Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 329378, 15 pages
Research Article

A Mathematical Revisit of Modeling the Majority Voting on Fixed-Income Quadratic Taxations

1Department of Statistics, Forecasting and Mathematics, Faculty of Economics and Business Administration, University Babeş Bolyai, 400591 Cluj-Napoca, Romania
2Laboratoire d'Economie d'Orléans, Faculté de Droit d'Economie et de Gestion, 45067 Orléans, France

Received 3 November 2010; Accepted 30 November 2010

Academic Editor: Mohamed El-Gebeily

Copyright © 2010 Paula Curt et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Analyzing voting on income taxation usually implies mathematically cumbersome models. Moreover, a majority voting winner does not usually exist in such setups. Therefore, it is important to mathematically describe those cases in which a majority winner exists, at least for the basic models of voting on income taxation. We provide a complete mathematical description of those income distribution functions for which a majority winning tax exists (or does not exist), in the quadratic taxation model à la Roemer (1999), with tax schedules that are not necessarily purely redistributive. As an intermediate step, we identify by the corner method what are the most preferred taxes of the individuals, when taxation is not purely redistributive. Finally, we prove that for both purely and nonpurely redistributive quadratic taxations, the sufficient inequality condition of De Donder and Hindriks (2004) on the income distribution functions, for the existence of a Condorcet winner, can be relaxed to a broader condition.