I'm more curious do you have to pass a background check to be a representative?
As far as I could find, there are four GOP congressmen running with records (sans Chelsea), and one Democrat:
* Joe Arpaio (R) - Contempt of court: https://www.nytimes.com/2017/07/31/us/sheriff-joe-arpaio-con...
* Don Blankenship (R) - Conspiricy to violate federal mine safety laws: https://www.nytimes.com/2016/04/07/us/donald-blankenship-sen...
* Michael Grimm (R) - Felony tax fraud: https://www.nytimes.com/2017/10/01/nyregion/staten-island-co...
* Greg Gianforte (R) - Assault of a reporter critical to him: https://www.nytimes.com/2017/06/13/us/politics/greg-gianfort...
* David Alcorn (D) - stalking: http://dailycaller.com/2017/11/13/dem-candidate-arrested-on-...
The former implies the reporter was an important asset to Gianforte and that's how I parsed it at first.
It is a bit strange that someone who can’t vote (a felon) could be elected and then vote on our behalf.
Most states allow felons to vote: https://en.wikipedia.org/wiki/Felony_disenfranchisement#In_t...
And really, with the separation of powers, how else would it work? The legislators are supposed to oversee things the executive does, do you think that it would be constitutional for the executive to tell the legislature to go fly a kite if the legislature asked to be told things? That, itself, could/would be unconstitutional...
edit: source: https://www.cia.gov/library/center-for-the-study-of-intellig...
[1] Burdick vs United States: https://scholar.google.com/scholar_case?case=392852811788210...
https://medium.com/@brendanlilly/are-presidential-pardons-an...
The qualifications to run for Congress, on the other hand, are explicitly spelled out in the original document. It's not clear to me anything other than a federal law can add any additional restrictions like, say, the Hatch Act does.
It seems like the converse is true, though, states don't get to define qualifications - U.S. Term Limits, Inc. v. Thornton, 514 U.S. 779 (1995)
"Second, even if the States possessed some original power in this area, it must be concluded that the Framers intended the Constitution to be the exclusive source of qualifications for Members of Congress, and that the Framers thereby "divested" States of any power to add qualifications."