Article 1, Section 5, Clause 1: Qualifications of Members

Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members,and a Majority of each shall constitute a Quorum to do Business; but a smaller Number may adjourn from day to day, and may be authorized to compel the Attendance of absent Members, in such Manner, and under such Penalties as each House may provide.

It was already well-established tradition in 1787 that a legislature should be the judge of its own elections and of the qualifications of its own members.  There was thus no debate of this subclause at the Convention. The courts have intervened against attempts to add to the qualifications for members of Congress that are prescribed in the Constitution, but have ruled that the decision whether someone is qualified under the Constitutional prescription is not a matter the courts are empowered to take up.

This power includes the power to investigate election fraud.

The second subclause, defining a quorum, was the only part of the clause that was seriously debated in the Convention. Some members wished to require two-thirds of the members to be present to constitute a quorum. Others wished for Congress to be able to do urgent business with less than a majority present. Neither proposal found enough support.

The concern here was with a minority abusing the quorum requirements.  If a third of the members opposed an action, and two-thirds were required for a quorum,  the minority could block action by absenting themselves and preventing a vote. On the other hand, if less than a  majority were enough to constitute a quorum, a minority could pass bills without the broad support with which laws ought to be passsed.

The final subclause, giving the power to compel attendance to a smaller number in each chamber, was uncontroversial. The power granted to a smaller number to adjourn from day to day is largely a parliamentary rule allowing the chamber to carry over its business without having to constantly call for a quorum.

In practice, quorum rules are largely ignored today by either chamber except when a call for a quorum is made as a delaying tactic. At present, the vote of fifteen Representatives is sufficient to  order the Sergeant at Arms of the House to round up members and compel them to attend. In the Senate, oddly, a majority is required.