Existence of homogeneous representations of interval orders on a cone in a topological vector space

Necessary and sufficient conditions are presented for the existence of a pair <u,v> of positively homogeneous of degree one real functions representing an interval order on a real cone K in a topological vector space E (in the sense that, for every x,yK, xy if and only if u(x)v(y)), with u lower semicontinuous, v upper semicontinuous, and u and v utility functions for two complete preorders intimately connected with . We conclude presenting a new approach to get such kind of representations, based on the concept of a biorder.This research has been supported by the Integrated Action of Research HI2000-0116 (Spain-Italy). Also, the work of coauthors Candeal and Induráin has been partially supported by the research project PB98-551 Estructuras ordenadas y aplicaciones (M.E.C. Spain, December 1999).     

Positional information and preference aggregation

A new version of independence (I⁺) is proposed for social welfare functions based on the following notion of agreement. Two weak orders R and R’ on a finite set S agree on a pair {x,y}, denoted byif R|_{x,y} = R’|_{x,y} and [z R*x and z R*y for some z∈S] if and only if [z’ (R’)* x and z’(R’)*y for some z’∈S]. The last part says that x and y are strictly under z with respect to R exactly when x and y are strictly under z’ with respect to R’. Some examples and results on social welfare functions that satisfy (I⁺), Pareto, and nondictatorship are given.I am grateful for the comments and suggestions made by an anonymous referee on an earlier version of this paper.     

Subcyclic sets of linear orders

A set T of linear orders of [n] = {1,2, . . . ,n} is subcyclic if every 3-set in [n] has one order that appears in no order in T. With g(n) the maximum cardinality of a subcyclic set for n, Raz [8] proved that g(n)<cⁿ for some c>0, thus resolving a longstanding conjecture of a similar upper bound for maximum acyclic sets. The present paper proves that g(4)=14 and g(5)=42 with both maxima attained only by subcyclic sets with a particular structure for all quadruples in [n]. We conjecture a similar result for larger n, in which case g(n) is the n^th Catalan number and min(c)=4 for Raz’s bound.     

Monotonicity in Condorcet Jury Theorem

Consider a committee of experts dealing with dichotomous choice problem, where the correctness probabilities are all greater than We prove that, if a random subcommittee of odd size m is selected randomly, and entrusted to make a decision by majority vote, its probability of deciding correctly increases with m. This includes a result of Ben-Yashar and Paroush (2000), who proved that a random subcommittee of size m3 is preferable to a random single expert.Research supported in part by the Israel Science Foundation (Grant\#186/01)     

Inequality and welfare evaluation of heterogeneous income distributions

This paper establishes the principles that should govern the welfare and inequality analysis of heterogeneous income distributions. Two basic criteria – the equity preference condition and the compensation principle – are shown to be fundamentally incompatible. The paper favours the latter, thereby vindicating the traditional method of dealing with heterogeneous samples. However, inequality and welfare comparisons will usually be well defined only if equivalent incomes are obtained using constant scale factors; and researchers will need to distinguish clearly between inequality of nominal incomes and inequality of living standards. Furthermore, household observations must always be weighted according to family size.     

Progressive taxation and redistributive taxation: Different labels for the same product?

The paper examines different approaches to measure tax progressivity. In particular the distributional aspect of taxation is considered in some depth. For each member of a parametric class of inequality concepts, including more than only the relative and the absolute view of inequality, a necessary and sufficient condition for a tax function to be inequality reducing with respect to this concept for all admissible pre-tax income distributions is derived, both in strong and weak form. Only three very natural properties are required to prove this result: each tax liability is less than the corresponding pre-tax income, taxation does not reverse ranks on the income scale, and inequality is reduced if a rich gives to a poor such that they do not interchange their ranks. A definition of tax progressivity based on the shown equivalence is suggested. It is demonstrated that inequality reducing taxation is equivalent to progressive taxation in the sense of an increasing average tax rate if and only if the concept of relative inequality is used.An early version of this paper was presented at the seminar on Distributive Justice and Inequality at the Wissenschaftskolleg, Berlin, May 20–24, 1986. Some of the material contained previously circulated under the heading Generalized concepts of tax progression and inequality reduction.The author is indebted to Peter Lambert whose survey of tax progressivity inspired the present analysis incredibly. James Foster, John Weymark, and two anonymous referees provided helpful comments. Remaining errors and omissions are all mine.     

Social factors in facial display and communication: A reply to Chovil and others

This paper discusses the Chovil (1991) study, questioning the assumption that the notion of facial display as communication is incompatible with that of facial display as readout of motivational/emotional response. It is argued that (a) the Chovil paper oversimplifies the view of the competition; (b) social factors can facilitateor inhibit expression depending upon the nature of the emotion being expressed and the expressor's personal relationship with the other; and (c) social factors produce strong social emotions, so that any manipulation of sociality must also manipulate emotion.Preparation of this paper was supported in part by NIMH grant MH-40753 to Ross Buck, and by the University of Connecticut Research Foundation.     

The NIP graph of a social welfare function

We consider the fraction of pairs of m distinct alternatives on which a social welfare function f may be nondictatorially independent and Pareto when the domain of f satisfies the free k-tuple property. When k = 4 we improve the existing upper bound to . When there are at least 26 alternatives and we obtain an original upper bound, . To obtain these results we define and analyze the graph formed from the nondictatorial independent and Pareto pairs and combine the results of this analysis with known results from extremal graph theory. The authors extend special thanks to the two reviewers and the editor for their comments.     

Consequentialist demographic norms and parenting rights

This paper extends the author's recent work on dynamically consistent consequentialist social norms for an unrestricted domain of decision trees with risk to trees in which the population is a variable consequence — i.e., endogenous. Given a form of ethical liberalism and ethical irrelevance of distant ancestors, classical utilitarianism is implied (provided also that a weak continuity condition is met). The repugnant conclusion that having many poor people may be desirable can be avoided by denying that individuals' interests extend to the circumstances of their birth. But it is better avoided by recognizing that potential parents have legitimate interests concerning the sizes of their families.That action is best, which procures the greatest happiness for the greatest numbers. Francis Hutchison (1725).An abiding interest in concepts of optimality for the choice of population has been stimulated by frequent discussions with Partha Dasgupta. This paper was presented at the seminar on Distributive Justice and Inequality at the Wissenschaftskolleg zu Berlin, May 1986. I am grateful to the audience for their helpful comments, especially Maurice Salles and Patrick Suppes, and especially to John Weymark for carefully reading and suggesting distinct improvements to the earlier version.     

Making work matter: Satisfied detectives and dissatisfied campus police

Dirty work is part of all occupations. A comparison of two low-status occupations — detectives and campus police — revealed that workers in some occupations can surmount the tarnished image that goes along with dirty work, while others cannot. The detectives, but not the campus police, found ways to make their work matter. The former created a valued core identity, found an appreciative audience, and built collegiality. The constraints of campus police work kept the campus police from using the same strategies, and left them feeling that all their work was dirty. Under certain conditions, workers can redefine the core of a bad job into meaningful work.Order of authorship is alphabetical. Support for this research was provided in part by a grant from the University Research Council of the University of North Carolina at Chapel Hill. An earlier version of the paper was presented at the annual meeting of the Southern Sociological Society, Norfolk, Virginia, 1989. We thank Howard Aldrich, Howard Becker, Carl Klockars, Richard Simpson, Donna K. Darden, and Charles Watson for their comments on earlier drafts.     

Room assignment-rent division: A market approach

A group of friends consider renting a house but they shall first agree on how to allocate its rooms and share the rent. We propose an auction mechanism for room assignment-rent division problems which mimics the market mechanism. Our auction mechanism is efficient, envy-free, individually-rational and it yields a non-negative price to each room whenever that is possible with envy-freeness.We would like to thank seminar participants at Barcelona, Boston College, Duke, Koç, Málaga, MIT, Michigan, NYU, conference participants at the First Brazilian Workshop of Game Theory Society (Sao Paulo 2002), SED 2002-Conference on Economic Design (New York City 2002), The Sixth International Meeting of the Society for Social Choice and Welfare (Pasadena 2002), an anonymous referee for their comments and Ahmet Alkan, Selçuk Karabati, Bari Tan, nsan Tunali for insightful discussions. Sönmez gratefully acknowledges the research support of KoçBank via the KoçBank scholar program and Turkish Academy of Sciences in the framework of the Young Scientist Award Program via grant TS/TÜBA-GEBP/2002-1-19. Any errors are our own responsibility.     

Urban forest cover of the Chicago region and its relation to household density and income

Urban forests and herbaceous open space play a vital role in the environmental and aesthetic health of cities, yet they are rarely identified in land-use inventories of urban areas. To provide information on urban forests and other vegetative land cover in Illinois cities, Landsat Thematic Mapper (TM) data from June 27, 1988, were classified for the Chicago metropolitan region (9,717 km²). Ten land-cover classes were identified, including two types of forestland (occupying 5.8% of the total area), residential land with trees (14.6%) or without trees (7.8%), cropland (37.5%), two types of grassland (7.7%), urban with impervious surfaces (23.1%), water (1.6%), and miscellaneous vegetation (2.1%). Correlation analyses indicated that household income and household density are strongly related to land covers in the region, particularly those with tree cover and urbanized land. Population changes for 1980–1985 and 1985–2010 (projected) show a pattern of increasing density in the urbanized zone concurrent with continued urban sprawl, primarily into current cropland.     

Topological aggregation of inequality preorders

An inequality preorder is defined as a complete preorder on a simplex which satisfies the properties of continuity and strict Schur-convexity (the mathematical equivalent of Dalton's principle of transfers). The paper shows that it is possible to aggregate individual inequality preorders into a collective one if we are interested in continuous anonymous aggregation rules that respect unanimity. The aggregation problem is studied within a topological framework introduced by Chichilnisky.We are grateful to J. Laine for helpful discussions and to an anonymous referee of this Journal for valuable comments     

Interpersonal utility theory

A triangulation strategy is sketched for constructing an empirical testable theory of interpersonal comparisons of utility units. Bargaining theory and the theory of the utility curves of money are tentatively suggested as triangulation points.During 1981–82, I presented these ideas in talks at Chicago, Michigan, Oberlin, Princeton, Stanford and Yale. I have benefitted from the comments I received then as well as from comments of the referees.     

A quantitative theory of preferences: Some results on transition functions

We investigate a general theory of combining individual preferences into collective choice. The preferences are treated quantitatively, by means of preference functions (a,b), where 0(a,b) expresses the degree of preference of a to b. A transition function is a function (x,y) which computes (a,c) from (a,b) and (b,c), namely (a,c)=((a,b),(b,c)). We prove that given certain (reasonable) conditions on how individual preferences are aggregated, there is only one transition function that satisfies these conditions, namely the function (x,y)=x·y (multiplication of odds). We also formulate a property of transition functions called invariance, and prove that there is no invariant transition function; this impossibility theorem shows limitations of the quantitative method.Research supported in part by the National Science Foundation.     

The Impact of the Therapist's Curiosity on the Treatment Process of Children and Adolescents

Therapists bring their own initiative, interest, and wonder—their professional curiosity—into treatment sessions. Some children and adolescents pull away in reaction to this curiosity, bristling or withdrawing, if only for a moment. This can happen abruptly, even in response to the first hello, but most often it occurs subtly, over the course of treatment. These children and adolescents may be replaying the ruptures in relationships they experienced when they have expressed their own initiative and curiosity to important others in their lives. Therapists need to utilize opportunities to understand the dynamics, explore where the original ruptures may have occurred, and bring the experience into therapeutic focus. Case vignettes illustrate these dynamics.     

The Unmaking of Management? Change and Continuity in British Management in the 1990s

In the late 1980s, a series of reports —notably, The Making of Managers by CharlesHandy-outlined a development path for management in theU.K. This was to be based on the development of aneducation and training base and the model set by leadingcorporations. A decade later, this paper reviews currenttrends in managerial work and employment against theexpectations of the late 1980s. In doing so, it distinguishes between the objectivecondition of British management and itsinstitutionalized meaning within wider British society.It argues that recent accounts of changes in managerialwork and employment have focused solely on incremental changes inthe empirical domain and have neglected importantdiscursive shifts in the way management is understoodand enacted within organizations. These shifts have been catalyzed by the emergence of a series oforganizational initiatives-first, Total QualityManagement (TQM) and, latterly, lean production andBusiness Process Reengineering (BPR)-which aim tosystematically deconstruct management by emphasizing workerempowerment, delayering, downsizing, and theredistribution of managerial functions. In short,initiatives such as these are contributing to theunmaking of management. Managerial groups aresubject to intensification and polarization, whilemanagerial practices are diffused throughout the workprocess.     

Inclusive Governance and “Minority” Groups: The Role of the Third Sector in Wales

Following the establishment of a national legislature in Wales in 1999 the third sector has entered into a pioneering cross-sectoral partnership with the Welsh government. This paper presents the results of a research project that has studied the new structures of devolved governance through the expectations and participation of voluntary organizations representing three marginalized or minority groupings: women, disabled people, and those from an ethnic minority background. The findings reveal that despite varying levels of expectation expressed by minority voluntary groups, active engagement of minority groups in policy making has been a feature of the Assembly's first months. Nevertheless, formidable challenges face both sectoral partners in the new system of governance, not least in creating organizational structures that facilitate partnership working in the devolved polity.     

Disagreement point monotonicity,transfer responsiveness,and the egalitarian bargaining solution

This paper provides an axiomatization of the egalitarian bargaining solution. The central axiom used (together with some standard properties of bargaining solutions) in this characterization is a transfer responsiveness condition. First, it ensures that no transfer paradox can occur if bargaining power is transferred from one agent to another by decreasing one agent's and increasing the other agent's component of the disagreement point. Second, the extent of external effects of such a transfer is limited by requiring that agents not involved in the transfer neither gain more than the winner nor lose more than the loser of the transfer. Journal of Economic Literature Classification No.: C78.I thank William Thomson whose comments on an earlier version led to substantial improvements.     

Making Minorities: Cultural Space,Stigma Transformation Frames,and the Categorical Status Claims of Deaf,Gay, and White Supremacist Activists in Late Twentieth Century America

This article compares the efforts of movement activists in three dissimilar groups to replace a stigmatized status with a valued one by portraying their groups as resembling established minorities (claims of contiguity in cultural space) and as differing from groups stigmatized as deviant (claims of distance). The most common claims assert similarity to African Americans, and frequently incorporate civil rights themes (exemplifying frame diffusion). Tactically, these minority status claims exploit both the resonance of cultural pluralism and state recognition of minorities. Strategically, minority status framing enables stigmatized groups to claim legitimacy without changing — simultaneously asserting both normality and difference.