[kijin]

If we read early works (from the late 80s) in what is now called "deliberative democracy", we can see that it began as a response to certain models of democracy that emphasize preferences and procedures -- up to and including the participatory models of the 70s and early 80s. Although deliberative democracy is not a direct response to Arrow's impossibility theorem in particular, it was intended to sidestep its troubling implications as well as other problems with the older models.

There are two major factions within the deliberative democracy camp. One is indeed interested in consensus building and eventually-consistent rationality. This is the "Rawlsian" faction led by Gutmann and Thompson. The other faction, however, focuses more on actual practices of negotiation through which pre-existing preferences and power structures are transformed. This is the "critical theory" faction led by John Dryzek and the late Iris Marion Young. Personally, I think the latter remains closer to the original aims of deliberative democracy and presents a better contrast to the older models it was intended to transplant. The Rawlsians just took the opportunity to cram their own agenda into democratic theory, as they always do with everything they touch.

Your claims (2) and (3) seem to contradict each other. If it is so abundantly clear that a procedure that satisfies Arrow's conditions is desirable, why do you say that Arrow's theorem is just a mathematical result that doesn't explain anything IRL?

Arrow's theorem is surprising and troubling only if you believe in some sort of sacred relationship between the trinity of democracy, voting, and satisfaction of all pre-existing preference. To the contrary, I find it both trivial and intuitive that it is impossible to satisfy all of the preferences of all human beings, and I would be very surprised and troubled if someone claimed to be able to do so.

[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.