Continuously Representable Paretian Quasi-Orders

Two forms of continuity are defined for Pareto representations of preferences. They are designated “continuity” and “coordinate continuity.” Characterizations are given of those Pareto representable preferences that are continuously representable and, in dimension two, of those that are coordinate-continuously representable.     

Representability of Ordinal Relations on a Set of Conditional Events

Any dynamic decision model should be based on conditional objects and must refer to (not necessarily structured) domains containing only the elements and the information of interest. We characterize binary relations, defined on an arbitrary set of conditional events, which are representable by a coherent generalized decomposable conditional measure and we study, in particular, the case of binary relations representable by a coherent conditional probability.     

Positionalist voting functions

Positionalist voting functions are those social choice functions where the positions of the alternatives in the voter's preference orders crucially influence the social ordering of the alternatives. An important subclass consists of those voting functions where numbers are assigned to the alternatives in the preference orders and the social ordering is computed from these numbers. Such voting functions are called representable. Various well-known conditions for voting functions are introduced and it is investigated which representable voting functions satisfy these conditions. It is shown that no representable voting function satisfies the Condorcet criterion. This condition and Arrow's independence condition, which are typical non-positionalist conditions, are shown to be incompatible. The Borda function, which is a well-known positionalist voting function, is studied extensively, conditions uniquely characterizing it are given and some modifications of the function are investigated.My thanks are due to professor Bengt Hansson for encouragement and several helpful suggestions.     

A note on manipulability of large voting schemes

A voting system is a rule which assigns to every possible combination of votes (by any number of individuals) an alternative. We define the notion of asymptotic nonmanipulability for voting systems, and prove that every representable positionalist voting system is asymptotically nonmanipulable. Various aspects of manipulation of large voting schemes and several examples are also discussed.     

Ranking sets additively in decisional contexts: an axiomatic characterization

Ranking finite subsets of a given set X of elements is the formal object of analysis in this article. This problem has found a wide range of economic interpretations in the literature. The focus of the article is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn (1996), Journal of Mathematical Psychology 40, 64–77 showed that the number of sufficient and necessary conditions that are needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this article proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu’s (1990), Recherches Economiques de Louvain 56, 383–390) characterization of the cardinality-based rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of “focal” elements is not given ex-ante; but brought out by the axioms.      

清末民初初等小学课程变迁考--以历史、地理、格致科为中心

1904年，清政府仿照日本学制，颁布《奏定学堂章程》，将历史、地理与格致科纳入中国初等小学课程体系。以京师为例，初小“三科”课程实施初具规模；然国情日艰，民基不稳，为配合预备立宪推广教育之旨，1909年学部上奏将“三科”一并纳入国语科。学部此次“己酉改制”实为宏济艰难，一开始便受到教育人士的质疑与诟病；1922年新学制将“三科”以自然科与社会科的形式重新纳入初小课程，这不仅是对教育规律与受教育者的尊重，也是中国新式教育逐步本土化的体现。     

Subjective utility with upper and lower probabilities on finite states

This article is concerned with thresholds of discrimination of preference judgments under uncertainty. We establish an axiomatic characterization for a threshold representation, where thresholds are represented by inexact measurement of subjective probabilities, i.e., upper and lower probabilities. Since upper and lower probabilities need not be additive, the representational form adopts the Choquet integration.     

A Theory of Rational Choice under Ignorance

This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called `Simultaneous Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons.     

香港市民阶层流动意识探析:结构与认同下难圆的“香港梦”

1960年代香港经济的腾飞给香港市民带来了乐观的阶层流动意识,“香港梦”成了描述香港社会阶层结构相对开放的一个大众话语。但1980年代中期以来,阶层结构进入一个稳定的时期,客观的远距离阶层流动消失,这种乐观感也随之消失,1990年代的金融风暴和住房泡沫的破灭,使香港进入了一个“中下流”社会。本文基于阶层化的理论,以经验数据为准,发现中下层的市民客观阶层与主观阶层定位都处于低下地位,而拥有比较悲观的向上流动意识,这反过来又制约他们向上流动,“香港梦”失去了现实的社会基础。     

On the characterization of weighted simple games

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions.     

Expected utility with lower probabilities

An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory to characterize uncertainty neutrality and different degrees of uncertainty aversion.We are grateful to Birgit Grodal, Salvatore Modica, David Schmeidler, and an anonymous referee for comments, help, and encouragement. Financial support from the Danish Social Sciences Research Council is acknowledged.     

Nash Equilibrium with Lower Probabilities

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings.     

Monetary policy,trade-offs and the transmission of UK Monetary Policy

We provide a new method to model changes in monetary policy of the Bank of England (BoE) as well as the impact of these changes on UK economy. This is important as central bankers have widened the range of instruments in their monetary policy toolbox. Specifically, we estimate a proxy for the monetary policy stance and then analyse a time-varying parameter vector autoregressive with stochastic volatility model to explain the BoE’s trade-offs when making policy decisions and as well as to demonstrate dynamic impacts of monetary policy on inflation and economic growth. The empirical results show that our estimated monetary policy proxy is better at capturing the BoE’s policy when the interest rate lower bound becomes binding.     

Information evaluation under nonadditive expected utility

We examine the choice-of-single-stage-experiment problem (Raiffa and Schlaifer, 1961) under the assumption that the decider's (weak) preference relation satisfies Schmeidler's (1989) or Gilboa's (1987) axiomatization and is thus representable by a nonadditive expected-utility functional as a Choquet integral w.r.t. a monotone probability measure on events. The basic properties of information value, certainty equivalent of information cost, net gain of information, and optimal choice of experiment that obtain (La Valle, 1968) when satisfies the Anscombe-Aumann (1963) or Savage (1954) axiomatizations continue to obtain in the more general Schmeidler-Gilboa context-provided that there is no incentive to randomize the choice of experiment. When this proviso fails, information value can in general be assigned only to the set of available experiments.     

When an Event Makes a Difference

For (S, Σ) a measurable space, let and be convex, weak^* closed sets of probability measures on Σ. We show that if ∪ satisfies the Lyapunov property , then there exists a set A ∈ Σ such that min_μ1∈ μ₁(A) > max_μ2 ∈ (A). We give applications to Maxmin Expected Utility (MEU) and to the core of a lower probability.     

京沪白话报:启蒙的两种路向——《中国白话报》、《京话日报》之比较

本文讨论《中国白话报》与《京话日报》所代表的晚清京沪白话报纸不同的启蒙路向 ,试图从启蒙姿态、社会功能、地域文化等方面解释白话报这一启蒙形式在京沪两地遭遇不同命运的原因。两种启蒙路向在中国社会有效性的不同 ,也预示“五四”等启蒙运动从此到彼的某种转向 ,以及这种选择给予“启蒙”的影响。     

M-矩阵与其逆矩阵的Hadamard积最小特征值的新下界

关于M-矩阵与其逆矩阵的Hadamard积A。A-1,给出A。A-1的最小特征值下界的一些新的估计式,新下界估计式只依赖于矩阵的元素,易于计算。算例表明,新估计式有效地改进了Fiedler和Markham的猜想,也改进了其它已有的结果。     

A possibilistic hierarchical model for behaviour under uncertainty

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent to some of the earlier, possibilistic models and also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions.     

Optimism as a Mediator of the Relation Between Perceived Parental Authoritativeness and Adjustment Among Adolescents: Finding the Sunny Side of the Street

Authoritative parenting has been associated with positive outcomes for children and adolescents, but less is known about the mechanisms responsible for such effects. Two longitudinal studies examined the hypothesis that the relation between authoritative parenting and adolescents’ adjustment is mediated by adolescents’ level of dispositional optimism. In Study 1, university students’ perceptions that their parents were authoritative predicted higher self‐esteem, lower depression, and better university adjustment during the students’ transition into, and throughout, university. Importantly, these relations were mediated by students’ levels of optimism. In Study 2, high school students’ perceptions that their parents were authoritative predicted higher self‐esteem and lower depression six years later when they were young adults, and these relations again were mediated by students’ level of dispositional optimism.     

浅析城市低龄男性老人的角色转换和家庭再融入

在我国,男性长期以来无论是在家庭中还是社会生活中一直都扮演着支柱的角色,展现以强者的姿态。然而,不能忽视的是男性较之于女性在人生各个时期所要承受的更多更大的压力。本文以城市低龄男性老人为研究对象,通过对其社会角色转换的描述和分析展现出低龄男性老人所面临的问题和困境,并进一步讨论了他们的社会参与问题,尤其是家庭再融入。