Typically, legislatures have broad latitude to organize committees and set up rules, by majority vote. Anything that is not mandated by existing legislation or the relevant Constitution is changeable if the body votes for it, and no other branch would get up in their business over it.
However, this case may be an exception:
It takes, by statute, 68 votes for a quorum and 68 votes to pass anything in the chamber. There’s no wiggle room here. When Democrats boycotted the opening session Tuesday, NBC News reported, “Minnesota Secretary of State Steve Simon, who controls the chamber’s gavel between sessions, adjourned the state House and said there was no quorum.” The state House, legally, could not act. Nevertheless, in a half-empty chamber, the 67 Republicans plowed ahead and elected state Rep. Lisa DeMuth as the speaker.
That means there is a law that defines quorum for this body, which the Republicans purposely ignored to install a speaker. That Speaker election will, no doubt, be challenged in court. I’d be interested to know what the Republican justification is for this…
The only justification that makes sense is “See that ‘R’ after our names? That’s why”. And some judges would allow that.