P-values and Chaos Worlds

In First Aid for P-Values, Black Belt Bayesian discusses how a Bayesian can interpret the p-value to get some information. He references an article which argues that this can shift the frame of the discussion in a useful way, improving the nature of the statistical arguments without significantly changing the methodology. It emphasizes the role of evidence in shifting beliefs progressively, as opposed to proof/disproof.

While this does seem like a useful tool, it still leaves us with the problems of null hypothesis testing. One problem is that the null hypothesis is sometimes not very plausible. Arguing from a point of total randomness is an odd thing to do. What would we expect to see if the world was a chaotic place with no patterns? Hm, reality doesn't match that? Ok, well, our hypothesis is better than maximum entropy. Good!

Scott Alexander makes this error in a post which he explicitly predicted he'd regret writing. (Epistemic Warning: This is, perhaps, among the smaller problems with the post. A larger problem is that it makes readers think in simplistic tribes. Another possible problem is that it risks the same error it calls out. There's a reason he said he'd regret it.) He's discussing how strongly our friends and acquaintances are filtered in terms of beliefs:

And I don’t have a single one of those people in my social circle. It’s not because I’m deliberately avoiding them; I’m pretty live-and-let-live politically, I wouldn’t ostracize someone just for some weird beliefs. And yet, even though I probably know about a hundred fifty people, I am pretty confident that not one of them is creationist. Odds of this happening by chance? 1/2^150 = 1/10^45 = approximately the chance of picking a particular atom if you are randomly selecting among all the atoms on Earth.

 He goes on to use this number a couple more times as an indication of the strength of filtering:

I inhabit the same geographical area as scores and scores of conservatives. But without meaning to, I have created an outrageously strong bubble, a 10^45 bubble. Conservatives are all around me, yet I am about as likely to have a serious encounter with one as I am a Tibetan lama.

And:

A disproportionate number of my friends are Jewish, because I meet them at psychiatry conferences or something – we self-segregate not based on explicit religion but on implicit tribal characteristics. So in the same way, political tribes self-segregate to an impressive extent – a 1/10^45 extent, I will never tire of hammering in – based on their implicit tribal characteristics. 

 The problem is that this is a world-of-chaos-and-fire hypothesis he's comparing to. The number makes the strength of the filter incredible-sounding, almost physically implausible. But, that's just what you get when you use a bad model! Note that the "strength" would keep getting more extreme as we examine more data (just as a p-value gets extreme with more data, unless the null hypothesis is actually true).

It's not like there is a baseline world where everything is completely random, and an extra physical force on top of this which puts things into nonrandom configurations. (Except, perhaps, in the sense that everything is heading toward thermodynamic equilibrium.) We do not form associates with people randomly. It would be much more meaningful to compare possibly-realistic models and the level of friend filtering which they imply.

I'm not trying to call out Slate Star Codex here. That particular post happened to be an epistemic landmine, yes, but this mistake is easy to make and fairly common. What's interesting to me is the difference between what arguments feel meaningful vs actually are meaningful.

A List Of Nuances

Abram Demski and Grognor

(This article is also cross-posted to LessWrong.)

Much of rationality is pattern-matching. An article on lesswrong might point out a thing to look for. Noticing this thing changes your reasoning in some way. This essay is a list of things to look for. These things are all associated, but the reader should take care not to lump them together. Each dichotomy is distinct, and although the brain will tend to abstract them into some sort of yin/yang correlated mush, in reality they have a more complicated structure; some things may be similar, but if possible, try to focus on the complex interrelationships.

1. Map vs. Territory
1. Eliezer’s sequences use this as a jump-off point for discussion of rationality.
2. Many thinking mistakes are map vs. territory confusions.
1. A map and territory mistake is a mix-up of seeming vs being.
2. Humans need frequent reminders that we are not omniscient.
2. Cached Thoughts vs. Thinking
1. This document is a list of cached thoughts.
3. Clusters vs. Properties
1. These words could be used in different ways, but the distinction I want to point at is that of labels we put on things vs actual differences in things.
2. The mind projection fallacy is the fallacy of thinking a mental category (a “cluster”) is an actual property things have.
1. If we see something as good for one reason, we are likely to attribute other good properties to it, as if it had inherent goodness. This is called the halo effect. (If we see something as bad and infer other bad properties as a result, it is referred to as the reverse-halo effect.)
3. Categories are inference applicability heuristics; ruling X an instance of Y without expecting novel inferences is cargo cult classification.
4. Syntax vs. Semantics
1. The syntax is the physical instantiation of the map. The semantics is the way we are meant to read the map; that is, the intended relationship to the territory.
5. Semantics vs. Pragmatics
1. The semantics is the literal contents of a message, whereas the pragmatics is the intended result of conveying the message.
1. An example of a message with no semantics and only pragmatics is a command, such as “Stop!”.
2. Almost no messages lack pragmatics, and for good reason. However, if you seek truth in a discussion, it is important to foster a willingness to say things with less pragmatic baggage.
3. Usually when we say things, we do so with some “point” which is beyond the semantics of our statement. The point is usually to build up or knock down some larger item of discussion. This is not inherently a bad thing, but has a failure mode where arguments are battles and statements are weapons, and the cleverer arguer wins.
2. The meaning of a thing is the way you should be influenced by it.
6. Object-level vs. Meta-level
1. The difference between making a map and writing a book about map-making.
2. A good meta-level theory helps get things right at the object level, but it is usually impossible to get things right at the meta level before before you’ve made significant progress at the object level.
7. Seeming vs. Being
1. We can only deal with how things seem, not how they are. Yet, we must strive to deal with things as they are, not as they seem.
1. This is yet another reminder that we are not omniscient.
2. If we optimize too hard for things which seem good rather than things which are good, we will get things which seem very good but which may only be somewhat good, or even bad.
3. The dangerous cases are the cases where you do not notice there is a distinction.
1. This is why humans need constant reminders that we are not omniscient.
4. We must take care to notice the difference between how things seem to seem, and how they actually seem.
8. Signal vs. Noise
1. Not all information is equal. It is often the case that we desire certain sorts of information and desire to ignore other sorts.
2. In a technical setting, this has to do with the error rate present in a communication channel; imperfections in the channel will corrupt some bits, making a need for redundancy in the message being sent.
3. In a social setting, this is often used to refer to the amount of good information vs irrelevant information in a discussion. For example, letting a mediocre writer add material to a group blog might increase the absolute amount of good information, yet worsen the signal-to-noise ratio.
4. Attention is a scarce resource; yes everyone has something to teach you, but many people are much more efficient sources of wisdom than others.
9. Selection Effects
1. Filtered evidence.
1. In many situations, if we can present evidence to a Bayesian agent without the agent knowing that we are being selective, we can convince the agent of anything we like. For example, if I want to convince you that smoking causes obesity, I could find many people who became obese after they started smoking.
2. The solution to this is for the Bayesian agent to model where the information is coming from. If you know I am selecting people based on this criteria, then you will not take it as evidence of anything, because the evidence has been cherry-picked.
3. Most of the information you receive is intensely filtered. Nothing comes to your attention with a good conscience.
2. The silent evidence problem.
1. Selection bias need not be the result of purposeful interference as in cherry-picking. Often, an unrelated process may hide some of the evidence needed. For example, we hear far more about successful people than unsuccessful. It is tempting to look at successful people and attempt to draw conclusion about what it takes to be successful. This approach suffers from the silent evidence problem: we also need to look at the unsuccessful people and examine what is different about the two groups.
3. Observer selection effects.
10. What You Mean vs. What You Think You Mean
1. Very often, people will say something and then that thing will be refuted. The common response to this is to claim you meant something slightly different, which is more easily defended.
1. We often do this without noticing, making it dangerous for thinking. It is an automatic response generated by our brains, not a conscious decision to defend ourselves from being discredited. You do this far more often than you notice. The brain fills in a false memory of what you meant without asking for permission.
11. What You Mean vs. What the Others Think You Mean
1. The illusion of transparency.
2. The double illusion of transparency.
3. Wiio’s Laws
12. What You Optimize vs. What You Think You Optimize
1. Evolution optimizes for reproduction but in doing so creates animals with a variety of goals which are correlated with reproduction.
2. Extrinsic motivation is weaker than intrinsic motivation.
3. The people who value practice for its own sake do better than the people who only value being good at what they’re practicing.
4. “Consequentialism is true, but virtue ethics is what works.”
13. Stated Preferences vs. Revealed Preferences
1. Revealed preferences are the preferences we can infer from your actions. These are usually different from your stated preferences.
1. X is not about Y:
1. Food isn’t about nutrition.
2. Clothes aren’t about comfort.
3. Bedrooms aren’t about sleep.
4. Marriage isn’t about love.
5. Talk isn’t about information.
6. Laughter isn’t about humour.
7. Charity isn’t about helping.
8. Church isn’t about God.
9. Art isn’t about insight.
10. Medicine isn’t about health.
11. Consulting isn’t about advice.
12. School isn’t about learning.
13. Research isn’t about progress.
14. Politics isn’t about policy.
15. Going meta isn’t about the object level.
16. Language isn’t about communication.
17. The rationality movement isn’t about epistemology.
2. Everything is actually about signalling.
2. Humans Are Not Automatically Strategic
1. Never attribute to malice that which can be adequately explained by stupidity. The difference between stated preferences and revealed preferences does not indicate dishonest intent. We should expect the two to differ in the absence of a mechanism to align them.
2. Hidden Motives vs. Innocent Failure
3. People, ideas, and organizations respond to incentives.
1. Evolution selects humans who have reproductively selfish behavioral tendencies, but prosocial and idealistic stated preferences.
1. Near vs. Far
2. Social forces select ideas for virality and comprehensibility as opposed to truth or even usefulness.
1. Motte-and-bailey fallacy
3. Organizations are by default bad at being strategic about their own survival, but the ones that survive are the ones you see.
14. What You Achieve vs. What You Think You Achieve
1. Most of the consequences of our actions are totally unknown to us.
2. It is impossible to optimize without proper feedback.
15. What You Optimize vs. What You Actually Achieve
1. Consequentialism is more about expected consequences than actual consequences.
16. What You Seem Like vs. What You Are
1. You can try to imagine yourself from the outside, but no one has the full picture.
17. What Other People Seem Like vs. What They Are
1. When people assume that they understand others, they are wrong.
18. What People Look Like vs. What They Think They Look Like
1. People underestimate the gap between stated preferences and revealed preferences.
19. What Your Brain Does vs. What You Think It Does
1. You are running on corrupted hardware.
1. The brain’s machinations are fundamentally social; it automatically does things like signal, save face, etc., which distort the truth.
2. The reverse of stupidity is not intelligence.
1. Knowing that you are running on corrupted hardware should cause skepticism about the outputs of your thought-processes. Yet, too much skepticism will cause you to stumble, particularly when fast thinking is needed.
1. Producing a correct result plus justification is harder than producing only the correct result.
2. Justifications are important, but the correct result is more important.
3. Much of our apparent self-reflection is confabulation, generating plausible explanations after the brain spits out an answer.
4. Example: doing quick mental math. If you are good at this, attempting to explicitly justify every step as you go would likely slow you down.
5. Example: impressions formed over a long period of time. Wrong or right, it is unlikely that you can explicitly give all your reasons for the impression. Requiring your own beliefs to be justifiable would preempt impressions that require lots of experience and/or many non-obvious chains of subconscious inference.
6. Impressions are not beliefs and they are always useful data.
20. Clever Argument vs. Truth-seeking; The Bottom Line
1. People believe what they want to believe.
1. Believing X for some reason unrelated to X being true is referred to as motivated cognition.
2. Giving a smart person more information and more methods of argument may actually make their beliefs less accurate, because you are giving them more tools to construct clever arguments for what they want to believe.
2. Your actual reason for believing X determines how well your belief correlates with the truth.
1. If you believe X because you want to, any arguments you make for X no matter how strong they sound are devoid of informational context about X and should properly be ignored by a truth-seeker.
3. If you believe true things when doing so improves your life, that is no credit to you at all. Everyone does that.
21. Lumpers vs. Splitters
1. A lumper is a thinker who attempts to fit things into overarching patterns. A splitter is a thinker who makes as many distinctions as possible, recognizing the importance of being specific and getting the details right.
2. Specifically, some people want big Wikipedia and TVTropes articles that discuss many things, and others want smaller articles that discuss fewer things.
3. This list of nuances is a lumper attempting to think more like a splitter.
22. Fox vs. Hedgehog
1. “A fox knows many things, but a hedgehog knows One Big Thing.” Closely related to a splitter, a fox is a thinker whose strength is in a broad array of knowledge. A hedgehog is a thinker who, in contrast, has one big idea and applies it everywhere.
2. The fox mindset is better for making accurate judgements, according to Tetlock.
23. Traps vs. Gardens
1. Well-kept gardens die by pacifism.
1. Conversations tend to slide toward contentious and useless topics.
2. Societies tend to decay.
3. Systems in general work poorly or not at all.
4. Thermodynamic equilibrium is entropic.
5. Without proper institutions being already in place, it takes large amounts of constant effort and vigilance to stay out of traps.
2. From the outside of a broken Molochian system it is easy to see how to fix. But it cannot be fixed from the inside.