Sets of alternatives as Condorcet winners

We characterize sets of alternatives which are Condorcet winners according to preferences over sets of alternatives, in terms of properties defined on preferences over alternatives. We state our results under certain preference extension axioms which, at any preference profile over alternatives, give the list of admissible preference profiles over sets of alternatives. It turns out to be that requiring from a set to be a Condorcet winner at every admissible preference profile is too demanding, even when the set of admissible preference profiles is fairly narrow. However, weakening this requirement to being a Condorcet winner at some admissible preference profile opens the door to more permissive results and we characterize these sets by using various versions of an undomination condition. Although our main results are given for a world where any two sets – whether they are of the same cardinality or not – can be compared, the case for sets of equal cardinality is also considered. Received: 15 March 2001/Accepted: 31 May 2002 This paper was written while Barış Kaymak was a graduate student in Economics at Boğazi?i University. We thank ?ağatay Kayı and İpek ?zkal-Sanver who kindly agreed to be our initial listeners. The paper has been presented at the Economic Theory seminars of Bilkent, Ko? and Sabancı Universities as well as at the Fifth Conference of the Society for the Advancement of Economic Theory, July 2001, Ischia, Italy and at the 24^th Bosphorus Workshop on Economic Design, August 2001, Bodrum, Turkey. We thank Fuad Aleskerov, İzak Atiyas, ?zgür Kıbrıs, Semih Koray, Gilbert Laffond, Bezalel Peleg, Murat Sertel, Tayfun S?nmez, Utku ünver and all the participants. Remzi Sanver acknowledges partial financial support from İstanbul Bilgi University and the Turkish Academy of Sciences and thanks Haluk Sanver and Serem Ltd. for their continuous moral and financial support. Last but not the least, we thank Carmen Herrero and two anonymous referees. Of course we are the sole responsible for all possible errors.     

Nonresponse weighting adjustment using estimated response probability

To reduce nonresponse bias in sample surveys, a method of nonresponse weighting adjustment is often used which consists of multiplying the sampling weight of the respondent by the inverse of the estimated response probability. The authors examine the asymptotic properties of this estimator. They prove that it is generally more efficient than an estimator which uses the true response probability, provided that the parameters which govern this probability are estimated by maximum likelihood. The authors discuss variance estimation methods that account for the effect of using the estimated response probability; they compare their performances in a small simulation study. They also discuss extensions to the regression estimator.     

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.     

Constrained allocation problems with single-peaked preferences: An axiomatic analysis

We introduce a new class of problems that contains two existing classes: allocation problems with single-peaked preferences and bankruptcy problems. On this class, we analyze the implications of well-known properties such as Pareto optimality, strategy-proofness, resource-monotonicity, no-envy, equal treatment of equals, and two new properties we introduce, hierarchical no-envy and independence of nonbinding constraints. Unlike earlier literature, we consider rules that allow free-disposability. We present characterizations of a rule we introduce on this domain. We relate this rule to well-known rules on the aforementioned subdomains. Based on this relation, we present a characterization of a well-known bankruptcy rule called the constrained equal awards rule. Received: 22 June 2000/Accepted: 21 March 2002 This paper is based on the first chapter of my Ph.D. thesis submitted to the University of Rochester. I wish to thank my advisor, William Thomson, for helpful comments and suggestions.     

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.