AN ANALYTIC FORM FOR THE CUMULATIVE DISTRIBUTION FUNCTION OF THE BELL-DOKSUM STATISTIC

A closed form analytic expression for the Bell-Doksum Statistic is developed. The use of the generalized hypergeometric function to evaluate the expression is demonstrated, and a table of critical values for 2 n 25 is presented.     

Size and structure of the household in England over three centuries

Abstract Data giving sizes and structures of households have been rare for any country before the institution of the official census, and have to be gleaned from surviving documents containing listings of inhabitants. This article, the first of two, describes the collection of listings of inhabitants of English communities which is being assembled by the Cambridge Group for the History of Population and Social Structure and the methods by which the hundred most informative of them have been submitted to analysis. When ranged alongside the information on mean household size derived from the official British census since its inception in 1801, the results of this analysis suggest the following. 1. Mean household size in England and Wales as a whole was relatively constant at 4·75 or a little below for the whole period from the sixteenth century until 19II, and has only fallen since that date. The reduction of about one-third starting in 1921 may therefore be the first of considerable magnitude ever to occur: it seems to have been particularly rapid between 1911 and 1931. 2. Mean household size in England and Wales has been surprisingly resistant to demographic fluctuation on the one hand and to the structural influences of industrialization on the other, until the last fifty or sixty years. 3. The traditional household in England has never been extended on any definition, at least since the sixteenth century. Mean household size varied with social status, and a majority lived in households of six or more members. But this distribution was due to the very large numbers of servants living in and not to the presence of resident kin, who seem to have been rare. 4. The relationship between fertility, mortality and mean household size is different from what has been supposed. This article ends by registering the paradox that proportion of children in a pre-industrial English community apparently seems to be negatively, not positively, related to its mean household size, and this theme will be taken up in the second article. These four points are illustrated by a series of tables drawn from the analysis of the one hundred communities.     

Malaria eradication and its effect on mortality levels: A comment

Abstract In his article 'Malaria eradication and its effect on mortality levels' (Population Studies d21, 3, November 1967) Dr. S. A. Meegama criticised the approach followed by Professor Peter Newman in an earlier investigation of the effects of malaria eradication in Ceylon. In the present series of comments and rejoinders, Professor Newman and Dr. Meegama discuss in detail their interpretations of the data and the methods they have used in assessing the role of malaria eradication.     

The voter who wasn’t there: Referenda,representation and abstention

We analyze single binary-choice voting rules and identify the presence of the No-Show paradox in this simple setting, as a consequence of specific turnout or quorum conditions that are included in actual rules. Since these conditions are meant to ensure a representative outcome, we formalize this concern and reach our main result: no voting rule can ensure representation if abstention is possible, unless restrictive assumptions are made on the preference domain of abstainers. We then focus on the main referendum systems and show that appropriate restrictions do make them compatible with representation. The main purpose of our paper is, however, to provide a tool for referendum design: rather than imposing arbitrary restrictions on the preference domain of non-voters, we recommend instead that a conscious choice be made on how abstention is to be interpreted and that this choice be used to derive the corresponding referendum rule.The idea for this paper started with some jocose but insightful notes written by José João Marques da Silva at the time of the first referendum held in Portugal (1998). When José João passed away in August 2000, ISEG lost a bright, interested and friendly scholar. May we dedicate this paper to his memory. This paper was presented at the 2002 Annual Meeting of the Public Choice Society and Economic Science Association, San Diego, CA and a preliminary version was presented at the 2001 Annual Meeting of the European Public Choice Society, Paris. We would like to thank Mathew Braham, Moshé Machover, Eric Maskin, Vincent Merlin, Hannu Nurmi, Katri Sieberg, Frank Steffen, and two anonymous referees for helpful comments. The usual proviso applies.