When school quality increases with the educational standard set by schools, education before college need not be a hierarchy with private schools offering better quality than public schools. In our model, private schools can offer a lower educational standard at a positive price because they attract students with a relatively high cost of effort, who would find the high standards of public schools excessively demanding. We estimate the key parameters of the model and show that majority voting supports a system where private schools have higher quality in the US and public schools have higher quality in Italy.