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.     

QUESTION WORDING AND PARTISANSHIP: CHANGE AND CONTINUITY IN PARTY LOYALTIES DURING THE 1992 ELECTION CAMPAIGN

Gallup macropartisanship varies more over time than aggregatemeasures of partisanship employing the standard Michigan SurveyResearch Center (SRC) party identification measure, but previousanalyses do not provide direct evidence about why Gallup macropartisanshipis more variable. Although these differences could result fromthe short-term focus of the Gallup party affiliation question,aggregate-level analyses cannot test the effects of questionwording directly. Between March and October 1992, we conducteda series of question-wording experiments, employing six statewidecomputer-assisted telephone interview (CATI) surveys of Michiganadults, including a four-wave panel study. Our analyses stronglysuggest that the Gallup measure responds more to short-termpolitical conditions and clearly demonstrate that the Gallupmeasure is less stable over time. These individual-level resultshelp explain why Gallup macropartisanship varies more over timethan aggregate measures of partisanship employing the standardSRC measure and raise questions about the degree to which onecan generalize from analyses using the Gallup data to the researchliterature on party identification.     

Government Risk Management Priorities: A Comparison of the Preferences of Asian Indian Americans and Other Americans

A survey was conducted of approximately 200 Asian Indian Americans and 200 other residents of New Jersey in order to understand the risk management priorities that they want government to have. We found that Asian Indian Americans, especially younger women, focused on personal/family risks, such as alcohol and drug abuse, sexual abuse, and domestic violence. The New Jersey comparison group, in contrast, placed war/terrorism and loss of health care services and insurance at the top of their priorities for government. These results suggest stressful acculturation-related issues within the Asian Indian community. Both populations want more risk management from government than they believe government is currently providing. Respondents who wanted more from government tended to dread the risk, be fearful of the consequences, trust government, and have a feeling of personal efficacy. Within the Asian Indian American sample, wide variations were observed by language spoken at home and religious affiliation. Notably, Muslims and Hindi language speakers tended not to trust government and hence wanted less government involvement. This study supports our call for studies of recent migrant populations and Johnson's for testing ethnic identity and acculturation as factors in risk judgments.     

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 transition to parenthood in Puerto Rico: Occupational status and the timing of first births

This study examines the relationship between occupational status and fertility timing during a period of rapid development in Puerto Rico. Our fundamental hypothesis is that women with higher status occupations face greater opportunity costs than those with less valued jobs and therefore will be more likely to postpone parenthood until later ages than women without such high costs. We test this hypothesis using event history techniques with data from the 1982 Puerto Rico Fertility and Family Planning Assessment, an island-wide survey of women between the ages of 15 and 49. The analysis examines the effects of occupational status on the timing of first births, and finds strong support for the basic hypothesis, especially regarding the post-ponement of teen births. After the teen years, the effects are less pronounced. Overall, it appears that employment opportunities have played an important role in childbearing decisions in Puerto Rico.An earlier version of this paper was presented at the annual meeting of the Population Association of America, Denver, Colorado, 30 April–2 May 1992.     

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.