A graphical analysis of some basic results in social choice

We use a simple graphical approach to represent Social Welfare Functions that satisfy Independence of Irrelevant Alternatives and Anonymity. This approach allows us to provide simple and illustrative proofs of May's Theorem, of variants of classic impossibility results, and of a recent result on the robustness of Majority Rule due to Maskin (1995). In each case, geometry provides new insights on the working and interplay of the axioms, and suggests new results including a new characterization of the entire class of Majority Rule SWFs, a strengthening of May's Theorem, and a new version of Maskin's Theorem. Received: 31 July 1999/Accepted: 27 March 2001     

Bayesian networks for imputation

Summary.  Bayesian networks are particularly useful for dealing with high dimensional statistical problems. They allow a reduction in the complexity of the phenomenon under study by representing joint relationships between a set of variables through conditional relationships between subsets of these variables. Following Thibaudeau and Winkler we use Bayesian networks for imputing missing values. This method is introduced to deal with the problem of the consistency of imputed values: preservation of statistical relationships between variables ( statistical consistency ) and preservation of logical constraints in data ( logical consistency ). We perform some experiments on a subset of anonymous individual records from the 1991 UK population census.     

Will taxpayers ever like taxes?: Responses to the U.S. Tax Reform Act of 1986

Major policy changes like the 1986 Tax Reform Act (TRA) in the United States provide natural experiments to study attitudinal and behavior responses to law. Surprisingly, public evaluations of the TRA became increasingly negative after passage, while general support for the tax system became more positive in response to the changes. To explain this puzzle, we propose a dynamic model of taxpayer attitudes that is consistent with the observed loose linkage between logically-connected concepts. We briefly review the political context, objectives and impacts of the 1986 Tax Reform Act, and present several studies testing the impact of self-interest, prior beliefs, and social discussion on changes in attitudes and behavior.Results suggest that the complexity of taxes and difficulty in knowing objective impacts weakens the role of self-interest in attitudinal changes, thereby strengthening the role of prior beliefs and discussion. Evaluations of tax laws are most responsive to more politically-oriented influences.     

On Preference, Freedom and Diversity

We study the problem of ranking sets of options in terms of freedom of choice. We propose a framework in which both the diversity of the options and the preferences of the agent over the options do play a role. We formulate some axioms that reflect these two aspects of freedom and we study their logical implications. Two different criteria for ranking sets are characterized, which generalize some of the rankings proposed so far in the literature.     

Estimating rating transition probabilites with missing data

In this article we provide a rigorous treatment of one of the central statistical issues of credit risk management. GivenK-1 rating categories, the rating of a corporate bond over a certain horizon may either stay the same or change to one of the remainingK-2 categories; in addition, it is usually the case that the rating of some bonds is withdrawn during the time interval considered in the analysis. When estimating transition probabilities, we have thus to consider aK-th category, called withdrawal, which contains (partially) missing data. We show how maximum likelihood estimation can be performed in this setup; whereas in discrete time our solution gives rigorous support to a solution often used in applications, in continuous time the maximum likelihood estimator of the transition matrix computed by means of the EM algorithm represents a significant improvement over existing methods.     

Bayesian analysis of elapsed times in continuous‐time Markov chains

The authors consider Bayesian analysis for continuous‐time Markov chain models based on a conditional reference prior. For such models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition, an infinitesimal rate matrix also characterizes this class of models. Experts often have good prior knowledge about the parameters of this matrix. The authors show that the use of a proper prior for the rate matrix parameters together with the conditional reference prior for the elapsed time yields a proper posterior distribution. The authors also demonstrate that, when compared to analyses based on priors previously proposed in the literature, a Bayesian analysis on the elapsed time based on the conditional reference prior possesses better frequentist properties. The type of prior thus represents a better default prior choice for estimation software.     

La médiane simpliciale d'Oja: Existence,unicité et stabilité

Oja (1983) examined various ways of measuring location, scatter, skewness, and kurtosis for multivariate distributions. Among other measures of location, he introduced a generalised median known in this paper under the name of the Oja median. In our study of the existence of that median, we show that Oja's definition can only be applied to distributions having a mean. In dimension d θ 2, we establish that the usual method of extension breaks down, which raises the question of the validity of the concept as a notion of median. Two fundamental theoretical properties of that median are also considered: uniqueness and consistency.