Una funzione ordinale di benessere sociale

In questo lavoro trattiamo il problema di come amalgamare preferenze di individui in una preferenza sociale in relazione a certe alternative determinando una preferenza sociale che soddisfa i due Assiomi e le Condizioni 1,4,5 di Arrow.

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Summary In this paper we deal with the problem of how to amalgamate individual preferences to form one social preference in relation to certain alternatives determining a social preference satisfying the 2 Axioms and the 1, 4, 5 Conditions of Arrow.

     

On irrelevant and infeasible alternatives

In a letter to the author Arrow makes an important recognition regarding the question of irrelevant alternatives by expressing his view that alternatives which are not among the superior ones can, in fact, affect the choice of the best alternative (it is a question of choosing the best chess player).It is clarified how alternatives become relevant in group decisions by Borda's method.     

Locally minimax tests for a multinormal data problem

LetX be ap-normal random vector with unknown mean and unknown covariance matrix and letX be partitioned asX=(X ₍₁₎ ,X ₍₂₎ , ...,X _(r) ) whereX _(j) is a subvector of dimensionp _j such that _j=1 ^r p _j =p. We show that the tests, obtained by Dahel (1988), are locally minimax. These tests have been derived to confront H_o: =0 versusH ₁: 0 on the basis of sample of sizeN, X ₁, ..., X_N, drawn fromX andr additional samples of sizeN _j, U _i ^(j) , i=1, ..., N_j, drawn fromX ₍₁₎, ...X _(r) respectively. We assume that the (r+1) samples are independent and thatN _j>p _j forj=0, 1, ..., r (N _oN andp _op). Whenr=2 andp=2, a Monte Carlo study is performed to compare these tests with the likelihood ratio test (LRT) given by Srivastava (1985). We also show that no locally most powerful invariant test exists for this problem.     

On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem when individual preferences are weak orders

We will show that in the case where there are two individuals and three alternatives (or under the assumption of the free-triple property), and individual preferences are weak orders (which may include indifference relations), the Arrow impossibility theorem [Arrow, K.J., 1963. Social Choice and Individual Values, second ed. Yale University Press] that there exists no binary social choice rule which satisfies the conditions of transitivity, Pareto principle, independence of irrelevant alternatives, and non-existence of dictator is equivalent to the Brouwer fixed point theorem on a 2-dimensional ball (circle). Our study is an application of ideas by Chichilnisky [Chichilnisky, G., 1979. On fixed points and social choice paradoxes. Economics Letters 3, 347–351] to a discrete social choice problem, and also it is in line with the work by Baryshnikov [Baryshnikov, Y., 1993. Unifying impossibility theorems: a topological approach. Advances in Applied Mathematics 14, 404–415].     

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.     

On statistical approaches to the study of the “Law of Initial Values”

This paper is concerned with the well-known Law of Initial Values (Wilder, 1931, 1967). First, possible causes of this phenomenon of initial value dependence are discussed. The limitations of a structural relationships based method for testing its effect in empirical data sets in social and behavioral science research are next discussed. Within the popular structural equation modeling methodology, a multiple-indicator model is then focused on, which allows studying the Law of Initial Values. The described approach is illustrated using data from a cognitive intervention study (Baltes, Dittmann-Kohli & Kliegl, 1986).     

A topological approach to Wilson’s impossibility theorem

We will present a topological approach to Wilson’s impossibility theorem [Wilson, R.B., 1972. Social choice theory without the Pareto principle. Journal of Economic Theory 5, 478–486] that there exists no non-null binary social choice rule which satisfies transitivity, independence of irrelevant alternatives, non-imposition and has no dictator nor inverse dictator. Our research is in line with the studies of topological approaches to discrete social choice problems initiated by [Baryshnikov, Y., 1993. Unifying impossibility theorems: a topological approach. Advances in Applied Mathematics 14, 404–415]. This paper extends the result about the Arrow impossibility theorem shown in [Tanaka, Y., 2006. A topological approach to the Arrow impossibility theorem when individual preferences are weak orders. Applied Mathematics and Computation 174, 961–981] to Wilson’s theorem.     

Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics

In this article a systematic study is given of the asymptotic behavior of two-sample tests based on U-Statistics with arbitrary antisymmetric kernels . Besides the investigation under the hypothesis and under fixed alternatives we determine the local power as a function of as well as its maximizing value _opt. Moreover formulas for the asymptotic relative efficiency ARE(₂,₁) of the ₂-test with respect to the ₁-test are derived. It turns out that _opt also yields the most efficient test in the sense that ARE(_opt,)1 for all (admissible) kernels .     

Eine Bemerkung zur Existenz erwartungstreuer Schätzer

Summary A theorem ofBickel andLehmann concerning the existence of unbiased estimates for parameters on the convex family of all absolutely continuous probability distributions is generalized to arbitrary convex families of absolutely continuous distributions. In contrast to the result ofBickel andLehmann, however, we give necessary and sufficient conditions for the existence of only approximately unbiased estimates. An example, which is borrowed from density estimation, shows that in general the term approximately cannot be ommitted.     

A reexamination of additivity of power in randomized social preference

We show that Barberá and Sonnenscheins (1978) power function becomes additive if we replace the Paretian condition by nonimposition and monotonicity. Since these conditions are very much in the spirit of Arrow (1951), our result sharpens the analogy to Arrows theorem.Received: 29 November 2001, Accepted: 4 May 2003, JEL Classification: D71Shasikanta Nandeibam: I would like to thank Professor Prasanta Pattanaik for very helpful discussions. I have also benefitted from the comments and suggestions of an associate editor. The usual disclaimer applies.     

On the reliability of the chi-square test

Summary The classical ₂ test of goodness of fit depends on the partition chosen to calculate it. In this work the covariance structure of the family of all ₂ tests obtained by translation (modulo 1) of a uniform partition of the interval [0, 1) it is determined, under the hypothesis of uniform distribution on [0, 1). This is used to define and compute an index which measure the indeterminacy of the ₂ test due to the arbitrary choice of the partition to compute it.     

Logic from space

This is one of the essential results of an inquiry into spacetime-sociology which was outlined and begun with in a research memorandum of the Institute for Advanced Studies, Vienna (IHS) 1992. It contains a proof that classical logic, or Boole's laws of thought, can be derived from an original concept of orientation that has emerged in human cognition during paleolithic worship activity. The original concept of orientation represents a genetic structure of orientation in both physical and social space. This is of a considerable importance. Because the original concept of orientation in its exact mathematical form is a symmetry in space, strictly a subgroup of the rotation-groupD ₃. Thus it belongs to the fields of mathematics and physics entirely and has nothing to do with logistics, linguistics or sociology. On the other hand binary logic is an important aspect of language and thought and seems to have little in common with the perception of objects in space. So there is a connection between logic and orientation in space. Mathematically this is represented by an isomorphism between the spatial symmetryD _2d of the Mandala of the quartered circle and the symmetry of classical logic.     

On the flexible functional forms

This note proposes a general structure of the so-called flexible functional forms able to describe direct utility functions. It is obtained by solving the functional equation:

Nash equilibrium reconsidered and an option for maximin

In this paper we will discuss some peculiarities of Nash equilibrium which are at odds with its standard applications: (a) the underlying dynamic interpretation, (b) the incentive independency if equilibria are mixed, and (c) the unprofitability if equilibrium and maximin are mixed and the game is 2-by-2. Maximin is proposed as an alternative solution concept in relevant situations.Institute of Economics, University of Hamburg, Von-Melle-Park 5, D-2000 Hamburg 13, Germany. This is a substantially revised version of the paper Anti-Nash and an Option for Maximin (Institute of Economics, University of Aarhus, Memo 1989-16), which the author presented at the Fourth Annual Congress of the European Economic Association, Augsburg, September 2–4, 1989.     

Social identity,inequality, and conflict: correction and extension

This paper corrects and extends the analysis in Social Identity, Inequality, and Conflict by James Robinson (Economics of Governance, 2(1), 2001). For conflict along class lines, Robinson finds the total impact of mobility on conflict to be ambiguous. Contrary to his result, I show that, under his assumptions, the effect of social mobility on class conflict is unambiguous. Higher mobility always decreases conflict. In my extension to Robinsons model, I explore mobilitys impact on class conflict in a society where the tax rate is not fixed. I demonstrate that if the tax rate is proportional to the population of the group in power relative to the total population of the society, then the effects of social mobility on class conflict are indeed ambiguous.Submitted: February 2002, Accepted: July 2003,I am grateful to an anonymous referee and Amihai Glazer for their comments. I would also like to thank Herschel Grossman for his help along the way.     

Contributions to nonparametric generalized failure rate function estimation

For a specified distribution functionG with densityg, and unknown distribution functionF with densityf, the generalized failure rate function (x)=f(x)/gG ^–1 F(x) may be estimated by replacingf andF byf _n and , wheref _n is an empirical density function based on a sample of sizen from the distribution functionF, and . Under regularity conditions we show and, under additional restrictions whereC is a subset ofR and _n. Moreover, asymptotic normality is derived and the Berry-Esséen type bound is shown to be related to a theorem which concerns the sum of i.i.d. random variables. The order boundO(n^–1/2+c _n ^1/2 ) is established under mild conditions, wherec _n is a sequence of positive constants related tof _n and tending to 0 asn.Research was supported in part by the Army, Navy and Air Force under Office of Naval Research contract No. N00014-76-C-0608. AMS 1970 subject classifications. Primary 62G05. Secondary 60F15.     

On the conceptualization of theoretical constructs

An attempt is made to bridge the gap between the theorists and modellists approaches to the conceptualization of theoretical constructs. The former approach assumes that every theoretical construct has a surplus meaning over and above its operationalization and measurement as a concept. The latter approach denies this: it only accepts theoretical constructs as functions of relations between observations, i.e. measured concepts.This gap can be bridged by explicating the definition of a theoretical construct before making attempts to operationalize and measure it. An explicated definition should cover all relevant aspects (or: facets) of a construct, systematically brought together in an ideal type model. On this basis, operationalization of the construct can be directly linked to model elements, so that any possibly remaining surplus value is made explicit. The distance between theoretical construct and the measured concept can then be made as small as seems feasible; in principle, the distance can be made zero. The manner in which conservative ideology is conceptualized in a longitudinal research project in the Dutch electorate is presented as an example of this strategy.     

What makes the clock tick? Time,populations, voters,and votes for the president in the United States

Our present analysis expands on the number of theoretical disciplines involved in the explanation of votes to presidential races in the United States. We do so by replacing the theoretically thin trend variable, previous studies have used, with the demographic factor.The demographic factor, which is obviously highly statistically correlated with the non-theoretical time trend, was hypothesized to have a significant impact upon partisan popularity and presidential races. As the demographic growth is due mostly to immigration and naturalization, and natural growth, especially among the poor, one would expect the growth to be beneficial to Democrats.     

Some brief notes on the “unfinished business” of qualitative inquiry

The paper argues that there are a variety of implicit issues in qualitative inquiry that need to be addressed if the area is to develop in some normal science sense. This unfinished business is concerned with a deeper investigation of basic terms that are now simply taken for granted, such as theme and pattern. It also includes the need to develop rules which will assist in making and justifying how qualitative interpretations are made from the implicit processes of inference. Specific suggestions are made for accomplishing these issues.