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

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.