Excuse my ignorance as a non-American, but I don't understand how Medicare and Medicaid can be called "single-payer", even if we bunch both of them together for the sake of the argument. Are certain healthcare providers restricted so as to only accept Medicare and/or Medicaid patients, and cannot by law accept those who are privately insured or would like to pay out of pocket? That is the only context in which I can imagine Medicare/Medicaid being called "single payer".