Arrow's paradox and mathematical theory of democracy

Two measures, the weight of coalitions and the probability of situations in decision making, are used to characterize the representativeness, i.e. the capability of individuals to represent the social preference. It is proved that there always exists an individual who represents a majority on average, and an individual who represents a majority in most cases. This result is applied to Arrow's social choice model. It follows that there always exists a dictator who is a representative of the society rather than a dictator in a proper sense. After the concept of dictator has been refined to a dictator in a proper sense, Arrow's axioms become consistent. The idea of optimal representation is extended to limited groups of representatives which make decisions on behalf of the whole society. We consider the cabinet (named by analogy with the cabinet of ministers) which consists of a few representatives with delimited domains of competence, and the council which makes decisions by means of voting. It is shown that the representativeness of optimal cabinets and councils tends to 100% of maximally possible values as the number of their members increases, independently of the size of the society. We suggest a geometric interpretation of optimal representatives, cabinets, and councils, based on approximation formulas for the indicators of representativeness derived for the model with a large number of independent individuals. Finally, for cabinets and councils we establish the consistency of different concepts of optimality with respect to different indicators of representativeness. Our consideration is applicable to multicriteria decision making. An appointment of a cabinet or a council corresponds to selecting a few partial criteria. Therefore, the obtained results can be used for reducing the set of partial criteria to a certain sufficient minimum. The concepts of dictator, cabinet, and council can be understood as models of president, government, and parliament, respectively. Thus our results justify reducing social choice to individual choice or small group choice. Although it is in use in all democratic systems, its acceptability is not evident at all. In other words, we justify the demoncraticity of such forms of political power as the president, the parliament, and the government.     

Sampling Strategies for Toxic Air Contaminants

Annual concentrations of toxic air contaminants are of primary concern from the perspective of chronic human exposure assessment and risk analysis. Despite recent advances in air quality monitoring technology, resource and technical constraints often impose limitations on the availability of a sufficient number of ambient concentration measurements for performing environmental risk analysis. Therefore, sample size limitations, representativeness of data, and uncertainties in the estimated annual mean concentration must be examined before performing quantitative risk analysis. In this paper, we discuss several factors that need to be considered in designing field-sampling programs for toxic air contaminants and in verifying compliance with environmental regulations. Specifically, we examine the behavior of SO2, TSP, and CO data as surrogates for toxic air contaminants and as examples of point source, area source, and line source-dominated pollutants, respectively, from the standpoint of sampling design. We demonstrate the use of bootstrap resampling method and normal theory in estimating the annual mean concentration and its 95% confidence bounds from limited sampling data, and illustrate the application of operating characteristic (OC) curves to determine optimum sample size and other sampling strategies. We also outline a statistical procedure, based on a one-sided t-test, that utilizes the sampled concentration data for evaluating whether a sampling site is compliance with relevant ambient guideline concentrations for toxic air contaminants.     

Grounded Neural Networking: Modeling Complex Quantitative Data

The latest advances in artificial intelligence software (neural networking) have finally made it possible for qualitative researchers to apply the grounded theory method to the study of complex quantitative databases in a manner consistent with the postpositivistic, neopragmatic assumptions of most symbolic interactionists. The strength of neural networking for the study of quantitative data is twofold: it blurs the boundaries between qualitative and quantitative analysis, and it allows grounded theorists to embrace the complexity of quantitative data. The specific technique most useful to grounded theory is the Self‐Organizing Map (SOM). To demonstrate the utility of the SOM we (1) provide a brief review of grounded theory, focusing on how it was originally intended as a comparative method applicable to both quantitative and qualitative data; (2) examine how the SOM is compatible with the traditional techniques of grounded theory; and (3) demonstrate how the SOM assists grounded theory by applying it to an example based on our research.     

Classifying At‐Risk High School Youth: The Influence of Exposure to Community Violence and Protective Factors on Academic and Health Outcomes

Using cluster analysis, 789 predominately Latino and African American high school youth were classified into varying academic at‐risk profiles using self‐reported levels of academic confidence, motivation to attend school, perceived family support, connections with teachers and peers, and exposure to violence. Six clusters emerged, 5 of which were identified as “at‐risk.” The clusters were examined in relation to academic stress, health status, grades, and school retention. Exposure to violence was one distinguishing feature of youth identified as most vulnerable, vulnerable, and resilient; however, youth identified as resilient recorded better academic outcomes.     

Age Cohort, Ancestry, and Immigrant Generation Influences in Family Relations and Psychological Well-Being among Black Caribbean Family Members

Immigration is contributing to the U.S. population becoming increasingly ethnically diverse. This article examines the role of family relations and well-being among different generations of Black Caribbean immigrants. Family disruptions, such as migration, can have complex effects on the support networks and emotional well-being of family members. Data from a recently completed national study of American Blacks in the United States, however, reveal significant similarities across ancestry and immigrant status in family contact, solidarity and well-being. It is concluded that intrafamilial relations may serve to overcome barriers of geographical distance in providing comparable levels of contact, solidarity, and well-being for both U.S.-born and immigrant Black Caribbean family members of different generations. Because of the increasing numbers of immigrant elders, these sources of family support will become increasingly more important in bridging the gaps between government resources and needed assistance in an aging society.     

Earnings of Chinese Immigrants in the Enclave and Mainstream Economy*

La documentation sur le sujet n'est pas décisive quant à savoir si léconomie ethnique enclavée enregistre un rendement économique comparable chez les travailleurs et les entrepreneurs immigrants à ceux qui se situent dans le courant économique principal. Les auteurs de cette étude utilisent des données du Recensement du Canada de 2001 sur la langue la plus utilisée au travail din de mesurer la participation des immigrants chinois à léconomie enclavée. Après les avoir comparés au capital humain ainsi qu'aux variations liées au travail et au milieu urbain, les résultats démontrent que le rendement est moins élevé chez les hommes et chez les femmes de l'enclave que celui des gens qui se trouvent dans le courant économique principal. Les caractéristiques de la langue et le type de travail qui s'effectue dans léconomie enclavée expliquent pourquoi le rendement y est inférieur à celui obtenu dans le courant économique principal. The literature in inconclusive as to whether the immigrant enclave economy offers returns to immigrant workers and entrepreneurs comparative to those in the mainstream economy. This study uses data from the 2001 Census of Canada on language most often used at work to measure enclave economy participation for Chinese immigrants. The findings show that returns are lower for men or women in the enclave than those in the mainstream economy, respectively, after controlling for human capital, work‐related and urban variations. Language features of and job type in the enclave economy explain why returns are inferior to that of the mainstream economy.     

The Development of Anticipatory Smiling

When do infants begin to communicate positive affect about physical objects to their social partners? We examined developmental changes in the timing of smiles during episodes of initiating joint attention that involved an infant gazing between an object and a social partner. Twenty‐six typically developing infants were observed at 8, 10, and 12 months during the Early Social‐Communication Scales, a semistructured assessment for eliciting initiating joint attention and related behaviors. The proportion of infant smiling during initiating joint attention episodes did not change with age, but there was a change in the timing of the smiles. The likelihood of infants smiling at an object and then gazing at the experimenter while smiling (anticipatory smiling) increased between 8 and 10 months and remained stable between 10 and 12 months. The increase in the number of infants who smiled at an object and then made eye contact suggests a developing ability to communicate positive affect about an object.     

Loss functions for estimation of extrema with an application to disease mapping

It is often of interest to find the maximum or near maxima among a set of vector‐valued parameters in a statistical model; in the case of disease mapping, for example, these correspond to relative‐risk “hotspots” where public‐health intervention may be needed. The general problem is one of estimating nonlinear functions of the ensemble of relative risks, but biased estimates result if posterior means are simply substituted into these nonlinear functions. The authors obtain better estimates of extrema from a new, weighted ranks squared error loss function. The derivation of these Bayes estimators assumes a hidden‐Markov random‐field model for relative risks, and their behaviour is illustrated with real and simulated data.