1,720,977 research outputs found
What's So Special About Euclidean Distance? A Characterization Result with Applications to Mobility and Spatial Voting
No full textIn this paper we provide an application-oriented characterization of a class of distance measures monotonically related to the Euclidean distance in terms of some general properties of distance functions between real-valued vectors. Our
analysis hinges upon two fundamental properties of distance measures that we call “value-sensitivity” and “order-sensitivity”. We show how these two general properties, combined with natural monotonicity considerations, lead to characterization
results that single out several versions of Euclidean distance from the wide class of separable distance measures. We then discuss and motivate our results in two different and apparently unrelated application areas — mobility measurement and spatial
voting theory — and propose our characterization as a test for deciding whether Euclidean distance (or some suitable variant) should be used in your favourite application context
What’s so special about Euclidean distance?
No full textIn this paper, we provide an application-oriented characterization of a class of distance functions monotonically related to the Euclidean distance in terms of some general properties of distance functions between real-valued vectors. Our analysis hinges upon two fundamental properties of distance functions that we call "value-sensitivity" and "order- sensitivity". We show how these two general properties, combined with natural monotonicity considerations, lead to characterization results that single out several versions of Euclidean distance from the wide class of separable distance functions. We then discuss and motivate our results in two different and apparently unrelated application areas-mobility measurement and spatial voting theory-and propose our characterization as a test for deciding whether Euclidean distance (or some suitable variant) should be used in your favourite application context
The Measurement of Rank Mobility
No full textIn this paper we investigate the problem of measuring social mobility when the social status of individuals is given by their rank. In order to sensibly represent the rank mobility of subgroups within a given society, we address the problem in terms of partial permutation matrices which include standard ("global") matrices as a special case. We first provide a characterization of a partial ordering on partial matrices which, in the standard case of global matrices, coincides with the well-known "concordance" ordering. We then provide a characterization of an index of rank mobility based on partial matrices and show that, in the standard case of comparing global matrices, it is equivalent to Spearman's ρ index
Do we value mobility?
Full text linkIs there a trade-off between people’s preference for income equality and income mobility? Testing for the existence of such a trade-off is difficult because mobility is a multifaceted concept. We analyse results from a questionnaire experiment based on simple precise concepts of income inequality and income mobility. We find no direct trade-off in preference between mobility and equality, but an indirect trade-off, applying when more income mobility can only be obtained at the expense of some income inequality. Mobility preference—but not equality preference—appears to be driven by personal experience of mobility
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