A hypothetical scenario: The incoming US Senate is divided 50-49 with one Independent Senator. That Independent, let's say "she", has not committed to caucus with either party. Should she remain truly independent, could the plurality party effectively rule as the majority by a 50-49 vote?
I am aware of some reasons why she would tend not to take this path, committee assignments particularly. I am curious as to what might happen if she acted in spite of these reasons.
A 50-49 vote is a victory for the yeas.
It is important to understand that the American system inherited much in the way of procedure from the British system. In the House of Commons, a motion is generally considered to pass if more vote in favor of it than against, and this would have been the default understanding of the founders at the time. It is also how both houses of Congress operate today.*
The US Constitution does apply a quorum requirement in Article I, Section 5:
Each House [of Congress] 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 also imposes a 2/3 supermajority requirement for treaties, impeachments, veto overrides, and Constitutional amendments. Other than that, the Constitution is largely silent on the question of how many votes you need for "ordinary" legislation and resolutions. Perhaps the founders simply thought this too obvious to write down, or perhaps they figured Congress would be able to work out details like this in its own rulemaking process.
In any event, SCOTUS and the rest of the federal government likely have no say here. The next paragraph of Section 5 is very clear:
Each House may determine the rules of its proceedings, punish its members for disorderly behavior, and, with the concurrence of two thirds, expel a member.
Congress gets to evaluate its own rules. If they do a bad job of it (in our subjective opinion), then that's their problem. The rest of the government, and especially the judiciary, is not supposed to be in the business of second-guessing Congress's rules, except to the extent that Congress actually violates the Constitution.
* In the Senate, debate cannot be forcibly ended without a 3/5 vote of "the Senators duly chosen and sworn" - which is usually 60 senators unless there's a vacancy. This is a separate rule, independent of the simple majority required to actually pass a law once debate does end.
There are actually a few organizing resolutions and, in the absence of renegade senators in the majority party, all resolutions will pass by unanimous consent. The renegade senators could only affect the election of the President pro tempore of the Senate.
I really don't see anything in the hypothetical scenario that would have any effect.
