bargaining, decision makers execute sequences of interdependent decisions under time pressure. Past decision support systems have focused on substituting for decision makers' cognitive deficits by relieving them of the need to explicitly account for sequential dependencies. However, these systems themselves are fragile to change and, further, do not enhance decision makers' own adaptive capacities. This study presents an alternative strategy that defines information systems requirements in terms of enhancing decision makers' adaptation. In so doing, the study introduces a simulation model of how decision makers learn patterns of sequential dependency. When a system was used to manage workflows in a way predicted by the model to enhance learning, decision makers in a bargaining experiment learned underlying patterns of sequential dependencythat helped them adapt to new situations. This result is rare if not unique in the study of dynamic decision environments. It indicates that a shift, away from substituting for short-term deficits and toward enhancing pattern learning, can substantially improve the effectiveness of decision support in dynamic environments. Based on the specific findings in this study, this shift has important implications for designing information system workflows and potential future applications in interface design.