trentmkelly/LessWrong-43k huggingface dataset:
Introduction to Game Theory: Sequence Guide
by Scott Alexander — 2012-06-28T03:32:29.950Z

This sequence of posts is a primer on game theory intended at an introductory level. Because it is introductory, Less Wrong veterans may find some parts boring, obvious, or simplistic - although hopefully nothing is so simplistic as to be outright wrong.
Parts of this sequence draw heavily upon material from The Art of Strategy by Avinash Dixit and Barry Nalebuff, and it may in part be considered a (very favorable) review of the book accompanied by an exploration of its content. I have tried to include enough material to be useful, but not so much material that it becomes a plagiarism rather than a review (it's probably a bad idea to pick a legal fight with people who write books called The Art of Strategy.) Therefore, for the most complete and engaging presentation of this material, I highly recommend the original book.
All posts will be linked from here as they go up:
1. Introduction to Game Theory: Sequence Guide
2. Backward Reasoning Over Decision Trees
3. Nash Equilibria and Schelling Points
4. Introduction to Prisoners' Dilemma
5. Real World Solutions to Prisoners' Dilemmas
6. Interlude for Behavioral Economics
7. What Is Signaling, Really?
8. Bargaining and Auctions
9. Imperfect Voting Systems
10. Game Theory As A Dark Art

Special thanks to Luke for his book recommendation and his strong encouragement to write this.
Bounded versions of Gödel's and Löb's theorems
by cousin_it — 2012-06-27T18:28:04.744Z

While writing up decision theory results, I had to work out bounded versions of Gödel's second incompleteness theorem and Löb's theorem. Posting the tentative proofs here to let people find any major errors before adding formality. Any comments are welcome!

Bounded Gödel's theorem

Informal meaning: if a theory T has a short proof that any proof of T's inconsistency must be long, then T is inconsistent.

Formal statement: there exists a total computable function f such that for any effectively generated theory T that includes Peano arithmetic, and for any integer n, if T proves in n symbols that "T can't prove a falsehood in f(n) symbols", then T is inconsistent.

Proof

If the theory T takes more than n symbols to describe, the condition of the theorem can't hold, so let's assume T is smaller than that.

Let's take g(n)>>n and f(n)>>exp(g(n)). For any integer n, let's define a program R that enumerates all proofs in the theory T up to length g(n), looking for either a proof that R prints something (in which case R immediately halts without printing anything), or a proof that R doesn't print anything (in which case R prints something and halts). If no proof is found, R halts without printing anything.

Assume that the theory T is consistent. Note that if the program R finds some proof, then it makes the proved statement false. Also note that the theory T can completely simulate the execution of the program R in exp(g(n)) symbols. Therefore if the program R finds any proof, the resulting contradiction in the theory T can be "exposed" using exp(g(n)) symbols. Since f(n)>>exp(g(n)), and the theory T proves in n symbols that "T can't prove a falsehood in f(n) symbols", we see that T proves in slightly more than n symbols that the program R won't find any proofs. Therefore the theory T proves in slightly more than n symbols that the program R won't print anything. Since g(n)>>n, the program R will find that proof and print something, making the theory T inconsistent. QED.

(The main idea of the proof is taken from Ron Maimon, originally due to Rosser, and adapted to the bounded case.)

Bounded Löb's theorem

Informal meaning: if having a bounded-size proof of statement S would imply the truth of S, and that fact has a short proof, then S is provable.

Formal statement: there exists a total computable function f such that for any effect...
Science and the Supernatural
by billswift — 2012-06-27T13:44:57.860Z

Can science test the supernatural? Yes!! is an interesting article about why there are not "two nonoverlapping magisteria". The core of the article is based on the paper Can Science Test Supernatural Worldviews? Abstract of the latter paper:

Several prominent scientists, philosophers, and scientific institutions have argued that science cannot test supernatural worldviews on the grounds that (1) science presupposes a naturalistic worldview (Naturalism) or that (2) claims involving supernatural phenomena are inherently beyond the scope of scientific investigation. The present paper argues that these assumptions are questionable and that indeed science can test supernatural claims. While scientific evidence may ultimately support a naturalistic worldview, science does not presuppose Naturalism as an a priori commitment, and supernatural claims are amenable to scientific evaluation. This conclusion challenges the rationale behind a recent judicial ruling in the United States concerning the teaching of “Intelligent Design” in public schools as an alternative to evolution and the official statements of two major scientific institutions that exert a substantial influence on science educational policies in the United States. Given that science does have implications concerning the probable truth of supernatural worldviews, claims should not be excluded a priori from science education simply because they might be characterized as supernatural, paranormal, or religious. Rather, claims should be excluded from science education when the evidence does not support them, regardless of whether they are designated as ‘natural’ or ‘supernatural’.

Three more specific quotes from one or both papers:

- Claims about the supernatural should be prohibited from science classes not because they’re religious, but because science has “proven” them wrong.

- To exclude, a priori, the supernatural would validate the complaint voiced by some ID adherents and other creationists that science is dogmatically committed to Naturalism and thus opposed in principle to considering supernatural explanations (Johnson, 1999; see Stenger, 2006a). On the other hand, if there is no fundamental barrier preventing science from evaluating supernatural claims, then to declare the study of supernatural phenomena out of bounds to scientific investigation i...
[SEQ RERUN] The Fear of Common Knowledge
by MinibearRex — 2012-06-27T03:14:05.720Z

Today's post, The Fear of Common Knowledge was originally published on 09 July 2008. A summary (taken from the LW wiki):

A discussion of an interesting kind of lie, in which someone tells a lie that the person they're speaking to knows is a lie, but doesn't know that the person who told the lie knows that they know it's a lie.

Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Where Recursive Justification Hits Bottom, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.
How to read a book
by Blackened — 2012-06-27T01:31:14.685Z

I'm considering reading the book by the title How to read a book. A friend of mine (his critical thinking is quite good, but certainly not as good as it could be, so I can't trust his opinion too much) said he has read it and that it helped him a lot. He said it had advice on reading comprehension, critical thinking ("don't automatically accept what you read") and that when people read something, they tend to forget it quite easily (and that the book addresses this issue). But he also quoted a part of the book, which said that only reading hard things will improve your reading - it might be true, but it doesn't sound intuitive to me (according to my rationalist intuition, obviously :D). Also, the book is written in 1940 and revised in 1972. Additionally, the author is religious (I think he's even highly religious). And if I remember correctly, it's not based on research - there is a quite high chance that I don't remember correctly. I checked its Amazon page, nothing said anything about research (browsed through all the low ratings to see if they complain about that, nobody did).

Should I bother reading it? If it delivers what it promises, it will obviously be so cost-effective that most rationalists should abandon reading whatever they're reading and switch to this book. But is there a version that is entirely based on research, with references or sound theory behind most claims?
Meetup : Brussels meetup
by Axel — 2012-06-26T16:02:29.102Z

Discussion article for the meetup : Brussels meetup

WHEN:
14 July 2012 12:00:00PM (+0200)

WHERE:
Museum of Natural Sciences Rue Vautier 29 B-1000 Brussels

We'll meet in the lobby as usual, I'll have a sign, should you arrive late we will have moved to the cafeteria (just go straight once you're past the entrance, you can't miss it) If you are in the neighborhood, consider dropping by. (getting there: http://www.naturalsciences.be/information/visitor/access)

Discussion article for the meetup : Brussels meetup
A (small) critique of total utilitarianism
by Stuart_Armstrong — 2012-06-26T12:36:38.339Z

In total utilitarianism, it is a morally neutral act to kill someone (in a painless and unexpected manner) and creating/giving birth to another being of comparable happiness (or preference satisfaction or welfare). In fact if one can kill a billion people to create a billion and one, one is morally compelled to do so. And this is true for real people, not just thought experiment people - living people with dreams, aspirations, grudges and annoying or endearing quirks. To avoid causing extra pain to those left behind, it is better that you kill off whole families and communities, so that no one is left to mourn the dead. In fact the most morally compelling act would be to kill off the whole of the human species, and replace it with a slightly larger population.

We have many real world analogues to this thought experiment. For instance, it seems that there is only a small difference between the happiness of richer nations and poorer nations, while the first consume many more resources than the second. Hence to increase utility we should simply kill off all the rich, and let the poor multiply to take their place (continually bumping off any of the poor that gets too rich). Of course, the rich world also produces most of the farming surplus and the technology innovation, which allow us to support a larger population. So we should aim to kill everyone in the rich world apart from farmers and scientists - and enough support staff to keep these professions running (Carl Shulman correctly points out that we may require most of the rest of the economy as "support staff". Still, it's very likely that we could kill off a significant segment of the population - those with the highest consumption relative to their impact of farming and science - and still "improve" the situation).

Even if turns out to be problematic to implement in practice, a true total utilitarian should be thinking: "I really, really wish there was a way to do targeted killing of many people in the USA, Europe and Japan, large parts of Asia and Latin America and some parts of Africa - it makes me sick to the stomach to think that I can't do that!" Or maybe: "I really really wish I could make everyone much poorer without affecting the size of the economy - I wake up at night with nightmare because these people remain above the poverty line!"

I won't belabour the point. I find those act...
Group rationality diary, 6/25/12
by cata — 2012-06-26T08:31:53.427Z

This is the public group instrumental rationality diary for the week of June 25th. (Based on the rate of participation in prior threads, I thought it might be a good idea to start posting every other week instead of every week. Only so much new stuff happens in a week.) It's a place to record and chat about it if you have done, or are actively doing, things like:

Established a useful new habit

Obtained new evidence that made you change your mind about some belief

Decided to behave in a different way in some set of situations

Optimized some part of a common routine or cached behavior

Consciously changed your emotions or affect with respect to something

Consciously pursued new valuable information about something that could make a big difference in your life

Learned something new about your beliefs, behavior, or life that surprised you

Tried doing any of the above and failed

Or anything else interesting which you want to share, so that other people can think about it, and perhaps be inspired to take action themselves. Try to include enough details so that everyone can use each other's experiences to learn about what tends to work out, and what doesn't tend to work out.

Thanks to everyone who contributes!

(Previously: 5/14/12, 5/21/12, 5/28/12, 6/4/12, 6/11/12)
[SEQ RERUN] Where Recursive Justification Hits Bottom
by MinibearRex — 2012-06-26T05:37:30.404Z

Today's post, Where Recursive Justification Hits Bottom was originally published on 08 July 2008. A summary (taken from the LW wiki):

Ultimately, when you reflect on how your mind operates, and consider questions like "why does occam's razor work?" and "why do I expect the future to be like the past?", you have no other option but to use your own mind. There is no way to jump to an ideal state of pure emptiness and evaluate these claims without using your existing mind.

Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Is Morality Given?, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.
Some simple existential risk math
by John_Maxwell — 2012-06-26T04:23:28.016Z

What's the best way to allocate resources towards decreasing existential risk?

Let's say we have n different risks. Define the functions r1(s1), r2(s2), ... , rn(sn), one for each risk. Each takes USD spent mitigating that particular risk as its input and outputs the probability that particular catastrophic scenario occurs. Probability of survival ("win probability") as a function of spending levels is given by

w(s1, s2, ... , sn) = (1 - r1(s1)) * (1 - r2(s2)) * ... * (1 - rn(sn))

In other words, we win if none of the catastrophic scenarios occur.

What are the characteristics of r1(s1), r2(s2), ... , rn(sn)?

Well obviously their output has to be between 0 and 1, since they are returning probabilities. And, assuming that spending money on this risk actually helps, their output values will go down as their input values go up.

Furthermore: For any given existential risk, we could imagine a number of different interventions. Each intervention will decrease the risk by a certain amount, and each has an associated price tag. Those interventions that are "efficient" have an especially high risk reduction to cost ratio. Assuming the people doing the existential risk reduction spending are good at picking efficient interventions, we should expect them to encounter diminishing returns as they spend more.

And: No risk's probability can go below zero, so if we assume the value of a risk function decreases monotonically, then the risk function must approach zero asymptotically, suggesting that heavily diminishing returns will be reached at some point.

What are the characteristics of w(s1, s2, ... , sn)?

It's pretty easy to prove that if you can decrease any risk by a constant amount, you are best off applying the decrease to the catastrophe that has the highest probability of occurring.

A quick example calculation: Let's say you have three risks which you are 80%, 90%, and 90% likely to avert. Decreasing the last risk by 10% yields a win probability of 72%. Decreasing the first risk by 10% yields a win probability of 72.9%, almost a 1% increase.

Of course, cutting the probability of a risk that's 20% likely to occur in half is more realistic than completely eliminating a risk that's 10% likely to occur. So this favors working to reduce the risk that's 20% likely to occur even more.

Diagram: This is a two-risk model. The graph is z=(1-x)(1...
[META] [POLL] Comment author/Post author?
by Dorikka — 2012-06-26T03:41:43.743Z

I'm noticing that comments are now shown with 'Comment author:' besides the commenter's name while posts appear to be shown with 'Post author:' beside the author's name (on the actual page of the post, not the 'New' page). This is mildly aesthetically displeasing to me. I'm curious whether other people share my opinion and, if so, whether there was another motivation for the change.

I've posted a poll below. I'd appreciate if everyone who views this post votes on something, even if it's the 'No preference.' option, so that the information is more accurate.
"Extortionate" strategy beats tit-for-tat in iterated Prisoner's Dilemma
by teageegeepea — 2012-06-26T01:19:59.083Z

Less Wrong had a Prisoner's Dilemma contest some time back, whose results I've forgotten. Perhaps it should be rerun with William H. Press & Freeman Dyson's proposed extortionate strategies.

I hope Pinker gives a response at Edge.org, since P.D played a significant role his book "The Better Angels of Our Nature" as a source of morality embedded in the nature of logic/reality.

Hat-tip to Marginal Revolution.
Framing a problem in a foreign language seems to reduce decision biases
by MBlume — 2012-06-25T17:25:55.048Z

The researchers aren't entirely sure why speaking in a less familiar tongue makes people more "rational", in the sense of not being affected by framing effects or loss aversion. But they think it may have to do with creating psychological distance, encouraging systematic rather than automatic thinking, and with reducing the emotional impact of decisions. This would certainly fit with past research that's shown the emotional impact of swear words, expressions of love and adverts is diminished when they're presented in a less familiar language.

Paywalled article (can someone with access throw a PDF up on dropbox or something?): http://pss.sagepub.com/content/early/2012/04/18/0956797611432178

Blog summary: http://bps-research-digest.blogspot.co.uk/2012/06/we-think-more-rationally-in-foreign.html
Seeking a "Seeking Whence 'Seek Whence'" Sequence
by Will_Newsome — 2012-06-25T11:10:22.098Z

One of the sharpest and most important tools in the LessWrong cognitive toolkit is the idea of going meta, also called seeking whence or jumping out of the system, all terms crafted by Douglas Hofstadter. Though popularized by Hofstadter and repeatedly emphasized by Eliezer in posts like "Lost Purposes" and "Taboo Your Words", Wikipedia indicates that similar ideas have been around in philosophy since at least Anaximander in the form of the Principle of Sufficient Reason (PSR). I think it'd be only appropriate to seek whence this idea of seeking whence, taking a history of ideas perspective. I'd also like analyses of where the theme shows up and why it's appealing and so on, since again it seems pretty important to LessWrong epistemology. Topics that I'd like to see discussed are:

How conservation of probability in Bayesian probability theory and conservation of phase space volume in statistical mechanics are related—a summary of Eliezer's posts on the topic would be great.

How conservation of probability &c. are related to other physical/mathematical laws, e.g. Noether's theorem and quantum mechanics' continuity equation.

The history of the idea of conservation laws; whether the discovery of conservation laws was fueled by PSR-like philosophical-like concerns (e.g. Leibniz?), by lower level intuitive concerns, or other means.

How conservation of probability &c. are related to the idea of seeking whence [pdf] (e.g., "follow the improbability").

How the PSR relates to conservation of probability &c. and to seeking whence.

How going meta and seeking whence are related/equivalent.

Which philosophers have used something like the PSR (e.g. Spinoza, Leibniz) and which haven't; those who haven't, what their reasons were for not using it.

What kinds of conclusions are typically reached via the PSR or have historically been justified by the PSR, and whether those conclusions fit with LW's standard conclusions. If it disagrees with LW's standard conclusions, where does the PSR not apply or not apply as strongly; alternatively, why standard LW conclusions might be mistaken.

Whether Schopenhauer's four-fold division of the PSR makes sense. (Schopenhauer's a relatively LW-friendly continentalesque philosopher.) A summary of any criticisms of his four-fold division.

What makes the PSR, going meta, "JOOTS"-ing and seeking w

...
Four Short Stories on Error Checking
by brilee — 2012-06-25T04:58:47.681Z

(Cross-posted from my blag)

1. My microwave clock has been broken since a power outage. It now reads something like 7 hours behind the real time. I've been too lazy to fix it, but the bright side is that it's 7 hours behind, and not 15 minutes behind. If it were 15 minutes behind, then who knows - I might mistake it to be the correct time, and end up fifteen minutes late to an appointment.

2. During the early years of computing, scientists and engineers were responsible for running numerical simulations of various sorts. To do this, they needed randomized starting conditions. Von Neumann favored the "middle square" method. While this method was not a very good pseudo-random number generator, its speed made up for its shortcomings in those early days. Additionally, a useful property of the middle-square method was that when it fell into a short cycle, it was immediately obvious. While other methods may have had undetectable cycles of intermediate length, the middle-square method would invariably output legitimate pseudorandom numbers for some time, then fall into a cycle of length 1, 2 or 4. (1)

3. One day, I was playing with some traffic models. My goal was to be able to correctly model the behavior of a line of cars as they accelerated from a standstill when the light turned from red to green. (2) I had collected some actual data at an intersection, and was planning to test my model against the data, as well as to fit some parameters. I ran a short program to fit these parameters and plot the actual times vs. my program's predicted times. To my astonishment, I had almost a perfect fit! Upon deeper inspection, it turned out that my program had merely gotten the times right by coincidence - while the cars behaved nicely long enough to get to the intersection, afterwards, their velocities oscillated with exponentially growing amplitude. I would have missed this if I had not insisted on checking the raw numbers from the simulation. I recoded my simulation and got a worse fit, but at least it didn't blow up as it had before.

(This last story is fiction. Or so, I hope)

4. The US News and World Report was doing its annual ranking of universities. They had recently changed the weightings on some of the subscores. Upon running their algorithm, an unexpected candidate rose to the top - Caltech! (Zing.) They concluded that there must have been a mis...