analogy between Arrow's Impossibility and Goodman's Grue?

[gusl]

A few days ago I thought of a loose analogy between Arrow's Impossibility Theorem (no democracy can be reasonable) and Goodman's Grue sort of idea: it's impossible to reason independently of your choice of representation, and such a choice must be arbitrary.

I had a very tenuous grasp on it, and now it seems to be gone. Can anyone see an interesting connection?

Comments

[jcreed.livejournal.com]

What is Goodman's Grue thing? I'm aware that Grue usually has something to do with things being blue and green at various times, but I'm not familiar of most applications of the idea I think.

[gustavolacerda.livejournal.com]

Someone recently said to me: "newspapers are forced to have a 50% / 50% split on every controversial issue: on every issue, for every FOR column, they need to publish an AGAINST, and vice-versa".

Grue-like arguments show that this is impossible.

On the issue of whether "God is a woman", such a newspaper will need to publish 50% of their articles arguing that God is a woman, and 50% arguing that God is not a woman.

On the issue of whether "God is a man", the same newspaper will need to publish 50% arguing that God is a man, and 50% arguing that God is not a man.

Of course, this means that the opinion "God has no gender" gets 0% representation.

[gustavolacerda.livejournal.com]

When I think of "Goodman's Grue", I think "it's impossible to be unbiased".

Since you're at CMU, have you seen any talks by Kevin Kelly? He's on my list of "very interesting people". He argues that Bayesianism is bad when inferences are not invariant under "Goodman's grue transformations", i.e. change of language. He also restricts his criticism to those using Bayesianism as a "meta-method", although I'm not sure what he means.

Our priors often depend on how we choose represent things. Also, when we talk about Kolmogorov Complexity, it's always relative to a computing architecture (he says the additive constant is important), and this choice of underlying machine is, to some extent, arbitrary.

[selfishgene.livejournal.com]

When thinking, we emulate the real world by neural means. This is often successful for our purposes, but never a perfect representation.
A democracy emulates the desires of the populace. This can never be done perfectly either. Any structure A, which is designed to mimic structure B, must differ at some point; there are no exact copies.
In practice the situation is worse, because democracy is a scam by the rich and powerful. It is never intended to genuinely reflect public opinion.