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.     

The Independence of Aptitudes,Interests, and Career Beliefs

The importance of client beliefs in career counseling depends on their ability to add unique information about the client over and above that contributed by aptitudes and interests. The Career Beliefs Inventory was administered to 200 Australian students in grade 10 together with measures of Holland's RIASEC interest themes and scholastic aptitudes. The correlations between scales from the three domains showed clearly that beliefs made a contribution distinct from that provided by aptitudes and interests. Even though the results may reflect possible sampling or method variance, career beliefs in this sample added unique information to that traditionally used in career counseling.     

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.     

The validity of survey responses on abortion: Evidence from Estonia

This paper presents results of a validation survey of abortion conducted in Tallinn, Estonia in April and May 1992. The sample was drawn from patient records in a maternity hospital. Women who had an abortion in that hospital in 1991 were asked about recent abortions as part of a survey about women’s health. More than 80% of the respondents reported having a recent abortion. Some respondents misreported their abortion as a miscarriage. Moreover, some variation in reporting was associated with respondents’ characteristics. Ethnic Estonians were less likely to report their abortion than were Russians, women over age 40 were less likely to report the abortion than younger women, and women who had the abortion late in the first trimester were less likely to report that abortion. There was some evidence that unmarried women were less likely than married women to report their abortion, and that women who had borne three or more children were less likely to report their abortion than women who had borne fewer children. These differences probably stem from the extent to which pregnancy or abortion is considered stigmatizing for women in different situations.     

Local polynomial estimation of Poisson intensities in the presence of reporting delays

Summary.  The system for monitoring suicides in Hong Kong has considerable delays in reporting as the cause of death needs to be determined by a coroner's investigation. However, timely estimates of suicide rates are desirable to assist in the formulation of public health policies. This motivated us to develop a non-parametric procedure to estimate the intensity function of a Poisson process in the presence of reporting delays. We give closed form estimators of the Poisson intensity and the delay distribution, conduct simulation studies to evaluate the method proposed and derive their asymptotic properties. The method proposed is applied to estimate the intensity of suicide in Hong Kong.     

Bayesian analysis of directed graphs data with applications to social networks

Summary.  A fully Bayesian analysis of directed graphs, with particular emphasis on applica- tions in social networks, is explored. The model is capable of incorporating the effects of covariates, within and between block ties and multiple responses. Inference is straightforward by using software that is based on Markov chain Monte Carlo methods. Examples are provided which highlight the variety of data sets that can be entertained and the ease with which they can be analysed.     

Stripping in the New Millennium: Thinking about Trends in Exotic Dance and Dancers' Lives

With the increasing presence of sex and sexuality in American popular culture, the stripping industry is undoubtedly undergoing important subcultural and organizational transition. What are the implications of these changes for the individuals involved? The current paper reviews much of the literature on exotic dance to consider the potential transformations in the organization of the sex industry and how these changes may impact the lives of those involved. Specifically, I note some key differences in the literature that suggest how exotic dance has shifted. I then pose some questions for empirical inquiry. I argue that transformations in the exotic industry are creating new opportunities and challenges for women, and may be particularly deleterious for poor and minority women. I call for sociologists to investigate the consequences of organizational transferal in sexual labor, reevaluate the dynamics of agency and exploitation, and consider the potential differential impact of these trends on poor women and women of color.