Rights do indeed go to the majority, but they also go to everyone else. That's why rights are defined exactly as they are, meaning that everyone enjoys them equally. Does the majority have more of a say as to what is a right and what isn't, that is another argument.
In his inaugural address, Thomas Jefferson plainly states, "All too will bear in mind this sacred principle, that though the will of the majority is in all cases to prevail, that will, to be rightful, must be reasonable." This 'sacred principle' of the will of the majority always ruling is true on every continent and within every social construct. So, in understanding this principle, we must realize that in order to have a just society, we must have an enlightened public.
It is a somewhat flawed system but that is why many different countries exist today. People left from one country because they felt that their interests weren't being represented because they were in the minority. It is hard to think of a better solution to majority rules because either way you look at it, someone is being untreated unfairly in their eyes.
I don't think that rights go to the majority, at least not in the way that the question is being asked. Rights apply to everyone, even if the majority has a bit more of a say as to what those rights are and how they are determined in this world.