I have read too many texts on Arrows impossibiity theorem. The examples are always artificially constrained, like 3 candidate supermarket locations around a la

I have read too many texts on Arrows impossibiity theorem. The examples are always artificially constrained, like 3 candidate supermarket locations around a lake, with inhabitants distributed around it. consider 3 groups objectively each preffering: 1) A over B over C 2) B over C over A 3) C over A over B Then 2 thirds of the population agrees A is better than B, but also that B is better than C yet also that C is better than A! In fact the world and human incentives are much more high dimensional than the problem statement. (people could propose a rent reduction when further away from the supermarket, if not democratically then economically, so instead of a democratic issue, its housing owners bickering over the coming supermarket location, which just reveals housing is not very democratically distributed, in a democracy the prices could be agreed to depend on supermarket distance). In fact there is only good news for democracy: by detecting preference cycles, we KNOW the kind of thing that is going on. And we know that A,B,C is a false trilemma, and formal statements depicting rules or laws can be mathematically much much richer in structure than a simple limited list of "choices". I value the contribution of Arrow, but at the same time one shouldn't try to understand the concept of democracy by reading the Arrow impossibility literature. The moment democracy has been reduced to simply a predetermined multiple choice form, is the moment democracy is no longer understood.