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Arrow's impossibility theorem is often trotted out as an argument against ranked preference, but in federal elections non-dictatorship is an irrelevant consider

by ABCLAW 10y ago

Arrow's impossibility theorem is often trotted out as an argument against ranked preference, but in federal elections non-dictatorship is an irrelevant consideration, as information-scarcity prevents a voter from leveraging his unique position as the deciding vote. 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.

thaumasiotes 10y ago
> in federal elections non-dictatorship is an irrelevant consideration, as information-scarcity prevents a voter from leveraging his unique position as the deciding vote 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.
- ABCLAW 10y ago
  We do use systems that exhibit it under certain constraints, as per my example. Additionally, these constraints are highly common in practice. 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?
  - thaumasiotes 10y ago
    > We do use systems that exhibit it under certain constraints, as per my example. 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.

by ABCLAW 10y ago

thaumasiotes 10y ago

> in federal elections non-dictatorship is an irrelevant consideration, as information-scarcity prevents a voter from leveraging his unique position as the deciding vote 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.

ABCLAW 10y ago
We do use systems that exhibit it under certain constraints, as per my example. Additionally, these constraints are highly common in practice. 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?
- thaumasiotes 10y ago
  > We do use systems that exhibit it under certain constraints, as per my example. 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.