His constituency is all of Kentucky. Senators do not split their states, they represent it as a whole.
McConnell rules through the consent of half the senate, not alone.
This is literally the purpose of the senate. We are a union of states, and the senate is where each state is granted equal power. One could argue that states should have been defined differently, but the point was that large states should not have absolute control over small states.
Edit: I'm loving the downvotes without comments. They're clear indication that some people are either not arguing in good faith or that they simply do not understand how and why the us is set up the way it is.