群体决策中Suzumura一致性选择函数理性化的充要条件

研究了Suzumura一致性选择函数的展示偏好描述,在已有的展示偏好定义基础上,给出了Suzumura一致性选择函数的展示偏好公理,并证明了该公理是Suzumura一致性选择函数理性化的充要条件.     

Social choice for bliss-point problems

This paper's concern is the axiomatic determination of social choice correspondences Ψ for a class of n-person problems that are characterized by some — generally — non-feasible bliss-point u(V)(?V∈τ . Meeting appropriate assumptions of ‘planner's rationality’ it is shown that Ψ is necessarily norm-induced, i.e. one can find some norm |·| in Rⁿ s.t. Ψ(V) = {u?V|6u-u(V)6=min{6v-u(V)6|v,V}}. The mathematical problem of recovering. from Ψ is one of integration which has its well-known parallel in the theory of revealed preference.     

Ranking fuzzy choice functions by their rationality indicators

In this paper we study two rationality indicators and two normality indicators of a fuzzy choice function. They express the degree of rationality or normality of this fuzzy choice function. This way we can establish a hierarchy in a given family of fuzzy choice functions with respect to their degree of rationality.     

Some properties of choice functions based on valued binary relations

Choice functions based on t-norms of valued binary relations are introduced. Strict preference is also specified with the use of a t-norm. Properties of the choice functions are investigated and rationality conditions are studied. Some classical particular cases are presented.     

Unions and the axiom of choice

We study statements about countable and well‐ordered unions and their relation to each other and to countable and well‐ordered forms of the axiom of choice. Using WO as an abbreviation for “well‐orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the countable union of countable sets is WO. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bases,spanning sets,and the axiom of choice

Two theorems are proved: First that the statement “there exists a field F such that for every vector space over F, every generating set contains a basis” implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over ?₂ has a basis implies that every well‐ordered collection of two‐element sets has a choice function. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equity,efficiency and rights in social choice

The impossibility of a Paretian liberal presented by Sen shows the incompatibility of the Pareto principle with a mild claim of libertarian rights when they are required of the collective choice rule with unrestricted domain. In view of the profound implications of this paradox, it is no wonder that there are many serious attempts in the literature to seek for a general resolution thereof. In this paper, we try to explore an avenue which has been left relatively less cultivated in the attempts to try to find a way out of this paradox, the essential idea thereof being to restrict the ‘legitimate’ exercise of the liberatarian rights by the claims of justice or equity. It will be shown that the gist of the successful resolution of the Pareto libertarian paradox along this line lies in the impartiality of the principle of justice held by the individuals and the prevalence of the sympathetic acceptance of each other's subjective preferences.     

Binariness and rational choice

The concept of numerical representability of preferences together with maximality is at the heart of the concept of rationality embodied in classical optimization models. The difficulty of representing social preferences arises from inherent intransitivities thrown up by democratic voting procedures and by non-binary choice rules which need to be adopted to cope with these intransitivities. An alternative (weaker) concept of representability is developed and it is shown that this concept can partially accommodate intransitivity and non-binariness. ‘Weak transitivity’ and ‘weak binaries’ conditions are provided and it is shown that these conditions are necessary and sufficient for ‘weak representability’. While the weak transitivity condition would be violated by social aggregation procedures, the non-binary functions used by social choice theorists do indeed satisfy the condition of ‘weak binariness’.     

政府支出结构、扭曲性税收及内生贴现因子

在一个无穷期限模型中,假设经济主体具有完全理性,通过将常数贴现因子转换为关于效用水平的内生变量,利用跨期优化方法重新考虑了政府支出结构、扭曲性税收对宏观经济变量的影响.尤其关注这两种变量的长期和短期变化对资本积累路径的影响,理论模型表明,当贴现因子内生化后,政府支出结构和扭曲性税收对宏观经济的影响会更为复杂,尤其体现在生产性支出上.     

The rigid relation principle,a new weak choice principle

The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well‐orders are rigid, but we prove that it is neither equivalent to the axiom of choice nor provable in Zermelo‐Fraenkel set theory without the axiom of choice. Thus, it is a new weak choice principle. Nevertheless, the restriction of the principle to sets of reals (among other general instances) is provable without the axiom of choice.     

Dynamic consumption and portfolio choice under prospect theory

This paper explicitly derives the optimal dynamic consumption and portfolio choice of an individual with prospect theory preferences. The individual is loss averse, endogenously updates his reference level over time, and distorts probabilities. We show that the optimal consumption strategy is rather insensitive to economic shocks. In particular, in case the individual sufficiently overweights unlikely unfavorable events, our model generates an endogenous floor on consumption. As a result, an individual with prospect theory preferences typically implements a (very) conservative portfolio strategy. We discuss implications of our results for the design of investment-linked annuity products.     

Countable choice and compactness

We work in set-theory without choice ZF. Denoting by the countable axiom of choice, we show in that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p1 (respectively p=0), and some closed subset F of [0,1]^I which is a bounded subset of ℓ^p(I), we show that (respectively DC, the axiom of Dependent Choices) implies the compactness of F.     

Benford's law and distractors in multiple choice exams

Suppose that in a multiple choice examination the leading significant digit of the correct options follows Benford's Law, while the leading digit of the distractors is uniform. Consider a strategy for guessing at answers that selects the option with the lowest leading digit with ties broken at random. We provide an expression for both the probability that this strategy selects the correct option and also the generalization to the probability of selecting the option with the lowest r significant digit string.     

Existence of equilibrium for generalized games in choice form and applications

This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies admit equilibrium; second, to study the solvability of several types of systems of vector quasi-equilibrium problems as an application. Our work outlines that there still is much to be gained from using the results concerning the existence of equilibrium of games as tools of research for other optimization problems.     

Multivalued social choice functions and strategic manipulation with counterthreats

In this paper, we examine the manipulability properties of social decision rules which select a non-empty subset of the set of alternatives. Assuming that if an individual prefers x to y, then he prefers the outcome set {x, y} to {y}, and also {x} to {x, y}, we show that a wide class of scf's which allow ties even in pairwise choice violates one of the weakest notions of strategyproofness — a single individual can profitably misrepresent his preferences, even when he takes into account the possibility of countercoalitions. This class of scf's also violates exact consistency — no equilibrium situation gives the same outcome set as the ‘true profile’.     

Metric spaces and the axiom of choice

We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.     

Stigmergy in comparative settlement choice and palaeoenvironment simulation

Decisions on settlement location in the face of climate change and coastal inundation may have resulted in success, survival or even catastrophic failure for early settlers in many parts of the world. In this study, we investigate various questions related to how individuals respond to a palaeoenvironmental simulation, on an interactive tabletop device where participants have the opportunity to build a settlement on a coastal landscape, balancing safety, and access to resources, including sea and terrestrial foodstuffs, while taking into consideration the threat of rising sea levels. The results of the study were analyzed to consider whether decisions on settlement were predicated to be near to locations where previous structures were located, stigmergically, and whether later settler choice would fare better, and score higher, as time progressed. The proximity of settlements was investigated and the reasons for clustering were considered. The interactive simulation was exhibited to thousands of visitors at the 2012 Royal Society Summer Science Exhibition at the “Europe's Lost World” exhibit. 347 participants contributed to the simulation, providing a sufficiently large sample of data for analysis. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–73, 2016     

Determining the effects of observed and unobserved heterogeneity on consumer brand choice

This paper investigates the effects of heterogeneity in consumer choice behaviour. Omitted consumer heterogeneity may lead to badly biased results, and wrong inferences concerning marketing strategies to follow. In this research we study the extent and the cause of this bias. We distinguish between observed and unobserved heterogeneity, by partialing out the effects of unmeasured heterogeneity and modelling it explicitly. The following questions will be addressed: What is unobserved heterogeneity and how much of it can be explained? How should heterogeneity be incorporated in consumer choice models? A hazard model is used for the analysis. The hazard model will yield patterns of switching among brands, as well as, the effect of marketing mix variables on brand choice and purchase timing. Differences between switchers and repeat purchasers are studied and the extent to which brand choice can be explained. Our model is estimated using scanner panel data. We find that it is important to include both observed and unobserved heterogeneity in order to obtain a better fit of the model. Our results show that it may be sufficient to only include observed heterogeneity to obtain unbiased parameter estimates. Including observed heterogeneity also reduces the aggregation or heterogeneity bias in the hazard function. © 1998 John Wiley & Sons, Ltd.