What you don't see here is that if you have a government, it inevitably imposes the rules the majority agree with upon the minority who disagree. There is no way for the minority to do anything but wait until the next election and hope. So conflicts are not really resolved, but rather one side orders the other to shut up and do as they say.
A true resolution would be when both sides agree on the price. An simple example would be this:
I would like to throw a party on my lawn, but my neighbor disagrees. I really want that party though, cos it's my birthday, so I would go to my neighbor and try to convince him to let me have a party. I can see he wouldn't appreciate the noise so I would offer him something in exchange for his inconvenience: maybe I would let him use my bathtub for the next month, or maybe I would simply give him some money. If it wasn't just my one neighbor, but maybe 3 or 5 of them, I would have to convince them all and pay them all and that would make my party very expensive, so I would consider cancelling it.
Now on a larger scale, imagine you'd have various law firms, each protecting their clients interests and bargaining on their behalf. So, for instance, clients of one firm wouldn't like gay people to marry, while clients of that other firm, obviously many of the are gay, would be in favor of it. Even if we suppose that those who oppose gay marriage are the majority, they still probably wouldn't be able to outbid the minority here. That's because when people are asked to pay to teach others how to live, it becomes painfully obvious most of them are not ready spend their money on it.