This paper studies voting over quadratic taxation when income is fixed and taxation non distortionary. The set of feasible taxes is compact and self-interested voters have corner preferences. We first show that, if a majority winning tax policy exists, it involves maximum progressivity. We then give a necessary and suficient condition on the income distribution for a majority winner to exist. This condition appears to be satisfied for a large class of distribution functions.
De Donder, P., & Hindriks, J. (2004). Majority support for progressive income taxation with corner preferences. Public Choice, 118(3-4), 437-449. https://doi.org/10.1023/B:PUCH.0000019907.16784.cb (Original work published 2004)