Afriat’s theorem for indivisible goods

We identify a natural counterpart of the standard GARP for demand data in which goods are all indivisible. We show that the new axiom (DARP, for “discrete axiom of revealed preference”) is necessary and sufficient for the rationalization of the data by a well-behaved utility function. Our results complement the main finding of Polisson and Quah (2013), who rather minimally modify the original consumer problem with indivisible goods so that the standard GARP still applies.     

On Vind’s theorem for an economy with atoms and infinitely many commodities

We extend Vind’s classical theorem on the measure of blocking coalitions valid in finite dimensional atomless economies (see Vind (1972)), to include the possibility of infinitely many commodities as well as the presence of atoms. The commodity space is assumed to be an ordered Banach space which has possibly the empty positive cone. The lack of interior points is compensated by an additional assumption of a cone of arbitrage that allows us to use Lyapunov’s convexity theorem in its weak form. The measure space of agents involves both negligible and non negligible traders. The extension is proved in the general class of Aubin coalitions for which a suitable version of Grodal’s result (Grodal (1972)) is also formulated. Our results wish to point out the relevance of cone conditions dealing with blocking coalitions of arbitrary measure or weight.     

A many-to-many ‘rural hospital theorem’

We show that the full version of the so-called ‘rural hospital theorem’ generalizes to many-to-many matching problems where agents on both sides of the problem have substitutable and weakly separable preferences. We reinforce our result by showing that when agents’ preferences satisfy substitutability, the domain of weakly separable preferences is also maximal for the rural hospital theorem to hold.     

Generic impossibility of Arrow’s impossibility theorem

Our major objective is to show that if there are infinitely many alternatives and society can be decomposed into the sum of two non-negligible coalitions, the set of all Arrovian collective choice rules that satisfy the ultrafilter property (its set of decisive coalitions form an ultrafilter), is nowhere dense in the set of all Arrovian collective choice rules. This result entails that (1) almost all Arrovian collective choice rules are non-dictatorial and (2) in any neighborhood of a dictatorial Arrovian collective choice rule, a nondictatorial Arrovian collective choice rule can be found, i.e., the property of admitting a dictator is not a locally stable property for Arrovian collective choice rules in the sense that the property does not withstand a small perturbation.     

An improved bound for the Shapley–Folkman theorem

We provide an up to 30% improvement in the Shapley–Folkman theorem error-bound, and briefly discuss its consequences for the course allocation problem.     

An introduction to Allan Gibbard’s oligarchy theorem paper

This note provides an introduction to the accompanying previously unpublished paper by Allan Gibbard in which he establishes his oligarchy theorem.     

An alternative direct proof of Gibbard’s random dictatorship theorem

We present an alternative proof of the Gibbards random dictatorship theorem with ex post Pareto optimality. Gibbard(1977) showed that when the number of alternatives is finite and larger than two, and individual preferences are linear (strict), a strategy-proof decision scheme (a probabilistic analogue of a social choice function or a voting rule) is a convex combination of decision schemes which are, in his terms, either unilateral or duple. As a corollary of this theorem (credited to H. Sonnenschein) he showed that a decision scheme which is strategy-proof and satisfies ex post Pareto optimality is randomly dictatorial. We call this corollary the Gibbards random dictatorship theorem. We present a proof of this theorem which is direct and follows closely the original Gibbards approach. Focusing attention to the case with ex post Pareto optimality our proof is more simple and intuitive than the original Gibbards proof.Received: 15 October 2001, Accepted: 23 May 2003, JEL Classification: D71, D72Yasuhito Tanaka: The author is grateful to an anonymous referee and the Associate editor of this journal for very helpful comments and suggestions. And this research has been supported by a grant from the Zengin Foundation for Studies on Economics and Finance in Japan.     

Goodness-of-fit testing of a count time series’ marginal distribution

Popular goodness-of-fit tests like the famous Pearson test compare the estimated probability mass function with the corresponding hypothetical one. If the resulting divergence value is too large, then the null hypothesis is rejected. If applied to i. i. d. data, the required critical values can be computed according to well-known asymptotic approximations, e. g., according to an appropriate \(\chi ^2\)-distribution in case of the Pearson statistic. In this article, an approach is presented of how to derive an asymptotic approximation if being concerned with time series of autocorrelated counts. Solutions are presented for the case of a fully specified null model as well as for the case where parameters have to be estimated. The proposed approaches are exemplified for (among others) different types of CLAR(1) models, INAR(p) models, discrete ARMA models and Hidden-Markov models.     

On the exact distribution of the Fisher-Behren’-Welch statistic

Summary For testing the significance of the difference between the unknown means of two normal populations having different unknown variances, we have the known Fisher-Behren’s-Welch test statistic. Several expressions for the distribution of this test statistic are available, and this paper is yet another attempt in the same direction. However, the expression given here appears to be, perhaps, more elegant and straight-forward than the ones available at present.     

Levers of logistics service providers’ efficiency in urban distribution

This paper identifies the most important factors that influence the productivity of the urban fleet of a Logistics Service Provider (LSP). Through a regression analysis on a dataset from distribution warehouses of a single LSP, three main levers are shown to have significant impacts on productivity, namely the network design, the vehicle loading strategy, and the business environment wherein the operations are carried out. This paper contributes to bridge the gap about the lack of works addressing the efficiency of LSPs operating in urban areas, by performing a detailed empirical analysis instead of taking an aggregated company perspective.     

Kalai and Muller’s possibility theorem: a simplified integer programming version

We provide a respecification of an integer programming characterization of Arrovian social welfare functions introduced by Sethuraman et al. (Math Oper Res 28:309–326, 2003). By exploiting this respecification, we give a new and simpler proof of Theorem 2 in Kalai and Muller (J Econ Theory 16:457–469, 1977).     

Bayes风险值

风险值(VaR)是最近几年发展起来的一种市场风险度量尺度，是目前国际上最常用的金融市场风险度量基准。传统的VaR估计方法基本上都依赖于历史数据，并且只能在市场处于正常变动时衡量所面临的风险。由于金融市场中影响资产收益状况的因素时刻都在变化之中，资产收益分布中的参数也是不断变化的，因此用Bayes方法预测未来收益状况的VaR更合适。本文给出了BVaR和BCVaR的概念，讨论了BVa／R的性质与特点，并对市场因子服从正态分布时组合BVaR以及非线性组合BVaR的计算进行了研究。     

Capture–recapture estimation based upon the geometric distribution allowing for heterogeneity

Capture–Recapture methods aim to estimate the size of an elusive target population. Each member of the target population carries a count of identifications by some identifying mechanism—the number of times it has been identified during the observational period. Only positive counts are observed and inference needs to be based on the observed count distribution. A widely used assumption for the count distribution is a Poisson mixture. If the mixing distribution can be described by an exponential density, the geometric distribution arises as the marginal. This note discusses population size estimation on the basis of the zero-truncated geometric (a geometric again itself). In addition, population heterogeneity is considered for the geometric. Chao’s estimator is developed for the mixture of geometric distributions and provides a lower bound estimator which is valid under arbitrary mixing on the parameter of the geometric. However, Chao’s estimator is also known for its relatively large variance (if compared to the maximum likelihood estimator). Another estimator based on a censored geometric likelihood is suggested which uses the entire sample information but is less affected by model misspecifications. Simulation studies illustrate that the proposed censored estimator comprises a good compromise between the maximum likelihood estimator and Chao’s estimator, e.g. between efficiency and bias.     

Feature weighted naïve Bayes algorithm for information retrieval of enterprise systems

Automated information retrieval is critical for enterprise information systems to acquire knowledge from the vast amount of data sets. One challenge in information retrieval is text classification. Current practices rely heavily on the classical naïve Bayes algorithm due to its simplicity and robustness. However, results from this algorithm are not always satisfactory. In this article, the limitations of the naïve Bayes algorithm are discussed, and it is found that the assumption on the independence of terms is the main reason for an unsatisfactory classification in many real-world applications. To overcome the limitations, the dependent factors are considered by integrating a term frequency–inverse document frequency (TF-IDF) weighting algorithm in the naïve Bayes classification. Moreover, the TF-IDF algorithm itself is improved so that both frequencies and distribution information are taken into consideration. To illustrate the effectiveness of the proposed method, two simulation experiments were conducted, and the comparisons with other classification methods have shown that the proposed method has outperformed other existing algorithms in terms of precision and index recall rate.     

On the distribution of the desirability index using Harrington’s desirability function

The concept of desirability is a means for complexity reduction of multivariate quality optimization. This paper provides a theoretical breakthrough regarding desirability indices, which application fields were formerly limited primarily by the lack of its distribution. Focussed are the distributions of Harrington’s desirability functions and different types of the desirability index.     

Using DEA for measuring teachers’ performance and the impact on students’ outcomes: evidence for Spain

This research contributes to the ongoing debate about differences in teachers’ performance. We introduce a new methodology that combines production frontier and impact evaluation insights that allows using DEA as an identification strategy of a treatment with high and low quality teachers within schools to assess their performance. We use a unique database of primary schools in Spain that, for every school, supplies information on two classrooms at 4th grade where students and teachers were randomly assigned into the two classrooms. We find considerable differences in teachers’ efficiency across schools with significant effects on students’ achievement. In line with previous findings, we find that neither teacher experience nor academic training explains teachers’ efficiency. Conversely, being a female teacher, having worked five or more years in the same school or having smaller class sizes positively affects the performance of teachers.     

A Cramér-type large deviation theorem for sums of functions of higher order non-overlapping spacings

Let U ₁, U ₂, . . . , U _n–1 be an ordered sample from a Uniform [0,1] distribution. The non-overlapping uniform spacings of order s are defined as \({G_{i}^{(s)} =U_{is} -U_{(i-1)s}, i=1,2,\ldots,N^\prime, G_{N^\prime+1}^{(s)} =1-U_{N^\prime s}}\) with notation U ₀ = 0, U _n = 1, where \({N^\prime=\left\lfloor n/s\right\rfloor}\) is the integer part of n/s. Let \({ N=\left\lceil n/s\right\rceil}\) be the smallest integer greater than or equal to n/s, f _m (u), m = 1, 2, . . . , N, be a sequence of real-valued Borel-measurable functions. In this article a Cramér type large deviation theorem for the statistic \({f_{1,n} (nG_{1}^{(s)})+\cdots+f_{N,n} (nG_{N}^{(s)} )}\) is proved.     

Causal complexity for passengers’ intentions to re-ride

This study explores the relationship among service range, ride convenience, motivation to ride, satisfaction with facilities, service satisfaction, and intention to re-ride. The conveyance of interest is the Puyuma Express because its transport service last year carries out the overall electrified era in eastern Taiwan and its vast passenger capacity breaks the record over the past 128 years. The very high passenger capacity includes passengers who are on their first ride but, to a much greater extent, passengers who are re-riding. This fact motivates this research. This work involves a carefully designed questionnaire, and uses both web-based and paper-based questionnaire surveys to collect data. The number of valid samples thus obtained was 228. Multiple regression analysis (MRA) and fuzzy set qualitative comparative analysis (fsQCA) are utilized to test proposed research framework. The two methods yield completely different results. MRA reveals that satisfaction with facilities, service satisfaction, ride convenience, and service range are together responsible for the strong intentions of passengers to re-ride. FsQCA identifies seven complex antecedent paths that are responsible for strong intentions to re-ride. The latter explains outcome more comprehensively than the former. The motivation to ride is an important condition in fsQCA and should not be eliminated as MRA suggests. This empirical study elucidates the causal complexity for passengers’ intentions to re-ride, and contributes to theory and practice in the domains of both transportation marketing and consumer behavior.     

Constructive and computable Hahn–Banach theorems for the (second) fundamental theorem of welfare economics

The Hahn–Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using non-constructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn–Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented economics intrinsically computational.