The True Epistemic Prisoner's Dilemma

9 MBlume 19 April 2009 08:57AM

I spoke yesterday of the epistemic prisoner's dilemma, and JGWeissman wrote:

I am having some difficulty imagining that I am 99% sure of something, but I cannot either convince a person to outright agree with me or accept that he is uncertain and therefore should make the choice that would help more if it is right, but I could convince that same person to cooperate in the prisoner's dilemma. However, if I did find myself in that situation, I would cooperate.

To which I said:

Do you think you could convince a young-earth creationist to cooperate in the prisoner's dilemma?

And lo, JGWeissman saved me a lot of writing when he replied thus:

Good point. I probably could. I expect that the young-earth creationist has a huge bias that does not have to interfere with reasoning about the prisoner's dilemma.

So, suppose Omega finds a young-earth creationist and an atheist, and plays the following game with them. They will each be taken to a separate room, where the atheist will choose between each of them receiving $10000 if the earth is less than 1 million years old or each receiving $5000 if the earth is more than 1 million years old, and the young earth creationist will have a similar choice with the payoffs reversed. Now, with prisoner's dilemma tied to the young earth creationist's bias, would I, in the role of the atheist still be able to convince him to cooperate? I don't know. I am not sure how much the need to believe that the earth is around 5000 years would interfere with recognizing that it is in his interest to choose the payoff for earth being over a million years old. But still, if he seemed able to accept it, I would cooperate.

I make one small modification. You and your creationist friend are actually not that concerned about money, being distracted by the massive meteor about to strike the earth from an unknown direction. Fortunately, Omega is promising to protect limited portions of the globe, based on your decisions (I think you've all seen enough PDs that I can leave the numbers as an excercise).

It is this then which I call the true epistemic prisoner's dilemma. If I tell you a story about two doctors, even if I tell you to put yourself in the shoes of one, and not the other, it is easy for you to take yourself outside them, see the symmetry and say "the doctors should cooperate".  I hope I have now broken some of that emotional symmetry.

As Omega lead the creationist to the other room, you would (I know I certainly would) make a convulsive effort to convince him of the truth of evolution. Despite every pointless, futile argument you've ever had in an IRC room or a YouTube thread, you would struggle desperately, calling out every half-remembered fragment of Dawkins or Sagan you could muster, in hope that just before the door shut, the creationist would hold it open and say "You're right, I was wrong. You defect, I'll cooperate -- let's save the world together."

But of course, you would fail. And the door would shut, and you would grit your teeth, and curse 2000 years of screamingly bad epistemic hygiene, and weep bitterly for the people who might die in a few hours because of your counterpart's ignorance. And then -- I hope -- you would cooperate.

The Epistemic Prisoner's Dilemma

33 MBlume 18 April 2009 05:36AM

Let us say you are a doctor, and you are dealing with a malaria epidemic in your village. You are faced with two problems. First, you have no access to the drugs needed for treatment. Second, you are one of two doctors in the village, and the two of you cannot agree on the nature of the disease itself. You, having carefully tested many patients, being a highly skilled, well-educated diagnostician, have proven to yourself that the disease in question is malaria. Of this you are >99% certain. Yet your colleague, the blinkered fool, insists that you are dealing with an outbreak of bird flu, and to this he assigns >99% certainty.

Well, it need hardly be said that someone here is failing at rationality. Rational agents do not have common knowledge of disagreements etc. But... what can we say? We're human, and it happens.

So, let's say that one day, OmegaDr. House calls you both into his office and tells you that he knows, with certainty, which disease is afflicting the villagers. As confident as you both are in your own diagnoses, you are even more confident in House's abilities. House, however, will not tell you his diagnosis until you've played a game with him. He's going to put you in one room and your colleague in another. He's going to offer you a choice between 5,000 units of malaria medication, and 10,000 units of bird-flu medication. At the same time, he's going to offer your colleague a choice between 5,000 units of bird-flu meds, and 10,000 units of malaria meds.

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Imaginary Positions

19 Eliezer_Yudkowsky 23 December 2008 05:35PM

Every now and then, one reads an article about the Singularity in which some reporter confidently asserts, "The Singularitarians, followers of Ray Kurzweil, believe that they will be uploaded into techno-heaven while the unbelievers languish behind or are extinguished by the machines."

I don't think I've ever met a single Singularity fan, Kurzweilian or otherwise, who thinks that only believers in the Singularity will go to upload heaven and everyone else will be left to rot.  Not one.  (There's a very few pseudo-Randian types who believe that only the truly selfish who accumulate lots of money will make it, but they expect e.g. me to be damned with the rest.)

But if you start out thinking that the Singularity is a loony religious meme, then it seems like Singularity believers ought to believe that they alone will be saved.  It seems like a detail that would fit the story.

This fittingness is so strong as to manufacture the conclusion without any particular observations.  And then the conclusion isn't marked as a deduction.  The reporter just thinks that they investigated the Singularity, and found some loony cultists who believe they alone will be saved.

Or so I deduce.  I haven't actually observed the inside of their minds, after all.

Has any rationalist ever advocated behaving as if all people are reasonable and fair?  I've repeatedly heard people say, "Well, it's not always smart to be rational, because other people aren't always reasonable."  What rationalist said they were?  I would deduce:  This is something that non-rationalists believe it would "fit" for us to believe, given our general blind faith in Reason.  And so their minds just add it to the knowledge pool, as though it were an observation.  (In this case I encountered yet another example recently enough to find the reference; see here.)

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The Mechanics of Disagreement

8 Eliezer_Yudkowsky 10 December 2008 02:01PM

Two ideal Bayesians cannot have common knowledge of disagreement; this is a theorem.  If two rationalist-wannabes have common knowledge of a disagreement between them, what could be going wrong?

The obvious interpretation of these theorems is that if you know that a cognitive machine is a rational processor of evidence, its beliefs become evidence themselves.

If you design an AI and the AI says "This fair coin came up heads with 80% probability", then you know that the AI has accumulated evidence with an likelihood ratio of 4:1 favoring heads - because the AI only emits that statement under those circumstances.

It's not a matter of charity; it's just that this is how you think the other cognitive machine works.

And if you tell an ideal rationalist, "I think this fair coin came up heads with 80% probability", and they reply, "I now think this fair coin came up heads with 25% probability", and your sources of evidence are independent of each other, then you should accept this verdict, reasoning that (before you spoke) the other mind must have encountered evidence with a likelihood of 1:12 favoring tails.

But this assumes that the other mind also thinks that you're processing evidence correctly, so that, by the time it says "I now think this fair coin came up heads, p=.25", it has already taken into account the full impact of all the evidence you know about, before adding more evidence of its own.

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Disjunctions, Antipredictions, Etc.

14 Eliezer_Yudkowsky 09 December 2008 03:13PM

Followup toUnderconstrained Abstractions

Previously:

So if it's not as simple as just using the one trick of finding abstractions you can easily verify on available data, what are some other tricks to use?

There are several, as you might expect...

Previously I talked about "permitted possibilities".  There's a trick in debiasing that has mixed benefits, which is to try and visualize several specific possibilities instead of just one.

The reason it has "mixed benefits" is that being specific, at all, can have biasing effects relative to just imagining a typical case.  (And believe me, if I'd seen the outcome of a hundred planets in roughly our situation, I'd be talking about that instead of all this Weak Inside View stuff.)

But if you're going to bother visualizing the future, it does seem to help to visualize more than one way it could go, instead of concentrating all your strength into one prediction.

So I try not to ask myself "What will happen?" but rather "Is this possibility allowed to happen, or is it prohibited?"  There are propositions that seem forced to me, but those should be relatively rare - the first thing to understand about the future is that it is hard to predict, and you shouldn't seem to be getting strong information about most aspects of it.

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True Sources of Disagreement

8 Eliezer_Yudkowsky 08 December 2008 03:51PM

Followup toIs That Your True Rejection?

I expected from the beginning, that the difficult part of two rationalists reconciling a persistent disagreement, would be for them to expose the true sources of their beliefs.

One suspects that this will only work if each party takes responsibility for their own end; it's very hard to see inside someone else's head.  Yesterday I exhausted myself mentally while out on my daily walk, asking myself the Question "What do you think you know, and why do you think you know it?" with respect to "How much of the AI problem compresses to large insights, and how much of it is unavoidable nitty-gritty?"  Trying to either understand why my brain believed what it believed, or else force my brain to experience enough genuine doubt that I could reconsider the question and arrive at a real justification that way.  It's hard to see how Robin Hanson could have done any of this work for me.

Presumably a symmetrical fact holds about my lack of access to the real reasons why Robin believes what he believes.  To understand the true source of a disagreement, you have to know why both sides believe what they believe - one reason why disagreements are hard to resolve.

Nonetheless, here's my guess as to what this Disagreement is about:

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Is That Your True Rejection?

47 Eliezer_Yudkowsky 06 December 2008 02:26PM

It happens every now and then, that the one encounters some of my transhumanist-side beliefs—as opposed to my ideas having to do with human rationality—strange, exotic-sounding ideas like superintelligence and Friendly AI.  And the one rejects them.

If the one is called upon to explain the rejection, not uncommonly the one says,

"Why should I believe anything Yudkowsky says?  He doesn't have a PhD!"

And occasionally someone else, hearing, says, "Oh, you should get a PhD, so that people will listen to you."  Or this advice may even be offered by the same one who disbelieved, saying, "Come back when you have a PhD."

Now there are good and bad reasons to get a PhD, but this is one of the bad ones.

There's many reasons why someone actually has an adverse reaction to transhumanist theses.  Most are matters of pattern recognition, rather than verbal thought: the thesis matches against "strange weird idea" or "science fiction" or "end-of-the-world cult" or "overenthusiastic youth".

So immediately, at the speed of perception, the idea is rejected.  If, afterward, someone says "Why not?", this lanches a search for justification.  But this search will not necessarily hit on the true reason—by "true reason" I mean not the best reason that could be offered, but rather, whichever causes were decisive as a matter of historical fact, at the very first moment the rejection occurred.

Instead, the search for justification hits on the justifying-sounding fact, "This speaker does not have a PhD."

But I also don't have a PhD when I talk about human rationality, so why is the same objection not raised there?

And more to the point, if I had a PhD, people would not treat this as a decisive factor indicating that they ought to believe everything I say.  Rather, the same initial rejection would occur, for the same reasons; and the search for justification, afterward, would terminate at a different stopping point.

They would say, "Why should I believe you?  You're just some guy with a PhD! There are lots of those.  Come back when you're well-known in your field and tenured at a major university."

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Underconstrained Abstractions

5 Eliezer_Yudkowsky 04 December 2008 01:58PM

Followup toThe Weak Inside View

Saith Robin:

"It is easy, way too easy, to generate new mechanisms, accounts, theories, and abstractions.  To see if such things are useful, we need to vet them, and that is easiest "nearby", where we know a lot.  When we want to deal with or understand things "far", where we know little, we have little choice other than to rely on mechanisms, theories, and concepts that have worked well near.  Far is just the wrong place to try new things."

Well... I understand why one would have that reaction.  But I'm not sure we can really get away with that.

When possible, I try to talk in concepts that can be verified with respect to existing history.  When I talk about natural selection not running into a law of diminishing returns on genetic complexity or brain size, I'm talking about something that we can try to verify by looking at the capabilities of other organisms with brains big and small.  When I talk about the boundaries to sharing cognitive content between AI programs, you can look at the field of AI the way it works today and see that, lo and behold, there isn't a lot of cognitive content shared.

But in my book this is just one trick in a library of methodologies for dealing with the Future, which is, in general, a hard thing to predict.

Let's say that instead of using my complicated-sounding disjunction (many different reasons why the growth trajectory might contain an upward cliff, which don't all have to be true), I instead staked my whole story on the critical threshold of human intelligence.  Saying, "Look how sharp the slope is here!" - well, it would sound like a simpler story.  It would be closer to fitting on a T-Shirt.  And by talking about just that one abstraction and no others, I could make it sound like I was dealing in verified historical facts - humanity's evolutionary history is something that has already happened.

But speaking of an abstraction being "verified" by previous history is a tricky thing.  There is this little problem of underconstraint - of there being more than one possible abstraction that the data "verifies".

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Singletons Rule OK

11 Eliezer_Yudkowsky 30 November 2008 04:45PM

Reply toTotal Tech Wars

How does one end up with a persistent disagreement between two rationalist-wannabes who are both aware of Aumann's Agreement Theorem and its implications?

Such a case is likely to turn around two axes: object-level incredulity ("no matter what AAT says, proposition X can't really be true") and meta-level distrust ("they're trying to be rational despite their emotional commitment, but are they really capable of that?").

So far, Robin and I have focused on the object level in trying to hash out our disagreement.  Technically, I can't speak for Robin; but at least in my own case, I've acted thus because I anticipate that a meta-level argument about trustworthiness wouldn't lead anywhere interesting.  Behind the scenes, I'm doing what I can to make sure my brain is actually capable of updating, and presumably Robin is doing the same.

(The linchpin of my own current effort in this area is to tell myself that I ought to be learning something while having this conversation, and that I shouldn't miss any scrap of original thought in it - the Incremental Update technique. Because I can genuinely believe that a conversation like this should produce new thoughts, I can turn that feeling into genuine attentiveness.)

Yesterday, Robin inveighed hard against what he called "total tech wars", and what I call "winner-take-all" scenarios:

Robin:  "If you believe the other side is totally committed to total victory, that surrender is unacceptable, and that all interactions are zero-sum, you may conclude your side must never cooperate with them, nor tolerate much internal dissent or luxury."

Robin and I both have emotional commitments and we both acknowledge the danger of that.  There's nothing irrational about feeling, per se; only failure to update is blameworthy.  But Robin seems to be very strongly against winner-take-all technological scenarios, and I don't understand why.

Among other things, I would like to ask if Robin has a Line of Retreat set up here - if, regardless of how he estimates the probabilities, he can visualize what he would do if a winner-take-all scenario were true.

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Whence Your Abstractions?

7 Eliezer_Yudkowsky 20 November 2008 01:07AM

Reply toAbstraction, Not Analogy

Robin asks:

Eliezer, have I completely failed to communicate here?  You have previously said nothing is similar enough to this new event for analogy to be useful, so all we have is "causal modeling" (though you haven't explained what you mean by this in this context).  This post is a reply saying, no, there are more ways using abstractions; analogy and causal modeling are two particular ways to reason via abstractions, but there are many other ways.

Well... it shouldn't be surprising if you've communicated less than you thought.  Two people, both of whom know that disagreement is not allowed, have a persistent disagreement.  It doesn't excuse anything, but - wouldn't it be more surprising if their disagreement rested on intuitions that were easy to convey in words, and points readily dragged into the light?

I didn't think from the beginning that I was succeeding in communicating.  Analogizing Doug Engelbart's mouse to a self-improving AI is for me such a flabbergasting notion - indicating such completely different ways of thinking about the problem - that I am trying to step back and find the differing sources of our differing intuitions.

(Is that such an odd thing to do, if we're really following down the path of not agreeing to disagree?)

"Abstraction", for me, is a word that means a partitioning of possibility - a boundary around possible things, events, patterns.  They are in no sense neutral; they act as signposts saying "lump these things together for predictive purposes".  To use the word "singularity" as ranging over human brains, farming, industry, and self-improving AI, is very nearly to finish your thesis right there.

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