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.     

Attracting Micro‐Enterprises To Learning

Micro‐enterprises, i.e. firms with less than 10 employees, are traditionally the hardest to engage in learning; they are also least likely to participate in such measures as business advice and guidance provision and initiatives to support information communication technology (ICT) adoption. Through a community‐based initiative initially targeting parents (unemployed or employed) to participate in ICT, 30 micro‐enterprises were attracted to learning for the first time. These companies had carefully avoided similar initiatives taking place locally, which emphasized business success and growth; they had only participated in this ICT skills training because of their children. The paper takes a case study approach to evaluate the reasons for participation, explores barriers and implications for those organizing similar activities, and calls for a more holistic view of owners and managers of small firms as fathers, mothers, etc. rather than just as ‘entrepreneurs’.     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.     

The evaluation of DNA evidence in pedigrees requiring population inference

Summary. The evaluation of nuclear DNA evidence for identification purposes is performed here taking account of the uncertainty about population parameters. Graphical models are used to detail the hypotheses being debated in a trial with the aim of obtaining a directed acyclic graph. Graphs also clarify the set of evidence that contributes to population inferences and they also describe the conditional independence structure of DNA evidence. Numerical illustrations are provided by re-examining three case-studies taken from the literature. Our calculations of the weight of evidence differ from those given by the authors of case-studies in that they reveal more conservative values.     

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.