Social choice and the closed convergence topology

This paper revisits the aggregation theorem of Chichilnisky (1980), replacing the original smooth topology by the closed convergence topology and responding to several comments (N. Baigent (1984, 1985, 1987, 1989), N. Baigent and P. Huang (1990) and M. LeBreton and J. Uriarte (1990a, b). Theorems 1 and 2 establish the contractibility of three spaces of preferences: the space of strictly quasiconcave preferences P _SCO, its subspace of smooth preferences P _infSCO ^supS , and a space P ₁ of smooth (not necessarily convex) preferences with a unique interior critical point (a maximum). The results are proven using both the closed convergence topology and the smooth topology. Because of their contractibility, these spaces satisfy the necessary and sufficient conditions of Chichilnisky and Heal (1983) for aggregation rules satisfying my axioms, which are valid in all topologies. Theorem 4 constructs a family of aggregation rules satisfying my axioms for these three spaces. What these spaces have in common is a unique maximum (or peak). This rather special property makes them contractible, and thus amenable to aggregation. However, these aggregation rules cannot be extended to the whole space of preferences P which is not contractible and therefore does not admit continuous aggregation rules satisfying anonymity and unanimity, Chichilnisky (1980, 1982). The results presented here clarify an erroneous example in LeBreton and Uriarte (1990a, b) and respond to Baigent (1984, 1985, 1987) and Baigent and Huang (1990) on the relative advantages of continuous and discrete approaches to Social Choice.Comments from Geoffrey M. Heal, Andreu Mas Colell, Jean Francois Mertens and Maurice Salles are gratefully acknowledged. Research support was provided by NSF SES 8409857.     

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     

Political–economic equilibrium when parties represent constituents: The unidimensional case

 A political–economic environment is studied in which two parties, representing different constituencies of citizens, compete over a proportional tax rate to be levied on private endowments, to finance a public good. Although parties know the distribution of citizen traits (preferences and endowments), they are uncertain about the distribution of traits among the citizens who will turn up at the polls. This uncertainty engenders an endogenously derived function π(t ₁, t ₂) giving the probability that any one tax policy t ₁ will defeat another t ₂ in the election. Equilibrium existence theorems are proved, and the nature of equilibrium is compared with the equilibrium that exists when Downsian parties (ones whose objective is to maximize the probability of victory) face uncertainty. Both constituency-representing parties and uncertainty are needed to generate equilibria in which parties propose different policies. Received: 4 April 1995/Accepted: 2 April 1996     

The C1 topology on the space of smooth preference profiles

This paper defines a fine C ¹-topology for smooth preferences on a “policy space”, W, and shows that the set of convex preference profiles contains open sets in this topology.  It follows that if the dimension(W)≤v(?)−2 (where v(?) is the Nakamura number of the voting rule, ?), then the core of ? cannot be generically empty. For higher dimensions, an “extension” of the voting core, called the heart of ?, is proposed. The heart is a generalization of the “uncovered set”. It is shown to be non-empty and closed in general. On the C ¹-space of convex preference profiles, the heart is Paretian. Moreover, the heart correspondence is lower hemi-continuous and admits a continuous selection. Thus the heart converges to the core when the latter exists. Using this, an aggregator, compatible with ?, can be defined and shown to be continuous on the C ¹-space of smooth convex preference profiles. Received: 3 April 1995/Accepted: 8 April 1998     

An axiomatic approach to intergenerational equity

We present a set of axioms in order to capture the concept of equity among an infinite number of generations. There are two ethical considerations: one is to treat every generation equally and the other is to respect distributive fairness among generations. We find two opposite results. In Theorem 1, we show that there exists a preference ordering satisfying anonymity, strong distributive fairness semiconvexity, and strong monotonicity. However, in Theorem 2, we show that there exists no binary relation satisfying anonymity, distributive fairness semiconvexity, and sup norm continuity. We also clarify logical relations between these axioms and non-dictatorship axioms. Received: 30 August 2000/Accepted: 18 March 2002 This paper is based on Chapt. 4 of my Masters Thesis [15] submitted to Kobe University, and won the Kanematsu Fellowship from the Research Institute for Economics and Business Administration of Kobe University in May 2001. I am grateful to Jun Iritani for helpful discussions and encouragement, two anonymous referees of this journal, three anonymous referees of the Kanematsu Fellowship, Eiichi Miyagawa, Noritsugu Nakanishi, Nguyen Huu Phuc, Hiroo Sasaki, Koji Shimomura, William Thomson, and Toyoaki Washida for detailed comments. I also thank participants at the spring meeting of Japanese Economic Association at Yokohama City University in May 2000, at the annual meeting of the Society for Environmental Economics and Policy Studies in Tsukuba in September 2000, and at the Kanematsu Fellowship Seminar at Kobe University in May 2001 for valuable comments.     

Preference,topology and measure

A symmetric difference metric topology on the collection of binary relations on a countably infinite set provides a new setting for the study of properties of preferences and, as an illustration, is used to lend credence and meaning to some simple intuitions about properties of binary relations. A finite measure on a \(\sigma \) -algebra over the same collection of binary relations is used to provide support for the topological results.     

Equity, continuity, and myopia: A generalization of Diamond’s impossibility theorem

 We consider social preferences over infinite horizon intergenerational consumption paths. We use the Mackey topology to define continuity of social preferences. Our main objective is to generalize one of Diamond’s impossibility theorems. First, we show that the trivial preference relation is the only asymmetric social preference relation satisfying equity and continuity. Second, we compare Campbell’s impossibility theorem with ours. Finally we use an order-based notion of myopia and establish another impossibility result. Received: 26 August 1994/Accepted: 5 June 1996     

Comparison functions and choice correspondences

In this paper, we introduce the concept of a comparison function, which is a mapping g that assigns numbers to ordered pairs of alternatives (x,y) with the property that g(x,y)=−g(y,x). The paper discusses how some well-known choice correspondences on tournaments such as the uncovered set, the minimal covering set and the bipartisan set can be extended to this general framework. Axiomatic characterizations and properties are studied for these correspondences. Received: 4 November 1996/Accepted: 13 April 1998     

Ranking profiles of capability sets

In this paper, we present an innovative approach for ranking profiles of capability sets on the basis of equity. An interesting way of capturing the notion of equity is to take into account the extent to which each of the different functioning vectors is shared by the population under consideration (of size n). This is done by defining the ‘common capability sets’ enjoyed by k individuals as the set of functioning vectors simultaneously available to at least k individuals (1 ≤ k ≤ n). These sets are closely related to the original capability sets and have some interesting properties that are examined throughout the paper. We define and axiomatically characterize a capability profile ranking that lexicographically compares the different common capability sets. We would like to thank for helpful discussion and comments to Jorge Alcalde-Unzu, Ritxar Arlegi, Miguel A. Ballester, Jose Enrique Galdón, Antonio Nicolò, Jorge Nieto, Prasanta Pattanaik, John Weymark and the anonymous referees of this paper. The project is supported by Spanish’ Comision Interministerial de Ciencia y Technologia (SEC2003-08105) and by the European Commission (MRTN-CT-2003-504796).     

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A _k is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B _l . If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained.     

Non-collegial simple games and the nowhere denseness of the set of preference profiles having a core

In recent papers, somewhat conflicting results on the generic emptiness of the core have been proven. Rubinstein (1979) has shown that the core is generically empty in the Kannai topology even without a restriction on the dimensionality of the alternative space. Schofield (1980) finds the core generically empty in the Whitney-C topology, but requires a dimensionality condition. This note explores the apparent conflict by proving a generalization of Rubinstein's result for the Whitney-C ⁰ topology, and showing that the result does not extend to the Whitney-C ¹ topology without a dimensionality condition.I would like to thank Kim Border and Richard McKelvey for their helpful discussion and comments. This research was supported in part by the National Science Foundation under Grant no. SES 78-2478781     

Egalitarian-equivalence and the Pareto principle for social preferences

The Pareto principle is often in conflict with the equity criteria in construction of social preferences: there exist two allocations x and y such that x Pareto dominates y, but y is an equitable allocation whereas x is not. The efficiency-first principle requires to rank an allocation x higher than y if (i) x Pareto dominates y or (ii) x and y are Pareto-noncomparable and x is equitable whereas y is not. The equity-first principle reverses the order of application of the two criteria. Adopting egalitarian-equivalence as the notion of equity, we examine rationality of the social preference functions based on the efficiency-first or the equity-first principle. The degrees of rationality vary widely depending on which principle is adopted, and depending on the range of egalitarian-reference bundles. We show several impossibility and possibility results as well as a characterization of the social preference function introduced by Pazner and Schmeidler (1978). We also identify the sets of maximal elements of the social preference relations in the set of feasible allocations. The results are contrasted with those in the case where no-envy is the notion of equity.This paper is a much extended version of a part of Tadenuma (1998). The author is grateful to Marc Fleurbaey, Serge-Chiristophe Kolm, Kotaro Suzumura, and William Thomson for helpful comments on the earlier version of the paper. ‘‘Financial support from the Ministry of Education, Culture, Sports, Science and Technology of Japan for the 21st Century Center of Excellence Project on the Normative Evaluation and Social Choice of Contemporary Economic Systems is gratefully acknowledged’’.     

Depressive Symptoms and Academic Achievement: The Role of Adolescents’ Perceptions of Teachers’ and Peers’ Behaviors

This present study, using a longitudinal design, investigated how depressive symptoms are related to academic achievement and whether the perceptions of teachers’ and peers’ behaviors moderated this relation. A sample of 302 adolescents (60.10% girls, M_age = 17.35) completed scales measuring the depressive symptoms and perception of their teachers’ support/equity and peers’ cooperation/cohesiveness behaviors at Time 1. The adolescents’ average grades were also collected. The adolescents’ depressive symptoms and average grades were measured again at Time 2. The results showed that depressive symptoms measured at Time 1 were negatively associated with academic achievement measured at Time 2. The adolescents’ perception of their peers’ cooperation/cohesiveness moderated the relation between depressive symptoms and academic achievement. The results’ implications for educational practice are discussed.     

Evolution of Equity Market Risk During the Crisis: Europe, Americas and Asia

A set of regional and country??s equity indices have been evaluated and analysed in their Value at Risk (VaR) and Conditional Value at Risk (CVaR) in this paper, using computational methods based on the Johnson systems. Comparing the main statistics and the values of the two cited measures of financial risk obtained using a roll-over mechanism in the period January 2008?CJuly 2012, the impact of the crisis on equity market risk can be shown. It seems that for all regions and countries the patterns are very similar: there is a peak of all the risk measures adopted at the beginning of the crisis (September 2008?CFebruary 2009) and another turbulent period in 2011 (from July to December). In other terms, the global patterns of the main financially relevant countries and their regional aggregations demonstrate that ??One Financial system??, and just one, is already at work, in theory and in practice. On the other hand, the scale of the risk measures differs from one country to another: e.g., with a probability of 1?%, the potential daily loss on an equity position in Latin America in the worst period arrives to about 25?%, the Emerging Markets as a whole show values around 20?% and Asia arrives to 15?%, while the US and European corresponding values are below 14?%. This is true whatever the risk measure and whatever the confidence interval (which, again, influences strongly the scale of the risk values). Looking in detail to the last period (April 2012?CJuly 2012), a general improvement could be appreciated: the risk measures are all around 4?% if not on one hand Italy and Spain (around 6?%), Greece (around 10?%) and on the other hand the ??virtuous?? Chile (around 1.5?%), again with reference to a probability of 1?%. Nevertheless, indices of performance (expected return over risk measure) have been evaluated and compared. They give sometimes different answers to the risk measures themselves.     

Application of multivariate longitudinal models in SIRT6, FBS,and BMI analysis of the elderly

Abstract

Objective: SIRT6 is a main regulator of metabolism and lifespan and its importance has been implicated in the prevention against aging-related diseases. The objective of this study was to examine the application of multivariate longitudinal models in SIRT6, FBS, and BMI analysis in the elderly men after eight weeks concurrent training with supplementation of l-arginine (l-Arg).

Methods: Thirty two elderly men with mean age of 63.09?±?3.71 years were randomly divided into four equal-sized groups (each n?=?8); Exercise?+?supplement (ES) group; exercise?+?placebo (EP) group; supplement (S) group and control (C) group. The ES and EP groups performed the eight weeks of concurrent training, three sessions per week. Group ES and group S consumed 1000?mg of l-Arg per day at 8:00?pm. Measurements of biochemical variables were done by ELISA Reader method. For analytical purposes, we used the paired sample t-test and multivariate longitudinal modeling with generalized estimating equation (GEE) methodology. All analyses have been implemented in R-3.4.1. p Values less than .05 were considered statistically significant.

Results: With respect to significant association between sirt6, FBS, and BMI, this study showed that synergy effect of training and supplementation was greater than the sum of their individual effects on SIRT6 (β?=?0.79, p?<?.001), FBS (β?=??5.56, p?=?.022), and BMI (β?=??3.89; p?=?.041). Also exercise alone had a significantly larger effect than supplementation alone on responses.

Conclusions: It can be concluded that the joint usage of concurrent training and supplement of l-Arg for elderly men could improve the metabolism and body composition.     

Bargaining over a finite set of alternatives

We analyze bilateral bargaining over a finite set of alternatives. We look for "good" ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued. Professor Sertel passed away on January 25, 2003.     

Psychometric Evaluation of the Affect Regulation Checklist: Clinical and Community Samples,Parent-Reports and Youth Self-Reports

The Affect Regulation Checklist (ARC) was designed to capture affect dysregulation, suppression, and reflection. Importantly, affect dysregulation has been established as a transdiagnostic mechanism underpinning many forms of psychopathology. We tested the ARC psychometric properties across clinical and community samples and through both parent-report and youth self-report information. Clinical sample: Participants included parents (n = 814; M_age = 43.86) and their child (n = 608; M_age = 13.98). Community sample: Participants included independent samples of parents (n = 578; M_age = 45.12) and youth (n = 809; M_age = 15.67). Exploratory structural equation modeling supported a three-factor structure across samples and informants. Dysregulation was positively associated with all forms of psychopathology. In general, suppression was positively associated with many forms of psychopathology, and reflection was negatively associated with externalizing problems and positively associated with internalizing problems.     

What older adolescents expect from physical activity: Implicit cognitions regarding health and appearance outcomes

Objective: To explore older adolescents' reflective and impulsive thoughts about health- and social/appearance-related physical activity (PA) outcomes and investigate how those thoughts relate to their PA behavior. Participants: One hundred and forty-four undergraduate students (109 women; 35 men) aged 17–19 years (M = 18.11, SD = 0.65) participated in this study in October 2015. Methods: Participants completed a Go/No-go Association Task that assessed automaticity of associations between PA words and either health outcomes or social/appearance outcomes. Questionnaires assessing PA behavior, attitudes, outcome expectations, and body image were also completed. Results: Participants demonstrated a positive automatic association between PA and social/appearance outcomes, F(1, 136) = 4.403, p < .05, η² = .031, but they showed no difference in their associations between PA and desirable or undesirable health outcomes, F(1, 136) = 2.405, p = .123, η² = .017. Conclusions: Older adolescents implicitly attend to the social/appearance outcomes of PA more than potential health outcomes, indicating that social recognition and a desirable physique may be the key PA motivators for adolescents.     

Aggregation of coarse preferences

We consider weak preference orderings over a set A _n of n alternatives. An individual preference is of refinement?≤n if it first partitions A _n into ? subsets of `tied' alternatives, and then ranks these subsets within a linear ordering. When ?<n, preferences are coarse. It is shown that, if the refinement of preferences does not exceed ?, a super majority rule (within non-abstaining voters) with rate 1− 1/? is necessary and sufficient to rule out Condorcet cycles of any length. It is argued moreover how the coarser the individual preferences, (1) the smaller the rate of super majority necessary to rule out cycles `in probability'; (2) the more probable the pairwise comparisons of alternatives, for any given super majority rule. Received: 29 June 1999/Accepted: 25 February 2000