Absorbing and generalized stable sets

Within the framework of an abstract system we establish the existing relationship between the following two solutions: The absorbing sets solution and the generalized stable sets solution.We are grateful to an anonymous referee for helpful comments. Financial support from the project 9/UPV-00035.321-13699/2001 is grateful acknowledged. Inarra gratefully acknowledges the hospitality of Brown University and the financial support from the Ministerio de Educación, Cultura y Deporte, PR 2003-0287.     

More on the stable,generalized stable,absorbing and admissible sets

We show the necessary and sufficient conditions for any two of the sets of stable, generalized stable, absorbing or admissible sets of an abstract decision problem to coincide. We show that all these conditions can be written as depending only on the number of predecessors or successors of some alternatives.     

A note on the paper ‘cost range and the stable network structures’

The analysis in the paper ‘cost range and the stable network structures’ missed a stable structure —— a line. We explain its reason and reinforce the initial conclusion.     

A note on female ejaculation

We developed a 14‐item Attitudes Toward Sexuality Scale (ATSS) to compare the sexual attitudes of early, middle, and late adolescents and their parents. One hundred forty‐one adolescents between the ages of 12 and 20 and their parents completed a questionnaire consisting of the ATSS and demographic information. The Cronbach alpha reliability coefficient for the adolescents was .75, and for the parents it was .84. A principal components analysis revealed four major dimensions of the scale: a large General factor, Legality/Morality, Alternative Modes of Sexual Expression, and Individual Rights. The correlation pattern between the ATSS and subscales of the Sex Knowledge and Attitudes Test, as well as with certain demographic variables, supports the construct validity of the ATSS. This is, therefore, a scale which may be used for research in which the sexual attitudes of adults and adolescents of various ages are to be measured and compared.     

A note on interdependent happiness

Based on two models of interdependent utilities [Becker, G., 1974. A theory of social interaction, Journal of Political Economy 82, 1064–1093; Fehr, E., Schmidt, K., 1999. A theory of fairness, competition, and cooperation, Quarterly Journal of Economics 114, 817–868] we derive a functional relationship between average happiness and the standard deviation of happiness within a country. This hypothesis is supported by an empirical investigation of 71 countries which shows that the average happiness in these countries depends only on income and on the standard deviation of happiness σ. The latter may be partly based on influences beyond income, for which no data are available. Income has the expected positive influence and σ has the expected negative influence, i.e. large differences in “autonomous” happiness have a dampening influence on “effective” happiness which also takes into account the happiness of others.     

A note on continuous social choice

 We discuss continuous social choice functions defined on the set of the equivalence classes induced by profiles of individual preferences corresponding to anonymity. It is shown that we can at best obtain the equivalent result of Chichilnisky’s impossibility theorem when the set of an equivalence classes is endowed with various reasonable topologies. Received: 28 February 1994/Accepted: 22 April 1996     

A note on images of networks

Visual imagery and visual representations have proven very useful in some of the most important discoveries in the history of science. It is not surprising, therefore, that the earliest students of network phenomena often made use of visual representations (e.g. sociograms) to assist in the analysis, interpretation and illustration of complex relational data: by creating such visual representations, human faculties for visual imagery and pattern recognition could be more fully utilized in the search for structural patterns in sociometric networks. What is somewhat surprising, though, is that the techniques for creating visual representations of relational data have remained virtually unchanged since the study of social networks began: the slow, tedious, pen-and-ink approach of forty years ago is still very much the method of the day.Readily available computer graphics technology, however, introduces potentially powerful possibilities, and some of these are explored. The results of this initial exploration suggest that the time is ripe for forging new tools that will facilitate the analysis of complex relational data, stimulate the development of network theory, and provide new perspectives from which to view previously hidden facets of society.     

A note on contestation-based tournament solutions

In tournaments, one alternative contests another if is a “winner” among only alternatives that beat it. This paper examines the consequences and limitations of the contestation relation by considering a procedure in which alternatives that are contested are iteratively eliminated from consideration. In doing so, a new family of tournament solutions are introduced and related to existing refinements of the Banks set. Findings show that iterated removal of contested alternatives a limited device for choosing from tournaments. These results contrast with results regarding the top-set of the contestation relation. Results highlight the role of the top-set operator for choice from tournaments.     

Generalized average rules as stable Nash mechanisms to implement generalized median rules

We consider a problem in which a policy is chosen from a one-dimensional set over which voters have single-peaked preferences. While Moulin (Public Choice 35:437–455, 1980) and others subsequent works have focused on strategy-proof rules, Renault and Trannoy (Mimeo 2011) and Renault and Trannoy (J Pub Econ Theory 7:169–199, 2005) have shown that the average rule implements a generalized median rule in Nash equilibria and provide an interpretation of the parameters in Moulin’s rule. In this article, we first extend their result by showing that a wide range of voting rules which includes the average rule can implement Moulin’s rule in Nash equilibria. Moreover, we show additionally that within this class, generalized average rules are Cournot stable. That is, from any strategy profile, any best response path must converge to a Nash equilibrium.     

石家大院纪行

一、历史沿革 石家大院位于天津市西青区杨柳青镇,避开市镇的车马喧嚣,在一片深巷之中,这座青砖陶瓦的重重院落显得格外突出.石家大院始建于清末(约1875年),至今已有130年的历史.据说当初石家宅院共有15进院落,占地6000多平方米.现在对外开放的并非当初建造时规模最大的,只是至今保存最完好的一座.     

A note on inferences regarding network subgroups

The evidence presented in Bernard et al. (1980) does not warrant their conclusion. We comment on their lack of concern with the substance of social differentiation in the systems they use as evidence. The substance of social structure is argued to affect the scope, adequacy and power of conclusions drawn from a network analysis and is accordingly a factor to be explicitly considered in justifying those conclusions. With these ideas in mind, our reanaly sis of one system on which good data are available, ostensibly supporting the Bernard et al. conclusion, illustrates how their conclusion regarding network subgroups in that system is unwarranted     

A note on weak ∞-Chichilnisky rules

 There does not exist a weak ∞-Chichilnisky rule as defined in Candeal et al. (1992). Received: 5 November 1992/Accepted: 22 April 1996     

A note on measures of similarity based on centrality

This note presents a measure of similarity between connected nodes in terms of centrality based on Euclidean distances, and compares it to ‘assortative mixing’ [Newman, M.E.J., 2002. Assortative mixing in networks. Physical Review Letters 89, 208701], which is based on Pearson correlation coefficient. This study suggests that the measure based on Euclidean distances may be more appropriate for relatively smaller (N < 500) and denser networks.