It makes quite a lot of sense as a downside in limited, party based voting situations. IE, if you were an independent in a theoretical senate where 50 republicans, 50 democrats and you were to vote on a party-line proposition.
If non-dictatorship were being violated, you'd know. The non-dictatorship criterion states that the following situation is impossible:
- Out of all the voters, there is one in particular, who we'll call K.
- The election outcome is always identical to whatever K voted, no matter what anyone else voted.
So, if it isn't possible that a single person ranked candidate A first, the rest of the country ranked candidate B first, and the election nevertheless ranked candidate A first, then the election system does not violate the non-dictatorship criterion.
With that in mind, I am totally confused as to the point you're trying to make? The reason we don't worry about dictatorship is that we don't use systems that exhibit it, not that we have one but nobody knows who it is.
The result is that Arrow's theorem itself isn't a rebuttal, as per my first point, and discussion should center around the other two elements of Arrow's theory. Specifically whether or not they are, in practice, worse than our current situation.
Which they aren't. So why trot out Arrow's theorem for the 90th time?
This is an error on your part. Your example does not violate non-dictatorship; the rules of the election permit anyone to vote against their party registration.
Arrow's theorem is about the design of elections, not predictions about how people will vote in practice.
FPTP is by far worse than any preferential vote count.
FPTP will literally throw your vote away if you do not vote for one of the two perceived """"popular"""" parties.
It will also "literally throw your vote away" if you do vote for one of the two perceived "popular" parties. This is an old observation.
And yet, interest groups that vote continue to get better results than interest groups that don't.
Of course, we may also need to consider the notion that the voting system is only a minor problem compared to other aspects of our governance model.