Prisoners in most states are barred from voting. The reason is that convicts have been stripped of most of their civic rights, and voting is the exclusive right of a citizen who is contributing to and living within society. Prisoners don't pay taxes, don't use public facilities, and generally don't have the opportunity to engage on matters within the public sphere. Therefore, some people—particularly on the right, and backed by 75% of Americans—argue that imprisoned people wouldn't be voting on anything that concerns them in their current situation. Even if these issues did concern them in some way, those who oppose voting by prisoners state that prisoners have lost the right to have a stake in what happens outside the prison walls.
People are equally worried that politicians would pander to the needs of the prisoners to get their votes. This sounds far-fetched until you realize that the prison system holds 2.3 million people. If it were a state, it would be the 36th-largest state in America.
Opponents to prisoners' voting rights argue that none of those people is in the system because they have a track record of making sound judgments. They have often made rash decisions that show a lack of understanding of society and their own position in it.
From that perspective, people argue that until prisoners have learned that they should control their behavior and think rationally, US states should keep laws in place that prevent them from voting.