Wertesynthese-Funktional oder dysfunktional?

Der Beitrag knüpft an den Kommentar zu einem Artikel von Sigrid Ro?teutscher durch Helmut Thome an (vgl. der Beitrag „‚Wertesynthese’: Ein unsinniges Konzept?” in KZfSS 57: 333–341). Er setzt der Grundsatzkritik Sigrid Ro?teutschers an der „Wertesynthese” (vgl. die Beitr?ge „Von Realisten und Konformisten — Wider die Theorie der Wertesynthese” in KZfSS 56: 407–432 und „Kein unsinniges Konzept, sondern traurige Realit?t” in KZfSS 57: 543–549) eine Beschreibung der Entstehungsgeschichte des Konzeptes der Wertesynthese und ihrer theoretischen Grundlagen entgegen. Weiterhin erfolgt eine Darstellung des aktuellen Erkenntnisstandes zur Wertesynthese. Es soll gezeigt werden, dass Konzept und Realit?t der „Wertesynthese” eine aussichtsreiche Forschungs-und Gesellschaftsperspektive er?ffnen.     

Extended Pareto rules and relative utilitarianism

This paper introduces the “Extended Pareto” axiom on Social Welfare Functions and gives a characterization of the axiom when it is assumed that the Social Welfare Functions that satisfy it in a framework of preferences over lotteries also satisfy the restrictions (on the domain and range of preferences) implied by the von-Neumann Morgenstern axioms. With the addition of 2 other axioms: “Anonymity” and a weak version of Arrow's Independence of Irrelevant Alternatives axiom: “Weak IIA” it is shown that there is a unique Social Welfare Function called “Relative Utilitarianism” that consists of normalising individual utilities between 0 and 1 and adding them. Received: 7 June 1994 / Accepted: 28 April 1997     

Some issues related to the topological aggregation of preferences: addendum

 The purpose of this addendum is to correct some results published in our paper “Some issues related to the topological aggregation of preferences” (SCW (1992) 9: 213–227). Received: 28 November 1992/Accepted: 22 April 1996     

The sensitivity of weight selection on the Condorcet efficiency of weighted scoring rules

A weighted scoring rule, Rule λ, on three alternative elections selects the winner by awarding 1 point to each voter's first ranked candidate, λ points to the second ranked candidate, and zero to the third ranked candidate. The Condorcet winner is the candidate that would defeat each other candidate in a series of pairwise elections by majority rule. The Condorcet efficiency of Rule λ is the conditional probability that Rule λ selects the Condorcet winner, given that a Condorcet winner exists. Borda rule (λ=1/2) is the weighted scoring rule that maximizes Condorcet efficiency. The current study considers the conditional probability that Borda rule selects the Rule λ winner, given that Rule λ elects the Condorcet winner with a large electorate. Received: 21 August 1996 / Accepted: 7 January 1997     

Outranking methods for multicriterion decision making: Arrow’s and Raynaud’s conjecture

 Outranking methods constitute a class of ordinal ranking algorithms for multicriterion decision making. This paper is concerned with four such methods: K?hler’s primal and dual algorithms, and Arrow–Raynaud’s primal and dual algorithms. Arrow and Raynaud made the conjecture that these four methods yield the totality of “prudent orders” whenever the outranking matrix has the “constant sum” property. This paper shows that their conjecture is not valid. Received: May 29, 1995/Accepted: November 13, 1995     

What is a problem?

Among others, the term “problem” plays a major role in the various attempts to characterize interdisciplinarity or transdisciplinarity, as used synonymously in this paper. Interdisciplinarity (ID) is regarded as “problem solving among science, technology and society” and as “problem orientation beyond disciplinary constraints” (cf. Frodeman et al.: The Oxford Handbook of Interdisciplinarity. Oxford University Press, Oxford, 2010). The point of departure of this paper is that the discourse and practice of ID have problems with the “problem”. The objective here is to shed some light on the vague notion of “problem” in order to advocate a specific type of interdisciplinarity: problem-oriented interdisciplinarity. The outline is as follows: Taking an ex negativo approach, I will show what problem-oriented ID does not mean. Using references to well-established distinctions in philosophy of science, I will show three other types of ID that should not be placed under the umbrella term “problem-oriented ID”: object-oriented ID (“ontology”), theory-oriented ID (epistemology), and method-oriented ID (methodology). Different philosophical thought traditions can be related to these distinguishable meanings. I will then clarify the notion of “problem” by looking at three systematic elements: an undesired (initial) state, a desired (goal) state, and the barriers in getting from the one to the other. These three elements include three related kinds of knowledge: systems, target, and transformation knowledge. This paper elaborates further methodological and epistemological elements of problem-oriented ID. It concludes by stressing that problem-oriented ID is the most needed as well as the most challenging type of ID.     

Strategy-proofness on Euclidean spaces

 In this paper we characterize strategy-proof voting schemes on Euclidean spaces. A voting scheme is strategy-proof whenever it is optimal for every agent to report his best alternative. Here the individual preferences underlying these best choices are separable and quadratic. It turns out that a voting scheme is strategy-proof if and only if (α) its range is a closed Cartesian subset of Euclidean space, (β) the outcomes are at a minimal distance to the outcome under a specific coordinatewise veto voting scheme, and (γ) it satisfies some monotonicity properties. Neither continuity nor decomposability is implied by strategy-proofness, but these are satisfied if we additionally impose Pareto-optimality or unanimity. Received: 18 October 1993/Accepted: 2 February 1996     

Topological aggregation, the case of an infinite population

 The literature on infinite Chichilnisky rules considers two forms of anonymity: a weak and a strong. This note introduces a third form: bounded anonymity. It allows us to prove an infinite analogue of the “Chichilnisky– Heal-resolution” close to the original theorem: a compact parafinite CW-complex X admits a bounded anonymous infinite rule if and only if X is contractible. Furthermore, bounded anonymity is shown to be compatible with the finite and the [0, 1]-continuum version of anonymity and allows the construction of convex means in infinite populations. With X=[0, 1], the set of linear bounded anonymous rules coincides with the set of medial limits. Received: 30 October 1993/Accepted: 22 April 1996     

An alternative proof of Gibbard's random dictatorship result

By using a line of reasoning similar to the one used by Gibbard (Gibbard A (1973) Econometrica 41: 587–601) in the deterministic framework, we provide a more transparent and intuitive proof of the following random dictatorship result in the probabilistic framework, which is a corollary credited to H.␣Sonnenschein of the more general result of Gibbard (Gibbard A (1977) Econometrica 45: 665–681): A decision scheme is Pareto optimific ex post and strategy proof if and only if it is a random dictatorship. Received: 13 February 1996 / Accepted: 14 April 1997     

Gamson’s law and hedonic games

This note adds one celebrated coalition formation game due to Gamson (Am Soc Rev 26:373–382 1961a, Am Soc Rev 26:565–573, 1961b) in the list of applications of the theory of hedonic games explored by Banerjee et al. (Soc Choice Welf 18:135–153, 2001) and Bogomolnaia and Jackson (Games Econ Behav 38: 204–230, 2002). We apply their results to study the original Gamson game and offer extensions both to a multi-dimensional characteristics space and to an infinite number of players.     

Rational choice and revealed preference without binariness

 This paper attempts to provide a unified account of the rationalization of possibly non-binary choice-functions by “Extended Preference Relations” (relations between sets and elements). The analysis focuses on transitive EPRs for which three choice-functional characterizations are given, two of them based on novel axioms. Transitive EPRs are shown to be rationalizable by sets of orderings that are “closed under compromise”; this novel requirement is argued to be the key to establish a canonical relationship between sets of orderings and choice-functions. The traditional assumption of “binariness” on preference relations or choice functions is shown to be analytically unhelpful and normatively unfounded; non-binariness may arise from “unresolvedness of preference”, a previously unrecognized aspect of preference incompleteness. Received: 28 August 1995/Accepted: 14 February 1996     

Objective measures of well-being and the cooperative production problem

 The concern for measuring well-being objectively (as opposed to subjectively, that is, relying only on preferences) is found in modern political philosophy, especially in J. Rawls’s, A. Sen’s and G. Cohen’s writings. This paper explains the implications of using an objective well-being index as equalisandum or, close to the so-called “safety net preoccupation”, to guarantee a well-being lower bound. In the simple production model studied here, five characterization results and two related theorems prove the convergence of both approaches. We come to the conclusion that the Proportional Solution is the dominant solution according to “objectivist” axioms. Received: 5 September 1994/Accepted: 29 June 1996     

Intermediate inequality and welfare

We introduce a new centrist or intermediate inequality concept, between the usual relative and absolute notions, which is shown to be a variant of the α-ray invariant inequality measures in Pfingsten and Seidl (1997). We say that distributions x and y have the same (x, π)-inequality if the total income difference between them is allocated among the individuals as follows: 100π% preserving income shares in x, and 100(1−π)% in equal absolute amounts. This notion can be made as operational as current standard methods in Shorrocks (1983). Received: 13 May 1998/Accepted: 25 January 1999     

Mindfulness and Cognitive Therapy in Depression Relapse Prevention: A Case Study

Depression is the most commonly diagnosed mental illness in the United States with relapse rates as high as 80–90% in some circumstances (Chen et al. in Res Soc Work Pract 16(5): 500–510, 2006; Mintz et al. in Arch Gen Psychiatry 49: 761–768, 1992; Teasdale et al. in J Consult Clin Psychol 68(4): 615–623, 2000). Cognitive therapy (CT) and psychopharmacology have been the mainstays of treatment for depression and relapse prevention, yet relapse remains a significant risk of this mental illness (DeRubeis et al. in Arch Gen Psychiatry 62: 409–416, 2005; Meyer and Scott in Behav Cogn Psychother 36: 685–693 2008; Rush et al. in Cognit Ther Res 1: 17–37, 1977). The literature review, case illustration and analysis examines the rationale for integrating mindfulness practice, and demonstrates the application of this practice in conjunction with cognitive therapy to reduce the risk of relapse in Major Depression.     

Characterizations of two power indices for voting games with r alternatives

In the first three sections of this paper we present a set of axioms which provide a characterization of an extension of the Banzhaf index to voting games with r alternatives, such as the United Nations Security Council where a nation can vote “yes”, “no”, or “abstain”. The fourth section presents a set of axioms which characterizes a power index based on winning sets instead of pivot sets. Received: 4 April 2000/Accepted: 30 April 2001     

Topological methods in social choice: an overview

 This paper gives an exposition of the topological framework for social choice theory developed by Chichilnisky, and reviews the mathematical concepts needed for understanding this framework. Within that context, this paper also discusses some classic results of Chichilnisky. Received: 30 December 1994/Accepted: 22 April 1996     

Sociology’s <Emphasis Type="Italic">Suicide</Emphasis>: A Forensic Autopsy?

For decades Durkheim’s theory of suicide has been tested and found wanting. Yet, rather than being consigned to the dust-bin of history, it lives on and is pointed to as an exemplar of the powers of sociological theory and research. If this rationalizing and/or dismissal of so many falsifications of the theory were an isolated phenomenon, it might be evidence of some lemming-like propensity for suicide or a disciplinary death-wish, among a few sociologists. But it appears to be a much more widespread and common occurrence. In this paper we explore some possible explanations of this ‘falsification denial’—‘The Social Misconstruction of Reality’ (Hamilton 1996), ‘When Prophecy Fails’ (Festinger et al. 1956), ‘Underdetermination’ (Duhem 1954; Quine Journal of Philosophy 67:178–183, 1970, Erkenntnis 9:313–328, 1975; Lakatos 1970), and ‘Boundary Maintenance’ (Erikson 1966), and we outline some of the more important and pernicious consequences of this falsification denial for the discipline and future of sociology.     

An axiomatization of the Nash bargaining solution

I prove that ‘Disagreement Point Convexity’ and ‘Midpoint Domination’ characterize the Nash bargaining solution on the class of two-player bargaining problems and on the class of smooth bargaining problems. I propose an example to show that these two axioms do not characterize the Nash bargaining solution on the class of bargaining problems with more than two players. I prove that the other solutions that satisfy these two properties are not lower hemi-continuous. These different results refine the analysis of Chun (Econ Lett 34:311–316, 1990). I also highlight a rather unexpected link with the result of Dagan et al. (Soc Choice Welfare 19:811–823, 2002).     

Informational geometry of social choice

 Elementary geometry is used to understand, extend and resolve basic informational difficulties in choice theory. This includes axiomatic conclusions such as Arrow’s Theorem, Chichilnisky’s dictator, and the Gibbard–Satterthwaite result. In this manner new results about positional voting methods are outlined, and difficulties with axiomatic approach are discussed. A topological result about “dictatorial” behavior is offered. Received: 15 December 1993/Accepted: 22 April 1996     

Acyclic sets of linear orders

 A set of linear orders on {1,2, ℕ, n} is acyclic if no three of its orders have an embedded permutation 3-cycle {abc, cab, bca}. Let f (n) be the maximum cardinality of an acyclic set of linear orders on {1,2, ℕ, n}. The problem of determining f (n) has interested social choice theorists for many years because it is the greatest number of linear orders on a set of n alternatives that guarantees transitivity of majority preferences when every voter in an arbitrary finite set has any one of those orders as his or her preference order. This paper gives improved lower and upper bounds for f (n). We note that f (5)=20 and that all maximum acyclic sets at n=4, 5 are generated by an “alternating scheme.” This procedure becomes suboptimal at least by n=16, where a “replacement scheme” overtakes it. The presently-best large-n lower bound is approximately f (n)≥(2.1708) ⁿ . Received: 5 April 1995/Accepted: 10 November 1995