Arrows theorem is misleading because it only applies to rank order systems.
Range voting (i.e. 0-5 rating system) satisfies all the criteria. [0] So yes, democracy is theoretically possible.
Good video, thanks for sharing that!
Re:Arrow's Theorem (2014)
by Judgmentality on Saturday November 11, 2017 @04:23AM
(#15675611)
Yep, this is when you have non transitive properties. A really cool embodiment of this same concept is non transitive dice.
Indeed, a non-transitive election like that means that there is no Condorcet winner. Some voting methods (including first past the post) are guaranteed to select a Condorcet winner if one exists, but when one doesn’t exist (if A>B>C>A), various voting methods will result in various winners.
I love reading about the theory behind voting methods, but one common criticism is that these edge cases are rare and thus a pure theoretical approach isn’t sufficient for getting a “desirable” (however you define that) outcome.
These situations are possible but rare and in such a case, it is arguable that all potential winners are legitimate.