Book Reviews

In censuses and surveys in most African countries it has become the practice to estimate informants' age by the method of the historical calendar. This involves an attempt to relate a remembered historical event, occurring during the subject's childhood, with his age at the time.

This paper attempts a first evaluation of the method with particular reference to the 1961–63 multi-round survey in rural Morocco. It is shown that in practice the method is highly complex and easily misunderstood by interviewers and respondents. An attempt to lay down a precise procedure by means of a very detailed questionnaire appeared to yield at best only marginally more accurate results than the simpler procedure used in an earlier round. The more complex questionnaire did, however, introduce new patterns of misuse by the interviewer. There was evidence that the historical calendar gave somewhat better data than eye estimates, but results were highly defective for both methods.

It is clear that the method is far from perfect. Interviewer training and supervision remain the key to accurate age determination. If the potential benefits of the complex historical calendar method are to be realized, training and supervision need to be even more thorough than where simpler methods are used.     

Property testing for cyclic groups and beyond

This paper studies the problem of testing if an input (Γ,°), where Γ is a finite set of unknown size and ° is a binary operation over Γ given as an oracle, is close to a specified class of groups. Friedl et al. (Proc. of STOC, 2005) have constructed an efficient tester using poly(log|Γ|) queries for the class of abelian groups. We focus in this paper on subclasses of abelian groups, and show that these problems are much harder: Ω(|Γ|^1/6) queries are necessary to test if the input is close to a cyclic group, and Ω(|Γ| ^c ) queries for some constant c are necessary to test more generally if the input is close to an abelian group generated by k elements, for any fixed integer k≥1. We also show that knowledge of the size of the ground set Γ helps only for k=1, in which case we construct an efficient tester using poly(log|Γ|) queries; for any other value k≥2 the query complexity remains Ω(|Γ| ^c ). All our upper and lower bounds hold for both the edit distance and the Hamming distance. These are, to the best of our knowledge, the first nontrivial lower bounds for such group-theoretic problems in the property testing model and, in particular, they imply the first exponential separations between the classical and quantum query complexities of testing closeness to classes of groups.     

Aggregation of preferences with a variable set of alternatives

A social choice correspondence called the Essential set is studied with the help of an axiom called Cloning Consistency. Cloning consistency is the requirement that the formal choice rule be insensitive to the replication of alternatives. The Essential set is the support of the optimal mixed strategies in a symmetric two-party electoral competition game. Received: 24 March 1998/Accepted: 3 March 1999     

Fundamentals of Theory and Practice Revisited: Boszormenyi‐Nagy and Contextual Therapy: An Overview

This paper provides an overview of the work of Ivan Boszormenyi‐Nagy, the originator of Contextual Therapy. The initial form of Contextual Therapy is surveyed, but closer attention is paid to more recent developments in the theory and practice. Several critiques of Contextual Therapy are introduced. The paper includes a detailed example of a first session conducted according to Boszormenyi‐Nagy's principles.     

Strategy-proof resolute social choice correspondences

We qualify a social choice correspondence as resolute when its set valued outcomes are interpreted as mutually compatible alternatives which are altogether chosen. We refer to such sets as “committees” and analyze the manipulability of resolute social choice correspondences which pick fixed size committees. When the domain of preferences over committees is unrestricted, the Gibbard–Satterthwaite theorem—naturally—applies. We show that in case we wish to “reasonably” relate preferences over committees to preferences over committee members, there is no domain restriction which allows escaping Gibbard–Satterthwaite type of impossibilities. We also consider a more general model where the range of the social choice rule is determined by imposing a lower and an upper bound on the cardinalities of the committees. The results are again of the Gibbard–Satterthwaite taste, though under more restrictive extension axioms.     

Fertility transition in Communist Albania, 1950-90

In 1945, at the end of the Second World War, Albania had the highest fertility in Europe with an average of more than six live births per woman. However when Albania emerged from behind the 'olive curtain' in 1990, fertility had fallen to three children per woman, despite a pro-natalist environment and in the virtual absence of contraception and abortion. Nevertheless, after five decades, Albania's position at the top of the European fertility league remains unchanged. This paper documents the fertility transition in Albania during the period 1950-90 and places the demographic results in the context of recent socioeconomic and cultural change.     

Global Political Economy: Power, Labour, Politics

This discussion examines the issue of globalisation in terms of the interaction of economy, politics and power. It begins by considering the claims implied by the language of globalisation. How extensive and inclusive is the global economy? The second section goes on to outline the broad geography of globalisation in terms of a balance of power that is both highly uneven but also subject to marked changes. While the global economy as this developed since the 1970s may have reproduced established patterns of colonial and post‐war economic power, in the current century, power is shifting away from these nineteenth‐ and twentieth‐century models to a new balance of regional power in which large Asian economies may dominate. Alongside these patterns of regional and national power, third, the discussion considers the uneven geography of capital and labour captured in models of an international division of labour that is organised by flows of capital investment but also of mobile workers. The final section offers an overview of the architecture of global politics, from the level of international institutions and nation‐states, to non‐governmental bodies that operate across borders to support or resist the workings of a global economy.     

Calibrated imputation in surveys under a quasi-model-assisted approach

Summary.  We propose to use calibrated imputation to compensate for missing values. This technique consists of finding final imputed values that are as close as possible to preliminary imputed values and are calibrated to satisfy constraints. Preliminary imputed values, potentially justified by an imputation model, are obtained through deterministic single imputation. Using appropriate constraints, the resulting imputed estimator is asymptotically unbiased for estimation of linear population parameters such as domain totals. A quasi-model-assisted approach is considered in the sense that inferences do not depend on the validity of an imputation model and are made with respect to the sampling design and a non-response model. An imputation model may still be used to generate imputed values and thus to improve the efficiency of the imputed estimator. This approach has the characteristic of handling naturally the situation where more than one imputation method is used owing to missing values in the variables that are used to obtain imputed values. We use the Taylor linearization technique to obtain a variance estimator under a general non-response model. For the logistic non-response model, we show that ignoring the effect of estimating the non-response model parameters leads to overestimating the variance of the imputed estimator. In practice, the overestimation is expected to be moderate or even negligible, as shown in a simulation study.     

Does majoritarian approval matter in selecting a social choice rule? An exploratory panel study

This study is an attempt to empirically detect the public opinion concerning majoritarian approval axiom. A social choice rule respects majoritarian approval iff it chooses only those alternatives which are regarded by a majority of “voters” to be among the “better half” of the candidates available. We focus on three social choice rules, the Majoritarian Compromise, Borda’s Rule and Condorcet’s Method, among which the Majoritarian Compromise is the only social choice rule always respecting majoritarian approval. We confronted each of our 288 subjects with four hypothetical preference profiles of a hypothetical electorate over some abstract set of four alternatives. At each hypothetical preference profile, two representing the preferences of five and two other of seven voters, the subject was asked to indicate, from an impartial viewpoint, which of the four alternatives should be chosen whose preference profile was presented, which if that is unavailable, then which if both of the above are unavailable, and finally which alternative should be avoided especially. In each of these profiles there is a Majoritarian Compromise-winner, a Borda-winner and a Condorcet-winner, and the Majoritarian Compromise-winner is always distinct from both the Borda-winner and the Condorcet-winner, while the Borda- and Condorcet-winners sometimes coincide. If the Borda- and Condorcet-winners coincide then there are two dummy candidates, otherwise only one, and dummies coincide with neither of the Majoritarian Compromise-, Borda- or Condorcet-winner. We presented our subjects with various types of hypothetical preference profiles, some where Borda respecting majoritarian approval, some where it failed to do so, then again for Condorcet, some profiles it respected majoritarian approval and some where it did not. The main thing we wanted to see was whether subjects’ support for Borda and Condorcet was higher when this social choice rule respected majoritarian approval than it did not. Our unambiguous overall empirical finding is that our subjects’ support for Borda and Condorcet was significantly stronger as they respect majoritarian approval.