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báo cáo hóa học:" The least core in fixed-income taxation models: a brief mathematical inspection"Journal of Inequalities andApplications This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon.The least core in fixed-income taxation models: a brief mathematical inspection Journal of Inequalities and Applications 2011, 2011:138 doi:10.1186/1029-242X-2011-138 Paula Curt (paula.curt@econ.ubbcluj.ro) Cristian M Litan (cristian.litan@econ.ubbcluj.ro) Diana Andrada Filip (diana.filip@econ.ubbcluj.ro) ISSN 1029-242X Article type Research Submission date 23 August 2011 Acceptance date 16 December 2011 Publication date 16 December 2011 Article URL http://www.journalofinequalitiesandapplications.com/content/2011/1/ This peer-reviewed article was published immediately upon acceptance. It can be downloaded, printed and distributed freely for any purposes (see copyright notice below). For information about publishing your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information about other SpringerOpen publications go to http://www.springeropen.com © 2011 Curt et al. ; licensee Springer.This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The least core in fixed-income taxation models: a brief mathematical inspection Paula Curt1 , Cristian M Litan1 and Diana Andrada Filip∗1,2 1 Department of Statistics, Forecasting and Mathematics, Faculty of Economics and Business Administration, University Babe¸ Bolyai, 400591 Cluj-Napoca, Romania s 2 Laboratoire d’Economie d’Orl´ans, e Facult´ de Droit, d’Economie et de Gestion, 45067 Orl´ans, France e e ∗ Corresponding author: diana.filip@econ.ubbcluj.ro Email addresses: PC: paula.curt@econ.ubbcluj.ro CML: cristian.litan@econ.ubbcluj.ro Abstract For models of majority voting over fixed-income taxations, we mathematically define the con- cept of least core. We provide a sufficient condition on the policy space such that the least core is not empty. In particular, we show that the least core is not empty for the framework of quadratic taxation, respectively piecewise linear tax schedules. For fixed-income quadratic taxation environ- ments with no Condorcet winner, we prove that for sufficiently right-skewed income distribution functions, the least core contains only taxes with marginal-rate progressivity.1 IntroductionThe literature of the positive theory of income taxation regards the tax schemes in democratic societiesas emerging, explicitly or implicitly, from majority voting (see Romer [1,2], Roberts [3], Cukierman and 1Meltzer [4], Marhuenda and Ortu˜o-Ortin [5, 6]). A very important mathematical difficulty related to nthis view is that the existence of a Condorcet majority winner is not guaranteed, since the policy spaceof tax schedules is usually multidimensional (see for example Hindriks [7], Grandmont [8], Marhuendaand Ortu˜o-Ortin [6], Carbonell and Ok [9]). n The possible inexistence of a Condorcet winner can be regarded as predicting political instabilitywith respect to the taxation system to be agreed on. However, the stability of tax schedules indemocratic societies is already a well-established stylized fact (see Grandmon ...