Felons should be allowed to vote because if they are an American citizen they still would have the same rights as other American citizens. Also if they are an American citizen pay taxes, etc we are not allowed to just take their right to vote away and they might be seen as a lower class citizen as others.
While some might argue that felons have lost the privilege to vote by committing a crime, they do still have to pay taxes. Of course, while they are actually incarcerated they should be denied the ability to vote. In prison, they are not contributing members of society. If a felon is released and paying taxes, they should be given the vote. Without suffrage, they are being taxed and being denied representation.
No, the argument of "No Taxation Without Representation" does not justify giving felons the vote, because felons were not what the founding fathers had in mind when they came up with that rule. Society has multiple interests in making sure that felons do not vote. That rule prevents people will bad judgment from influencing elections, and also gives felons an incentive to not commit crimes.