Examination-Type Preferences of College Science Students and Their Faculty in Israel and USA: A Comparative Study

The science-examination preferences of college science students and their science faculty were surveyed, using the TOPE questionnaire at a teacher training and a community college in Israel and the U.S., respectively. The results obtained in the two countries were “intrally” and “interly” compared, in total and by gender, in terms of significant/no significant differences in the preferences made and the reasons provided by the students and faculty for their ranking. The findings suggest that: (a) college science students prefer mostly, the Israelis more so than the Americans, the nonconventional, written exams in which time is unlimited and any materials are allowed; (b) American college science students prefer the traditional class science examination (G) significantly more than their Israeli counterparts; (c) the preference of higher order cognitive skills (HOCS)-oriented exams (B. I and H) is significantly higher for female science students in Israel compared with no gender difference concerning the preferred examinations in the US, and rejection of oral examinations by all in both countries, significantly more by female students; and (d) there exists a significant gap between the preferred type of examinations of science students and their faculty in both countries. In view of the HOCS-orientation and the goal of conceptual understanding in current reforms of science education worldwide, the consonance between these curriculum objectives and examination practices is advocated. This, in turn, requires that provisions be made to lessen the gap between science teachers and their students' examination type preferences for better science learning to occur.     

Stochastic dominance and parameter estimation: The case of symmetric stable distributions

Stochastic dominance rules can be applied to the selection of statistical estimators. This paper applies the procedure to estimators of location parameters of stable distributions: the mean and the median. It was found that the preference of one estimator over another depends on the characteristic exponent and on the sample size. Furthermore for some combinations of characteristic exponents and sample size we found that the stochastic dominance rule yields no preference implying that depending on one's utility function one may prefer the mean over the median or vise versa. This result differs from the common mean squared error criterion.     

Comparing influence theories in voting games under locally generated measures of dissatisfaction

The Isbell desirability relation (I), the Shapley?CShubik index (SS) and the Banzhaf?CColeman index (BC) are power theories that grasp the notion of individual influence in a yes?Cno voting rule. Also, a yes?Cno voting rule is often used as a tool for aggregating individual preferences over any given finite set of alternatives into a collective preference. In this second context, Diffo Lambo and Moulen (DM) have introduced a power relation which ranks the voters with respect to how ably they influence the collective preference. However, DM relies on the metric d that measures closeness between preference relations. Our concern in this work is: do I, SS, BC and DM agree when the same yes?Cno voting rule is the basis for collective decision making? We provide a concrete and intuitive class of metrics called locally generated (LG). We give a characterization of the LG metrics d for which I, SS, BC and DM agree on ranking the voters.     

A consensus-based probabilistic linguistic gained and lost dominance score method

This paper proposes a comprehensive Multiple Criteria Group Decision Making (MCGDM) method with probabilistic linguistic information based on a new consensus measure and a novel outranking method, Gained and Lost Dominance Score (GLDS). Firstly, new operations of the probabilistic linguistic term sets are introduced based on the adjusted rules of probabilistic linguistic term sets and the linguistic scale functions for semantics of linguistic terms. After defining a new consensus measure based on the correlation degree between probabilistic linguistic term sets, we develop a consensus reaching method to improve the consensus degree of a group. To rank alternatives reasonably, we further propose the GLDS method which considers both the “group utility” and the “individual regret” values. The core of the GLDS is to calculate the gained and lost dominance scores that the optimal solution dominates all other alternatives in terms of the net gained dominance flow and the net lost dominance flow. Then, we integrate the GLDS ranking method with the consensus reaching process and develop a consensus-based PL-GLDS method to solve the MCGDM problems with probabilistic linguistic information. Finally, the proposed method is validated by a case study of selecting optimal green enterprises. Some comparative analyses are given to show the efficiency of the proposed method.     

Pure strategy Nash equilibria and the probabilistic prospects of Stackelberg players

We consider the set of all m×n bimatrix games with ordinal payoffs. We show that on the subset E of such games possessing at least one pure strategy Nash equilibrium, both players prefer the role of leader to that of follower in the corresponding Stackelberg games. This preference is in the sense of first-degree stochastic dominance by leader payoffs of follower payoffs. It follows easily that on the complement of E, the follower’s role is preferred in the same sense. Thus we see a tendency for leadership preference to obtain in the presence of multiple pure strategy Nash equilibria in the underlying game.     

Partial stochastic dominance via optimal transport

In recent years, a range of measures of “partial” stochastic dominance have been introduced. These measures attempt to determine the extent to which one distribution is dominated by another. We assess these measures from intuitive, axiomatic, computational and statistical perspectives. Our investigation leads us to recommend a measure related to optimal transport as a natural default.     

A probabilistic framework for the design of instance-based supervised ranking algorithms in an ordinal setting

In this article, we present a probabilistic framework which serves as the base from which instance-based algorithms for solving the supervised ranking problem may be derived. This framework constitutes a simple and novel approach to the supervised ranking problem, and we give a number of typical examples of how this derivation can be achieved. In this general framework, we pursue a cumulative and stochastic approach, relying heavily upon the concept of stochastic dominance. We show how the median can be used to extract, in a consistent way, a single (classification) label from a returned cumulative probability distribution function. We emphasize that all operations used are mathematically sound, i.e. they only make use of ordinal properties. Mostly, when confronted with the problem of learning a ranking, the training data is not monotone in itself, and some cleansing operation is performed on it to remove these ‘inconsistent’ examples. Our framework, however, deals with these occurrences of ‘reversed preference’ in a non-invasive way. On the contrary, it even allows to incorporate information gained from the occurrence of these reversed preferences. This is exactly what happens in the second realization of the main theorem.     

Coevolution of role preference and fairness in the ultimatum game

Traditional economics assumes that humans are rational. However, it is known that humans behave fairly in the ultimatum game (UG). There are various explanations for this apparent paradox, such as the “inequity aversion.” However, the role preference (proposer or responder) of humans in the UG is obscure. I conducted a UG scenario experiment where subjects were asked their role preference in addition to their decision in the game. The results showed that the subjects prefer to be proposers rather than responders. In particular, it was found that rational subjects had a high preference for the proposer role. On the basis of these results, I conducted evolutionary simulations of the UG, where each individual has role preference intensity. A role is allocated to the individual proportional to the preference intensity. The results showed coevolution of role preference and fairness. The preference for the proposer role evolved when rational strategy evolved, whereas this preference weakened as rationality decreased. This indicates that fairness has a strong link with role preference; in other words, human fairness is always threatened by the “power and position” of some particular individuals. Hence, its equal distribution among individuals may be effective in maintaining a high level of fairness. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

不确定性对混合CVaR约束库存系统的影响

运用应用概率中的随机占优研究需求不确定性对混合CVaR约束库存系统最优订购量和最优利润的影响。引入刻画决策者风险态度的“风险偏好系数”,得到系统最优订购量和最优利润关于风险偏好系数的单调性。研究表明随机大需求总会导致系统较高的最优订购量和最优利润;在割准则序意义下,最优订购量可能随需求可变性的增加而增加也可能随需求可变性的增加而减少;在二阶随机占优且风险偏好系数大于等于1的情况下系统最优利润具有随机单调性,然而当风险偏好系数小于1时最优利润在二阶随机占优意义下的结论不一定成立,我们通过一个数值例子来说明。     

Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions

We present a new method, called UTA^GMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives A^R ⊆ A, called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set A: the necessary weak preference relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete relation. The UTA^GMS method is intended to be used interactively, with an increasing subset A^R and a progressive statement of pairwise comparisons. When no preference information is provided, the necessary weak preference relation is a weak dominance relation, and the possible weak preference relation is a complete relation. Every new pairwise comparison of reference alternatives, for which the dominance relation does not hold, is enriching the necessary relation and it is impoverishing the possible relation, so that they converge with the growth of the preference information. Distinguishing necessary and possible consequences of preference information on the complete set of actions, UTA^GMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTA^GMS software. Some extensions of the method are also presented.     

On the existence of nonlinear Dirac-geodesics on compact manifolds

We show that for super-linear nonlinearity, there exists a “non-trivial” nonlinear Dirac-geodesic on ${\mathbb{T}^n_{\Gamma}=\mathbb{R}^n/\Gamma}$ , a flat tori, in each “bosonic” sector. We also show that for any compact Riemannian manifold with “bumpy” metric, there exists a non-trivial nonlinear Dirac-geodesic in each bosonic sector if the nonlinearity is cubic or super-cubic and “large”. Our proof is based on critical point theory, in particular, a generalized linking argument applied to a strongly indefinite functional on a fibered Hilbert manifold.     

Realization of digraphs by preferences based on distances in graphs

Consider a graph G with two distinguished sets of vertices: the voters and the candidates. A voter v prefers candidate x to candidate y if d(v, x) < d(v, y). This preference relation defines an asymmetric digraph whose vertices are the candidates, in which there is an arc from candidate x to candidate y if and only if more voters prefer x to y than prefer y to x. T. W. Johnson and P. J. Slater (“Realization of Majority Preference Digraphs by Graphically Determined Voting Patterns,” Congressus Numerantium, vol. 67 [1988] 175-186) have shown that each asymmetric digraph of order n can be realized in this way using a graph of order O(n²). We present a new construction reducing the quadratic upper bound to a linear bound. © 1995 John Wiley & Sons, Inc.     

Characterizing an ℵ ∈ -saturated model of superstable NDOP theories by its\mathbb{L}_{\infty ,\aleph _ \in ^ - } -theory

Assume a complete countable first order theory is superstable with NDOP. We know that any ? _∈ -saturated model of the theory is ? _∈ -prime over a non-forking tree of “small” models and its isomorphism type can be characterized by its $\mathbb{L}_{\infty ,k} $ (dimension qualifiers)-theory, or, if you prefer, appropriate cardinal invariants. We go one step further by providing cardinal invariants which are as finitary as seem reasonable.     

Multi-criteria semantic dominance: A linguistic decision aiding technique based on incomplete preference information

A linguistic decision aiding technique for multi-criteria decision is presented. We define a relation between alternatives as multi-criteria semantic dominance (MCSD). It adopts the similar ideal of the stochastic dominance by utilizing the partial information of the decision maker’s preference, which is only ordinal or partially cardinal. The MCSD rules based on three typical types of semanteme functions are introduced and proven. By using these rules, all the alternatives under consideration are divided into two mutually exclusive sets called efficient set and inefficient set. The decision maker who has such a semanteme function will never choose the alternative from the corresponding inefficient set as the optimal one. In such a way, when we analyze the linguistic decision information, the inherent fuzziness of preference can be handled and several controversial operations of the linguistic terms can be avoided. An example is also provided to illustrate the procedure of the proposed method.     

Robust multi-criteria ranking with additive value models and holistic pair-wise preference statements

We consider a problem of ranking alternatives based on their deterministic performance evaluations on multiple criteria. We apply additive value theory and assume the Decision Maker’s (DM) preferences to be representable with general additive monotone value functions. The DM provides indirect preference information in form of pair-wise comparisons of reference alternatives, and we use this to derive the set of compatible value functions. Then, this set is analyzed to describe (1) the possible and necessary preference relations, (2) probabilities of the possible relations, (3) ranges of ranks the alternatives may obtain, and (4) the distributions of these ranks. Our work combines previous results from Robust Ordinal Regression, Extreme Ranking Analysis and Stochastic Multicriteria Acceptability Analysis under a unified decision support framework. We show how the four different results complement each other, discuss extensions of the main proposal, and demonstrate practical use of the approach by considering a problem of ranking 20 European countries in terms of 4 criteria reflecting the quality of their universities.     

均值限制相似优势粗糙集及决策分析模型研究

针对不完备信息系统中的偏好多属性决策问题,提出了一种基于均值限制相似优势粗糙集的决策分析模型.首先提出了均值限制相似优势关系的概念;然后在均值限制相似优势关系下得到知识的粗糙近似和属性约简,给出了分类决策规则.与相似优势关系和限制相似优势关系比较研究的结果表明:均值限制优势关系的分类精度和质量介于二者之间,而分类误差率则优于相似优势关系和限制相似优势关系,得到的决策规则可信度更高,决策模型与实际情况更加相符.     

Linear extensions of partial orders and reverse mathematics

We introduce the notion of τ‐like partial order, where τ is one of the linear order types ω, ω*, ω + ω*, and ζ. For example, being ω‐like means that every element has finitely many predecessors, while being ζ‐like means that every interval is finite. We consider statements of the form “any τ‐like partial order has a τ‐like linear extension” and “any τ‐like partial order is embeddable into τ” (when τ is ζ this result appears to be new). Working in the framework of reverse mathematics, we show that these statements are equivalent either to $\mathsf {B}{\Sigma }^{0}_{2}$ or to $\mathsf {ACA}_0$ over the usual base system $\mathsf {RCA}_0$.     

Semi-Markov processes and α-invariant distributions

A semi-Markov process is easily made Markov by adding some auxiliary random variables. This paper discusses the I-type quasi-stationary distributions of such “extended” processes, and the α-invariant distributions for the corresponding Markov transition probabilities; and we show that there is an intimate relation between the two. The results have relevance in the study of the time to “absorption” or “death” of semi-Markov processes. The particular case of a terminating renewal process is studied as an example.     

Valued preference-based instantiation of argumentation frameworks with varied strength defeats

A Dung-style argumentation framework aims at representing conflicts among elements called arguments. The basic ingredients of this framework is a set of arguments and a Boolean abstract (i.e., its origin is not known) binary defeat relation. Preference-based argumentation frameworks are instantiations of Dung's framework in which the defeat relation is derived from an attack relation and a preference relation over the arguments. Recently, Dung's framework has been extended in order to consider the strength of the defeat relation, i.e., to quantify the degree to which an argument defeats another argument. In this paper, we instantiate this extended framework by a preference-based argumentation framework with a valued preference relation. As particular cases, the latter can be derived from a weight function over the arguments or a Boolean preference relation. We show under some reasonable conditions that there are “less situations” in which a defense between arguments holds with a valued preference relation compared to a Boolean preference relation. Finally, we provide some conditions that the valued preference relation shall satisfy when it is derived from a weight function.