No taxation without representation
Felons still have to pay taxes once they are gainfully employed, so they should be able to represent themselves through voting.
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America was founded on the ideal of 'no taxation without representation'. After completing their sentences, many felons go on to be gainfully employed and pay taxes to the government. Since they are contributing to society, felons should be able to vote. It is unfair to make felons pay taxes to the government if they don't even have the ability to vote for their elected officials. They deserve to be represented by a government they help to fund.
While 'no taxation without representation' is a good idea, it does not work in practice. We do not offer everyone who pays taxes the right to vote - for instance, illegal immigrants, people under 18 - and equally, not everyone who votes pays taxes. Taxation is not the litmus test for the right to vote.
[P1] Felons who have served their sentence and go on to become employed contribute to society by paying taxes. [P2] Because they pay taxes, they should be able to vote and be represented by their government.
Rejecting the premises
[Rejecting P2] Paying taxes should not be used as the barometer for earning the right to vote.