Thanks to SMBC (Saturday Morning Breakfast Cereal), I was introduced to Arrow’s impossibility theorem. It’s really one of the most amazing ideas I’ve read, and it struck me that this might be a proof for anarcho-capitalism. I’ve studied most of the underlying concepts in one way or another, but have never studied this particular topic.
From my perspective it’s an attempt to see whether or not it is logically possible to rank an individual’s/communities preferences, as such invalidating the efficacy of government, which would require this.
Has anyone studied this further, and perhaps has some light to shed?
I don’t see it (directly) as an argument for anarcho-capitalism. It’s however an argument against the ideal of democracy. It shows that the ideal of democracy is unachievable; because not all the requirements for an ideal democracy can be achieved. It doesn’t follow however that anarcho-capitalism is better. Imagine someone who thinks the Hobessian fear is justified and is afraid all the poor will die a horrible death in an anarchist world; I don’t think you can show him the impossibilitie’s theorem and then he’ll go and say: ‘ah, now that’s interesting; now we don’t need, nor want the state anymore!’
If you look at the wikipedia page; you’ll see that they have discussed ways around the ‘problem’; and I think people will accept those, rather than common anarchy.
“There is no absolute truth”, is an absolute truth statement & thus self refuting.
“it struck me that this might be a proof for anarcho-capitalism.”
There are already proofs. Impossibility proof, via argumentation ethics from Hoppe.
“My entire argument, then, claims to be an impossibility proof. But not, as the mentioned critics seem to think, a proof that means to show the impossibility of certain empirical events, so that it could be refuted by empirical evidence [such as the existence of non-libertarian societies—RPM and GC]. Instead, it is a proof that it is impossible to justify non-libertarian property principles without falling into contradictions . . . empirical evidence has absolutely no bearing on it.” (Hoppe 1988, p. 53)
Yes, bad rational on my part, rejection of one does not imply the other.
However, I wasn’t looking for it to be a proof in that sense, such that you show it to someone and they are immediately logical and reject the other. But rather it’s a framework which attempts to analyze the rationale behind socialism or the measurement and interventionist ideas of the keynsian/neo-classical/etc schools of thought.
Though it would suggest that under these circumstances, this would be a rejection of a non-dictatorial interventionist government. This could be argued that it would also fit a communist government and a mixed economy. Though the assumptions and constraints would be argued by others, I think it’s a brilliant framework.
Arrow’s wiki page says he’s a neo-classical, so he would likely be a proponent of Keynes, though that’s not necessarily certain. Though that doesn’t mean his work isn’t worth looking at, analyzing.
Ahhh, okay, I was unaware of the existence of other proofs. I’ll have to give this one a read. Thanks for the help.
I think AdrianHealey got it mostly correct, Arrows Impossibility Theorem is just a prove that no democratic voting system can meet certain characteristics that we might find to be favourable. It doesn’t prove anything more than that and even with this in mind one could quite easily make many arguments in favour of democracy.
No, he is a mainstream neoclassical who has said some favorable things about new institutional economics in recent years. Arrow is one of the most cited economists of the 20th century. Also, he is a microeconomist and never really did any work in macro, so it wouldn’t make sense to call him a Keynesian. His work on information economics was influenced by Hayek.
“Arrows Impossibility Theorem is just a prove that no democratic voting system can meet certain characteristics that we might find to be favourable”
I think you’re right EconomistInTraining. I don’t think I’ll leave my condo association, just because their voting process violates certain mathematical principles in weird situations. It works well enough that I’m satisfied with it.
“Independence of irrelevant alternatives (IIA) - The social welfare function should provide the same ranking of preferences among a subset of options as it would for a complete set of options. Changes in individuals’ rankings of irrelevant alternatives (ones outside the subset) should have no impact on the societal ranking of the relevant subset.”
I don’t think this is valid at all. Suppose there are two parties, R and D. I insist that I will vote for no party that confuses me by offering two choices. At first there’s 1 R and 1 D and I want to vote for the R. But then a second R enters at the last minute, so I switch to voting for the D. There are probably a million variants of this kind of situation.
