On the information about individual utilities used in social choice

This paper investigates the consequences of the requirement tha a social choice method should convey as much information as possible about the individuals' values. It is first shown that if interpersonal comparisons of utilities are excluded, then the only information about individual values that can be used in the context of social choice is ordinal information. It is then argued that Arrow's independence condition demands that only a part of the information about the individual preferences be used in the social choice. Finally, it is shown that the requirement of maximal information gives strong support to Smith's (1973) ‘separability’ condition. In combination with Smith's result this shows that the choice methods that convey the most information about individual preferences are the ‘generalized point systems’ (also called ‘scoring functions’ or ‘ranking systems’).     

Coalitional power structure without the pareto principle

In this paper we have extended Arrow's analysis to a framework where for any given profile of individual preference orderings the decision procedure specifies a non-trivial probability distribution over possible social orderings. We have demonstrated that if the social decision procedure satisfies certain probabilistic versions of weak independence of irrelevant alternatives, then it is characterized by a ‘power’ structure for all possible coalitions of individuals without assuming either the Pareto Principle or its antecedents. A generalised version of Arrow's impossibility theorem follows as a special case of our result. We have weakened Arrow's independence condition, and have shown the existence of a hierarchy of dictators without imposing the Pareto criterion.     

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.     

Bidders and dispenser: manipulative hypergames in a multinational context

The object of this paper is to present an introduction to the basic ideas of Hypergame Analysis, and to illustrate these by building some models of a particular type of situation.Hypergame Analysis is an extension of the Game-theoretic framework, the purpose of which is to enable one to model situations in which the various parties are not well-informed of each other's preferences and strategies. we take as a basic structure not a single game, but a linked set of ‘perceived’ games: this, in essence, is what constitutes a Hypergame. Misperceptions may arise accidentally or be deliberately induced. Thus, a player may be acting ‘rationally’ relative to the game he perceives, but this game itself may have been ‘set up’ to suit the interests of some other party.The technique is used to explore situations in which several parties (the ‘bidders’) negotiate competitively with another (the ‘dispenser’) who is able to accept whichever bidder's offer is most advantageous to him. In particular, the ability of the dispenser to ‘play off’ one bidder against another is examined. This is related to an account of the siting of new plant by a Multi-National Corporation. Some general implications are suggested: especially, it is argued that to have a reasonable chance of producing adequate forecasts in such difficult situations, modelling techniques must embody at least this degree of conceptual complexity.     

Consistent social choice functions and systems of distinct representatives

This paper concerns Peleg's construction of a strongly consistent voting system. The authors characterize the alternatives selected by the corresponding social choice correspondence in terms of systems of distinct representatives. This result allows the use of ‘rapid’ computational algorithms for this correspondence.     

Asymptotic structural characteristics of fuzzy measure and their applications

In fuzzy measure theory, as Sugeno's fuzzy measures lose additivity in general, the concept ‘almost’, which is well known in classical measure theory, splits into two different concepts, ‘almost’ and ‘pseudo-almost’. In order to replace the additivity, it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called ‘waxing’ and ‘waning’, and to introduce some new concepts, such as ‘autocontinuity’, ‘converse-autocontinuity’ and ‘pseudo-autocontinuity’. These concepts describe some asymptotic structural characteristics of a fuzzy measure.In this paper, by means of the asymptotic structural characteristics of fuzzy measure, we also give four forms of generalization for both Egoroff's theorem, Riesz's theorem and Lebesgue's theorem respectively, and prove the almost everywhere (pseudo-almost everywhere) convergence theorem, the convergence in measure (pseudo-in measure) theorem of the sequence of fuzzy integrals. In the last two theorems, the employed conditions are not only sufficient, but also necessary.     

Geometric composite indicators with compromise Benefit-of-the-Doubt weights

This paper builds on Van Puyenbroeck and Rogge's (2017) ‘indirect’ multiplicative Benefit-of-the-Doubt (BoD) index number framework, in which the linear, data-driven BoD-model is used to estimate the importance of various sub-indicators within a geometric composite index (CI). We present an integrated framework that combines optimistic and pessimistic BoD-based weighting that enables to (1) establish the degree of unbalance in countries’ policy portfolio mix, (2) identify multiple underlying factors to explain inter-temporal evolution, and (3) explain for differences in country policy performances under the different weighting schemes following a multiplicative Bortkiewicz decomposition. In doing so, we use alternative optimistic and pessimistic BoD-models as existing models suffer from potential drawbacks in the identification of a country's comparative strengths and weaknesses. We illustrate our results with social inclusion data for the EU-countries for the period 2008-2013.     

Measures of fuzzy sets and measures of fuzziness

The measures presented in this paper are defined by using Weber's concept of decomposable measures m of crisp sets, having in particular the Archimedean decomposable operations in view (Section 2). Measures $\text{m}$ of fuzzy sets are introduced as integrals with respect to m. For the Archimedean cases, Weber's integral will be used as alternative to Sugeno's and Choquet's concepts (Section 3). What ‘fuzziness’ means will be described by functions of fuzziness F (another name: entropy N-functions) with respect to a negation. In addition to the types of functions of fuzziness which are induced by concave functions, we discuss also the ones which are induced by fuzzy connectives (Section 4). Now, using m for measuring the ‘importance of items’ and F for the ‘fuzziness’ of the possible values of a fuzzy set ?, m?(F ° ?) serves us as a measure of the fuzziness $\text{F}$? of ?. The concepts of De Luca and Termini, Capocelli and De Luca, Kaufmann, Knopfmacher, Loo, Gottwald, Dombi and, under the restriction to the Archimedean cases, also the concepts of Trillas and Riera and Yager turn out to be special cases (Section 5).     

How mathematical impossibility changed welfare economics: A history of Arrow's impossibility theorem

During the 20th century, impossibility theorems have become an important part of mathematics. Arrow's impossibility theorem (1950) stands out as one of the first impossibility theorems outside of pure mathematics. It states that it is impossible to design a welfare function (or a voting method) that satisfies some rather innocent looking requirements. Arrow's theorem became the starting point of social choice theory that has had a great impact on welfare economics. This paper will analyze the history of Arrow's impossibility theorem in its mathematical and economic contexts. It will be argued that Arrow made a radical change of the mathematical model of welfare economics by connecting it to the theory of voting and that this change was preconditioned by his deep knowledge of the modern axiomatic approach to mathematics and logic.     

A footnote to The crisis in contemporary mathematics

We examine the preparation and context of the paper “The Crisis in Contemporary Mathematics” by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as ‘a debasement of meaning.’ The ‘debasement’ comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the ‘debasement’ comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle.     

Beyond methodology choice: critical systems thinking as critically systemic discourse

Professional competence in applied disciplines such as OR/MS requires both technical expertise and critically reflective skills. Yet, a widespread misconception has taken hold of the OR/MS community: ‘critical’ and ‘emancipatory’ systems methodologies are opposed to ‘hard’ and ‘soft’ ones as if they were sensible alternatives. Accordingly, adequate ‘methodology choice’ is now widely considered a key condition of reflective professional practice; critical systems thinking (CST) is understood to deal mainly with this issue. The present paper argues that this conception of CST is neither theoretically sound nor conducive to reflective practice. An examination of the two major current strands of CST suggests some basic requirements of an alternative conception: (1) Reflective practice depends more on a framework of critical argumentation and discourse than on a framework of methodology choice. (2) A well-conceived discursive systems approach will give a proper place to the public sphere. (3) The much-discussed emancipatory orientation of CST inheres in the methodological requirements of discourse rather than in an arbitrary ‘commitment’ on the part of the systems practitioner. (4) Systemic boundary critique—the methodological core concept of critical systems heuristics (CSH)—allows us to translate these requirements into practical methodology. (5) Contrary to present conceptions of methodological pluralism or ‘complementarism’, boundary critique must not be subordinated to methodology choice, for it is constitutive of all critical inquiry and practice. These considerations lead to a reconstitution of CST, and to a new view of reflective professional practice in general, as critically systemic discourse.     

The weak null condition for Einstein's equations

We show that Einstein's equations of General Relativity expressed in wave coordinates satisfy a ‘weak null condition’. In a forthcoming article we will use this to prove a global existence result for Einstein's equations in wave coordinates with small initial data. To cite this article: H. Lindblad, I. Rodnianski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

A note on levene's tests for equality of variances

Consider testing for equality variances in a one-way analysis of variance. Levene's test is the usual F-test for equality of means computed on psuedo-observations, which one defines as the absolute deviations of the data points from an estimate of the group ‘center’. We show that, asymptotically, Levene's test has the correct level whenever the estimate of group ‘center’ is an estimate of group median. This explains why published Monte-Carlo studies have found that Levene's original proposal of centering at the sample mean has the correct level only for symmetric distributions, while centering at the sample median has correct level even for asymmetric distributions. Generalizations are discussed.     

From social welfare ordering to acyclic aggregation of preferences

One way to overcome Arrow's impossibility theorem is to drop the requirement that the collective preference be transitive. If it is quasi-transitive (strict preferences are transitive) an oligarchy emerges. If it is only acyclic, many non-oligarchic aggregation rules are available, yet the resulting decision rules are poorly decisive: Nakamura's theorem characterizes acyclic and neutral Arrowian aggregators. We propose a parallel characterization of acyclic and anonymous aggregation methods.     

Arrow's theorem is not a surprising result

Arrow's theorem asserts that it is impossible to find a procedure which aggregates n given complete preorders into one complete preorder and which has ‘rational’ properties.Some authors have proposed to solve this problem in building what could be called ‘preaggregation methods’. The purpose of this paper is to study the Arrow's problematic in this context.The obtained results lead to an interpretation of Arrow's theorem which shows that it is rather natural, although many authors present it as a surprising result or even as a paradox.The last section compares the structures of the sets of decisive sets associated to aggregation and preaggregation procedures.     

Technical change and the prospects for employment—A suitable case for analysis?

The problem of unemployment experienced in most major OECD countries is increasingly recognised as being ‘structural’ in the sense that short-term Government measures are unlikely to stimulate a return to levels of unemployment experienced in the 1950's and 1960's. In this paper a framework is presented for assessing the problem in terms of the possible insufficiency of the employment-creating potential of the capital stock which can be profitably utilised, and is illustrated with reference to UK manufacturing industry. From this perspective, trends in investment activity and the technologies associated with new plant and equipment have, in association with other economic developments, contributed significantly to our current difficulties. Finally, an attempt is made to put the analysis described here into the context of the current unemployment debate and to assess the role of formal analysis in this field.     

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’.     

Analysing factors affecting the choice of emergent human resource capital

Ever since the announcement that UK higher education (HE) fees were to increase up to £9000, many universities have expressed concern about how to attract the best students while offering choice and promoting student mobility through broader access. This in turn has led to questioning how such complexity might be modelled using sophisticated operational research (OR) techniques. Because higher education institutions (HEIs) are now beginning to compete ‘against’ rather than ‘with’ each other, potential students are paying increased attention to where and what they will study, as well as graduate opportunities after their degree. Hence, the quality of education services becomes increasingly vital for HEIs in order to attract potential students. This study seeks to develop a framework of those factors affecting international (non-EU) students’ choice of institution. A number of factors were identified and collated from the existing literature providing a solid foundation on which to base this research. A survey approach was utilised to determine the importance of identified factors based on data collected from students of two different types of institutions (a university and a feeder institution). Through a better understanding of factors such as social influence, financial and career opportunities, universities should be well placed to construct models underpinned by OR principles that will promote scenario modelling and planning within HE.     

Le probleme d'etoiles pour graphes est np-complet

Nous appelons problème de ‘recollement de voisinages’ (RV) (‘star problem’ ou ‘problème d'ètoiles’) le problème qui consiste à savoir, étant donnée une famille $\text{V}$ de parties d'un ensemble S, s'il existe un graphe (non orienté et sans boucle) dont la famille de voisinages coïncide avec $\text{V}$. L'objectif de cet article est de montrer que le problème RV est NP-complet. La preuve s'appuiera sur l'èquivalence entre RV et le probléme de trouver un automorphisme d'ordre 2 dans un graphe quelconque (AUT2). La NP-complétude de AUT2 a été démontrée par Anna Lubiw [5].     

Defending and improving the ‘slotting fee’: how it can benefit all the stakeholders dealing with a newsvendor product with price and effort-dependent demand

‘Slotting fee’ (hereafter ‘SF’) is an upfront fee a ‘supplier’ is required to pay a retailer in order to have his product sold on the retailer's shelves. It is becoming increasingly common, but also widely reviled. This paper considers a newsvendor product whose expected demand is dependent on retail price and sales effort. The question we pose is: given that the Stackelberg-dominant retailer has to choose a pricing contract with which she transacts with the supplier, how would the supply-chain stakeholders fare when the retailer implements SF instead of another practical pricing contract? We show that, contradicting its negative public image, SF empowers the dominant retailer to specify contract terms that will benefit all the stakeholder-groups. That is, the supplier's and the retailer's profits are higher, the production workers are asked to produce more, and the consumers pay a lower retail price. We also propose a new ‘composite’ contract format that incorporates both the SF and ‘buyback’ features. This composite format empowers the retailer to provide even greater benefits to the supply-chain's stakeholders.