I believe you are misinterpreting minority in this context (or maybe I am). Madison refers to it as any faction who isn't favored in a political decision. He isn't concerned with the broader context of a political party (I believe that's the reason why he carefully chooses the word "faction"). A political party is simply the more or less cohesive materialization of several factions. A political party is essentially a memeplex. Instead, here the concept of minority is exactly being used to define specific ideas or dogmas that aren't being represented and that could lead to instability.
The idea of abortion for instance, can be decided by the legislative branch one way or another. Usually by will of the majority (as it should). However, whatever the decision, it has the potential of bringing social unrest and instability. This is the weakness of democracy. The double bind of democracy.
Unless you live in an unstable political regime, you won't notice social unrest from the decision of electing one party or the other. But even under stable political regimes, social unrest, violence and the failure of governments can be attributed to a faction and a decision of the majority.
I'm forced to quote Nietzsche in his Preface to The Antichrist.
I won't cease to be amazed at how easily we wash our hands of our responsibilities in the political process we call democracy. And how easily we attribute to others those responsibilities. It pays to think real hard on the definition of Democracy, and what "Power to the People" is this if we constantly cave in to conformism and the blame game.Originally Posted by Friedrich Nietzsche
Let me be clear, in its broader sense it's never the politician fault. It's our fault. If we for once try to elevate ourselves we will finally hold the power democracy gives us. Your dogmatic, intellectually dishonest politician will have no power over anyone. It's a simple process that of elevating oneself over the rat scouring humanity. Of being deaf to that which limits our thinking. Why we insist on hiding in the hole of mediocrity of religious and political dogma thinking is something that baffles me.