I think the way voting should happen in the Senate is when there’s a question to be decided you ask who votes “yes” and who votes “no” and whichever side has more people on it wins. It works for the House of Representatives...Well, sort of.
That whole "when there's a question to be decided" hides a lot of the process. Questions need to be decided when the majority party say they need to be decided. A lot of things go into that. Supermajorities help; that's why a good deal of the House's business is conducted under the suspension procedure (which actually needs two-thirds of the votes, not a simple majority). Intensity on the part of the majority helps -- that's why they were willing to bring up the health care bill and climate change, both of which passed by only narrow margins. It also helps if the majority of the majority party, or the leadership of the majority party, favors something. If the leadership opposes a bill or an amendment, it's usually not going to get a vote at all, even if a clear majority of the House favors it.
In other words, the majority party governs in the House by dictating which issues have to be decided.
As I've said before, this isn't majority rule; it's majority party rule. It's only somewhat connected to actual majorities within the chamber. And that, in turn, is only tenuously connected to majorities across the nation. The Democrats get to be in control of the House for many reasons, chief among them being Katrina, the imploding economy in 2007-2008, and the disastrous course of the Iraq war in 2005-2006. Health care? Climate change? Most voters who want liberal solutions to those problems supported the Democrats in 2006 and 2008...and also in 2002 and 2004. There's very little evidence that underlying attitudes on those types of issues jumps around as the fortunes of political parties wax and wane. So majority party rules in government wind up changing policy as party control changes even though there's been no change on many issues among the voters.
All of which can, in fact, be justified. All parliamentary bodies need some kind of structure; otherwise, the result could easily be chaos (indeed, John Aldrich argues in his classic book Why Parties? that American parties originated as a solution to that chaos -- although see a somewhat different view from Seth Masket, looking at the California case). In particular, I think it's almost impossible to imagine a complex bill such as health care reform surviving a true majority-rules process, in which anyone who had an amendment could get a simple majority vote on it. Whether strict party control is the best kind of structure is a matter for debate. But it isn't a simple majority-rules system.