The least core in fixed-income taxation models: a brief mathematical inspection

For models of majority voting over fixed-income taxations, we mathematically define the concept 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 environments with no Condorcet winner, we prove that for sufficiently right-skewed income distribution functions, the least core contains only taxes with marginal-rate progressivity.