Because human beings are basically awesome, we're now able to build models of how political opinions take hold in a society by applying what we know about how ferrous metals become magnetised. How cool is that?
It works like this: you create a virtual society made of agents who have one bipolar attribute: they're either going to vote Blue or Red. Then you give them two means of making a decision: either external (mimicing political campaigning) or internal (driven from each agent's interactions with other agents). Then you use the external influence to set some initial conditions (say, 55/45 in favour of Blue) and then observe how your internal mechanisms affect the final outcome.
In the basic model, each agent is influenced by a local majority, so that they tend to vote for the same party as the agents they interact with. (This, of course, uses the techniques invented to understand magnetisation.) The basic model, however, is banal. As you can imagine, the initial majority usually stays the winner.
What's interesting is when you throw two new types of agents into the mix: "contrarians" (who vote against the local majority) and "inflexibles" (who never change their mind). These agents are hugely and disproportionately influential. For example, if you have more than about 1 in 6 contrarians, you end up with a 50/50 split. Similarly, if your inflexibles only vote Red, you only need that 1 in 6 to gain a Red majority as the vacillating Blues adapt their position by trying to meet them half way.
This is of course only a model. But I think you can see some current debates where a minority's utter unwillingness to compromise has given their position more influence that it might deserve, e.g: teaching creationism in schools; that immigration is basically a problem; that global warning is some kind of elaborate scam; that fruit and nut chocolate is anything other than an abhorrent mockery of all that is good and pure in this world. None of these positions has won influence on its merits: instead they've won favour because a) their proponents refuse to compromise and b) their opponents don't.
So contrary to what JS Mill/your better instincts/your parents might have told you, the way to win an argument is not to reason sweetly with your opponent, take their opinions on board, or otherwise engage with them. That only works if they're playing the same game. If not, you just have to stamp your feet harder, and yell louder, than they do.