This paper is concerned with the problem of ranking and quantifying the extent of deprivation exhibited by multidimensional distributions, where the multiple attributes in which an individual can be deprived are represented by dichotomized variables. To this end we first aggregate deprivation for each individual into a "deprivation count", representing the number of dimensions for which the individual suffers from deprivation. Next, by drawing on the rank-dependent social evaluation framework that originates from Sen (1974) and Yaari (1988) the individual deprivation counts are aggregated into summary measures of deprivation, which prove to admit decomposition into the mean and the dispersion of the distribution of multiple deprivations. Moreover, second-degree upward and downward count distribution dominance are shown to be useful criteria for dividing the measures of deprivation into two separate subfamilies. To provide a normative justification of the dominance criteria we introduce alternative principles of association (correlation) rearrangements, where either the marginal deprivation distributions or the mean deprivation are assumed to be kept fixed.
We use cookies to provide you with an optimal website experience. This includes cookies that are necessary for the operation of the site as well as cookies that are only used for anonymous statistical purposes, for comfort settings or to display personalized content. You can decide for yourself which categories you want to allow. Please note that based on your settings, you may not be able to use all of the site's functions.
Cookie settings
These necessary cookies are required to activate the core functionality of the website. An opt-out from these technologies is not available.
In order to further improve our offer and our website, we collect anonymous data for statistics and analyses. With the help of these cookies we can, for example, determine the number of visitors and the effect of certain pages on our website and optimize our content.