Weighted approval voting

To allow society to treat unequal alternatives distinctly we propose a natural extension of Approval Voting by relaxing the assumption of neutrality. According to this extension, every alternative receives ex-ante a non-negative and finite weight. These weights may differ across alternatives. Given the voting decisions of every individual (individuals are allowed to vote for, or approve of, as many alternatives as they wish to), society elects all alternatives for which the product of total number of votes times exogenous weight is maximal. Our main result is an axiomatic characterization of this voting procedure.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

Dividends and weighted values in games with externalities

We consider cooperative environments with externalities (games in partition function form) and provide a recursive definition of dividends for each coalition and any partition of the players it belongs to. We show that with this definition and equal sharing of these dividends the averaged sum of dividends for each player, over all the coalitions that contain the player, coincides with the corresponding average value of the player. We then construct weighted Shapley values by departing from equal division of dividends and finally, for each such value, provide a bidding mechanism implementing it.

Changes in the demand for private medical insurance following a shift in tax incentives

The 1998 Spanish reform of the Personal Income Tax eliminated the 15% deduction for private medical expenditures including payments on private health insurance (PHI) policies. To avoid an undesirable increase in the demand for publicly funded health care, tax incentives to buy PHI were not completely removed but basically shifted from individual to group employer-paid policies. In a unique fiscal experiment, at the same time that the tax relief for individually purchased policies was abolished, the government provided for tax allowances on policies taken out through employment. Using a bivariate probit model on data from National Health Surveys, we estimate the impact of said reform on the demand for PHI and the changes occurred within it. Our findings suggest that the total probability of buying PHI was not significantly affected. Indeed, the fall in the demand for individual policies (by 10% between 1997 and 2001) was offset by an increase in the demand for group employer-paid ones, so that the overall size of the market remained virtually unchanged. We also briefly discuss the welfare effects on the state budget, the industry and society at large.

Sharp A₂ inequality for haar shift operators

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Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Weak-type estimates for Haar shift operators: Sharp power on the A(p) characteristic

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Weighted norm inequalities for Fourier transforms of radial functions

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Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

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Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

Weighted Kernel regression

In the fixed design regression model, additional weights areconsidered for the Nadaraya--Watson and Gasser--M\"uller kernel estimators.We study their asymptotic behavior and the relationships between new andclassical estimators. For a simple family of weights, and considering theIMSE as global loss criterion, we show some possible theoretical advantages.An empirical study illustrates the performance of the weighted estimatorsin finite samples.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Weighted Euclidean biplots

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.