A lot of the short obits I'm reading aren't saying what I would, so here's my own shot:
In 7th or 8th grade, a teacher assigned a question that was something like: How should a government be organized? 8th-graders are such fonts of wisdom on this matter, right? I wrote something stupid, as 8th-graders are wont to do, and it inolved unanimity. The teacher only wrote, "How likely is that?"
Well, it actually quite depends on what we're voting for! For some policies, unanimity is very likely. You will not find anyone in Congress who seriously supports the Torture All the Two-Year-Olds With Hot Irons Act. The correct response, it turns out, is that there should be different approval thresholds for different laws, depending on the importance of the law. For, "Should we put atheists in jail?" a larger majority should be necessary to affect the law than for, "Should Bob be allowed to wear a blue shirt?" And one of the best formalizations of this argument is found in Buchanan and Tullock's Calculus of Consent. Here is the relevant section.
This principle is instated in U.S. law, but not radically enough. For example, to overturn the First Amendment, 2/3rds of states would need to be on board. But we have many, many more policy questions that are set at the 50% threshold that should not be.
RIP James Buchanan, you were a really smart dude. Perhaps surprisingly, you're the reason I don't care so much about the U.S. constitution like some people do. We know vastly more about how to arrange governments now, in large part thanks to you.