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On Mon, Oct 15, 2001 at 09:12:18AM -0400, Alex F. Bokov wrote:

*>
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*> This raises an interesting question: how to form a rational opinion
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*> when most sources of information claim to be unbiased and all of them
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*> are biased? The US goverment lies. The enemies of the US government
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*> lie. The mass media is owned by like a dozen people, and what are the
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*> chances that they're impartial in all this? I wonder if game theory or
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*> information theory have some strategies to offer in juxtaposing the
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*> 'information' coming from different sources so the opposing lies
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*> cancel each other out somewhat?
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A very good question. My personal strategy is to have as many new

sources as possible with as different biases as possible, comparing them

with each other. Sure, both CNN and Al Jazira are biased, but not in the

same way - and the bias of Slashdot is very different from the bias of

Dagens Nyheter.

Let's see if we can do some information theory here. Assume we have an

information source S (the Truth), which we get information about through

noisy and biased channels. In some cases we know the bias, in some cases

it is unknown. What is the optimal estimate of S?

To make things more concrete, assume S is a scalar we want to estimate

(like the probability of Bin Laden being a nice guy or the number of

dead in a bombing). From information channel i we receive an estimate

s_i, which is s_i = a_i S + N(b_i,c_i): - a_i is how much S is

distorted, b_i is the bias and c_i the standard deviation. The

distribution of s_i becomes f(s_i | S) = N(x-a_iS-b_i,c_i). Here I

assume independent channels (BIG assumption!).

Given data from s_i, we can then do a maximum likelyhood estimation of

a_i, b_i and c_i if we hold S constant (i.e compare the news about a

certain fact for a while).

Bayes rule says that the distribution of S given s_i is f(S | s_1, s_2,

...) = [integral f(S,s) ds] f(s | S) / integral [integral f(S,s) ds] f(s

| S) dS where f(S,s) is the joint distribution of S and s_1, s_2,.... We

already have f(s_i|S), so f(s|S)= product f(s_i|S). So we get f(S| s) =

f(S) product f(s_i|S) / <normalizing stuff>.

We still have the Bayes factor f(S) - we need an estimate of that. This

is where our own preconceptions and world assumptions come in. Usually I

think we simply assume it is normally distributed and rescaled to have

zero mean and 1 variance.

OK, this seems to suggest a method: gather s_i, for each channel create

a maximum likeliehood estimate of a_i, b_i and c_i given the assumption

S=N(0,1), put it into the formula above and we get a

posterior distribution of S.

If channels are of uncertain independence, we can either calculate

correlations between them for a while, and then select a set that are

uncorrelated. A more clever method would be to use principal component

analysis to create "virtual channels" that are weighted sums of the

channels that are mutually independent and hence could be used to

estimate S.

Caveat: I'm not a staticistician and this was just off the cuff - there

has to be some serious analysis on this, I just don't know where to

look (and I don't have the time).

*> I only have a crude approximation of such a strategy, where I assign
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*> higher credibility to an institution if liberals accuse it of being
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*> conservative and conservatives accuse it of being liberal. There are
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*> many domains this heuristic doesn't cover though, so I'm looking for
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*> others.
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A nice strategy, I like it!

This is a bit like finding a channel that is independent of two known

anticorrelated channels.

-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y

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