Ok, those who "pay no taxes"* don't get to vote. Fine. Those who don't get to vote don't have to pay taxes. At all. Period. They get a refund every year for what they paid in sales tax, property tax, gasoline tax, utility taxes, and anything else they paid.
Oh, wait... that would make YOUR tax bill go up as the lost money would have to be replaced from somewhere. Oh. My. God... we couldn't have that! No taxation without representation, ya know.
*- An incorrect assumption to begin with, but I'll play along.