[logicchop]

I think you are a bit confused. What would Arrow's theorem explain? There is no empirical phenomena that we are puzzled about that Arrow's theorem solves (unless you are wondering: Why is it so hard to come up with a voting system that doesn't have the potential for goof-ball results? - Answer, because it is impossible..)

I don't know what you mean by the "trinity" in which "satisfaction of all pre-existing preference" is a part.. That's obviously not relevant; we aren't interested in a system that satisfies preferences. What we are interested in is a system that (1) isn't a dictatorship, (2) is fair [i.e., everyone counts equally], (3) allows us to decide any kind of potential matter _as a group_.

If you look at the conditions this way it should be glaringly obvious what this has to do with the (possibility) of democracy..

[kijin]

If we're not interested in a system that satisfies preferences, then Arrow's impossibility theorem is irrelevant.

The conditions, of course, sound obvious and intuitive. Of course we don't want a dictatorship, and of course we want everyone to count as equally as possible. But it takes a very specific interpretation of your third condition to bootstrap the rest of Arrow's theorem. You have to interpret it in a way that emphasizes translating fixed individual preferences into group preferences as straightforwardly as possible. If you care about that, then yes, you should be worried about Arrow's theorem. Otherwise, Arrow's theorem is just a cool thought experiment that helps explain why said interpretation is wrong.

Deliberative democracy currently happens to be the most popular model of democracy among political theorists, and they don't care about Arrow's theorem because whatever preferences people have before they enter the democratic "procedure" isn't worth jack shit to them. As a result, Arrow's theorem is much less relevant to the possibility and fate of democracy as currently understood than it was 60 years ago.