[LINK] 23andme is 99$ now

5 Jabberslythe 12 December 2012 02:31AM

It's been reduced to 99$ and it seems like it is a permanent reduction. I was thinking of buying it at 299$ because it had not been on sale for a while, so I'm very pleased this happened.

Their press release on it:

http://blog.23andme.com/news/one-million-strong-a-note-from-23andmes-anne-wojcicki/

 

Lifeism in the midst of death

59 TobyBartels 09 December 2012 01:28PM

tl;dr:  My grandpa died, and I gave a eulogy with a mildly anti-deathist message, in a Catholic funeral service that was mostly pretty disagreeable.

I'm a little uncomfortable writing this post, because it's very personal, and I'm not exactly a regular with friends here.  But I need to get it out, and I don't know any other place to put it.

My grandfather (one of two) died last week, and there was a funeral mass (Catholic) today.  Although a ‘pro-life’ organisation, the Roman Catholic Church has a very deathist funeral liturgy.  It wasn't just ‘Stanley has gone on to a better place’, and all that; the priest had the gall to say that Grandpa had probably done everything that he wanted to do in life, so it was OK for him to die now.  I know from discussions with my mother and my aunt that Grandpa did not want to die now; although his life and health were not what they used to be, he was happy to live.  Yes, he had gone to his great-granddaughter's second birthday party, but he wanted to go to her third, and that will never happen.

There are four of us grandchildren, two (not including me) with spouses.  At first, it was suggested that each of us six say one of the Prayers of the Faithful (which are flexible).  Mom thought that I might find one that I was willing to recite, so I looked them up online.  It wasn't so bad that they end with ‘We pray to the Lord.’ recited by the congregation; I would normally remain silent during that, but I decided that I could say it, and even lead others in saying it, pro forma.  And I could endorse the content of some (at least #6 from that list) with some moderate edits.  But overall, the whole thing was very disturbing to me.  (I had to read HPMoR 45 afterwards to get rid of the bad taste.)  I told Mom ‘This is a part of the Mass where I would normally remain in respectful silence.’, and she apologised for ‘put[ting] [me] in an uncomfortable position’ (to quote from our text messages).  In the end, the two grandchildren-in-law were assigned to say these prayers.

But we grandchildren still had a place in the programme; we would give eulogies.  So I had to think about what to say.  I was never close to Grandpa; I loved him well enough, but we didn't have much in common.  I tried to think about what I remembered about him and what I would want to tell people about him.  It was a little overwhelming; in the end, I read my sibling's notes and decided to discuss only what she did not plan to discuss, and that narrowed it down enough.  So then I knew what I wanted to say about Grandpa.

But I wanted to say something more.  I wanted to say something to counter the idea that Grandpa's death was OK.  I didn't yet know how appalling the priest's sermon would be, but I knew that there would be a lot of excuses made for death.  I wanted to preach ‘Grandpa should not have died.’ and go on from there, but I knew that this would be disturbing to people who wanted comfort from their grief, and a lecture on death would not really be a eulogy.  Still, I wanted to say something.

(I also didn't want to say anything that could be interpreted as critical of the decision to remove life support.  I wasn't consulted on that decision, but under the circumstances, I agree with it.  As far as I'm concerned, he was killed on Monday, even though he didn't finally die until Wednesday.  In the same conversation in which Mom and I talked about how Grandpa wanted to live, we talked about how he didn't want to live under the circumstances under which he was living on Tuesday, conditions which his doctors expected would never improve.  Pulling the plug was the best option available in a bad situation.)

Enough background; here is my eulogy.  Some of this is paraphrase, since my written notes were only an outline.

When I was young, we would visit my grandparents every year, for Thanksgiving or Christmas.  Grandma and Grandpa would greet us at the door with hugs and kisses.  The first thing that I remember about their place was the candy.  Although I didn't realise it at the time, they didn't eat it; it was there as a gift for us kids.

Later I noticed the books that they had, on all topics: religion, history, humour, science fiction, technical material.  Most of it was older than I was used to reading, and I found it fascinating.  All of this was open to me, and sometimes I would ask Grandpa about some of it; but mostly I just read his books, and to a large extent, this was his influence on me.

Grandpa was a chemical engineer, although he was retired by the time I was able to appreciate that, and this explains the technical material, and to some extent the science fiction.  Even that science fiction mostly took death for granted; but Grandpa was with us as long as he was because of the chemists and other people who studied medicine and the arts of healing.  They helped him to stay healthy and happy until the heart attack that ended his life.

So, I thank them for what they did for Grandpa, and I wish them success in their future work, to help other people live longer and better, until we never have to go through this again.

I was working on this until the ceremony began, and I even edited it a little in the pew.  I wasn't sure until I got up to the podium how strong to make the ending.  Ultimately, I said something that could be interpreted as a reference to the Second Coming, but Catholics are not big on that, and my family knows that I don't believe in it.  So I don't know how the church officials and Grandpa's personal friends interpreted it, but it could only mean transhumanism to my family.

Nobody said anything, positive or negative, afterwards.  Well, a couple of people said that my eulogy was well done; but without specifics, it sounded like they were just trying to make me feel good, to comfort my grief.  After my speech, the other three grandchildren went, and then the priest said more pleasant falsehoods, and then it was over.

Goodbye, Grandpa.  I wish that you were alive and happy in Heaven, but at least you were alive and happy here on Earth for a while.  I'll miss you.

[Edit:  Fix my cousin's age.]

Firewalling the Optimal from the Rational

86 Eliezer_Yudkowsky 08 October 2012 08:01AM

Followup to: Rationality: Appreciating Cognitive Algorithms  (minor post)

There's an old anecdote about Ayn Rand, which Michael Shermer recounts in his "The Unlikeliest Cult in History" (note: calling a fact unlikely is an insult to your prior model, not the fact itself), which went as follows:

Branden recalled an evening when a friend of Rand's remarked that he enjoyed the music of Richard Strauss. "When he left at the end of the evening, Ayn said, in a reaction becoming increasingly typical, 'Now I understand why he and I can never be real soulmates. The distance in our sense of life is too great.' Often she did not wait until a friend had left to make such remarks."

Many readers may already have appreciated this point, but one of the Go stones placed to block that failure mode is being careful what we bless with the great community-normative-keyword 'rational'. And one of the ways we do that is by trying to deflate the word 'rational' out of sentences, especially in post titles or critical comments, which can live without the word.  As you hopefully recall from the previous post, we're only forced to use the word 'rational' when we talk about the cognitive algorithms which systematically promote goal achievement or map-territory correspondences.  Otherwise the word can be deflated out of the sentence; e.g. "It's rational to believe in anthropogenic global warming" goes to "Human activities are causing global temperatures to rise"; or "It's rational to vote for Party X" deflates to "It's optimal to vote for Party X" or just "I think you should vote for Party X".

If you're writing a post comparing the experimental evidence for four different diets, that's not "Rational Dieting", that's "Optimal Dieting". A post about rational dieting is if you're writing about how the sunk cost fallacy causes people to eat food they've already purchased even if they're not hungry, or if you're writing about how the typical mind fallacy or law of small numbers leads people to overestimate how likely it is that a diet which worked for them will work for a friend. And even then, your title is 'Dieting and the Sunk Cost Fallacy', unless it's an overview of four different cognitive biases affecting dieting. In which case a better title would be 'Four Biases Screwing Up Your Diet', since 'Rational Dieting' carries an implication that your post discusses the cognitive algorithm for dieting, as opposed to four contributing things to keep in mind.

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When (Not) To Use Probabilities

28 Eliezer_Yudkowsky 23 July 2008 10:58AM

Followup toShould We Ban Physics?

It may come as a surprise to some readers of this blog, that I do not always advocate using probabilities.

Or rather, I don't always advocate that human beings, trying to solve their problems, should try to make up verbal probabilities, and then apply the laws of probability theory or decision theory to whatever number they just made up, and then use the result as their final belief or decision.

The laws of probability are laws, not suggestions, but often the true Law is too difficult for us humans to compute.  If P != NP and the universe has no source of exponential computing power, then there are evidential updates too difficult for even a superintelligence to compute - even though the probabilities would be quite well-defined, if we could afford to calculate them.

So sometimes you don't apply probability theory.  Especially if you're human, and your brain has evolved with all sorts of useful algorithms for uncertain reasoning, that don't involve verbal probability assignments.

Not sure where a flying ball will land?  I don't advise trying to formulate a probability distribution over its landing spots, performing deliberate Bayesian updates on your glances at the ball, and calculating the expected utility of all possible strings of motor instructions to your muscles.

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Real World Solutions to Prisoners' Dilemmas

31 Yvain 03 July 2012 03:25AM

Why should there be real world solutions to Prisoners' Dilemmas? Because such dilemmas are a real-world problem.

If I am assigned to work on a school project with a group, I can either cooperate (work hard on the project) or defect (slack off while reaping the rewards of everyone else's hard work). If everyone defects, the project doesn't get done and we all fail - a bad outcome for everyone. If I defect but you cooperate, then I get to spend all day on the beach and still get a good grade - the best outcome for me, the worst for you. And if we all cooperate, then it's long hours in the library but at least we pass the class - a “good enough” outcome, though not quite as good as me defecting against everyone else's cooperation. This exactly mirrors the Prisoner's Dilemma.

Diplomacy - both the concept and the board game - involves Prisoners' Dilemmas. Suppose Ribbentrop of Germany and Molotov of Russia agree to a peace treaty that demilitarizes their mutual border. If both cooperate, they can move their forces to other theaters, and have moderate success there - a good enough outcome. If Russia cooperates but Germany defects, it can launch a surprise attack on an undefended Russian border and enjoy spectacular success there (for a while, at least!) - the best outcome for Germany and the worst for Russia. But if both defect, then neither has any advantage at the German-Russian border, and they lose the use of those troops in other theaters as well - a bad outcome for both. Again, the Prisoner's Dilemma.

Civilization - again, both the concept and the game - involves Prisoners' Dilemmas. If everyone follows the rules and creates a stable society (cooperates), we all do pretty well. If everyone else works hard and I turn barbarian and pillage you (defect), then I get all of your stuff without having to work for it and you get nothing - the best solution for me, the worst for you. If everyone becomes a barbarian, there's nothing to steal and we all lose out. Prisoner's Dilemma.

If everyone who worries about global warming cooperates in cutting emissions, climate change is averted and everyone is moderately happy. If everyone else cooperates in cutting emissions, but one country defects, climate change is still mostly averted, and the defector is at a significant economic advantage. If everyone defects and keeps polluting, the climate changes and everyone loses out. Again a Prisoner's Dilemma,

Prisoners' Dilemmas even come up in nature. In baboon tribes, when a female is in “heat”, males often compete for the chance to woo her. The most successful males are those who can get a friend to help fight off the other monkeys, and who then helps that friend find his own monkey loving. But these monkeys are tempted to take their friend's female as well. Two males who cooperate each seduce one female. If one cooperates and the other defects, he has a good chance at both females. But if the two can't cooperate at all, then they will be beaten off by other monkey alliances and won't get to have sex with anyone. Still a Prisoner's Dilemma!

So one might expect the real world to have produced some practical solutions to Prisoners' Dilemmas.

One of the best known such systems is called “society”. You may have heard of it. It boasts a series of norms, laws, and authority figures who will punish you when those norms and laws are broken.

Imagine that the two criminals in the original example were part of a criminal society - let's say the Mafia. The Godfather makes Alice and Bob an offer they can't refuse: turn against one another, and they will end up “sleeping with the fishes” (this concludes my knowledge of the Mafia). Now the incentives are changed: defecting against a cooperator doesn't mean walking free, it means getting murdered.





Both prisoners cooperate, and amazingly the threat of murder ends up making them both better off (this is also the gist of some of the strongest arguments against libertarianism: in Prisoner's Dilemmas, threatening force against rational agents can increase the utility of all of them!)

Even when there is no godfather, society binds people by concern about their “reputation”. If Bob got a reputation as a snitch, he might never be able to work as a criminal again. If a student gets a reputation for slacking off on projects, she might get ostracized on the playground. If a country gets a reputation for backstabbing, others might refuse to make treaties with them. If a person gets a reputation as a bandit, she might incur the hostility of those around her. If a country gets a reputation for not doing enough to fight global warming, it might...well, no one ever said it was a perfect system.

Aside from humans in society, evolution is also strongly motivated to develop a solution to the Prisoner's Dilemma. The Dilemma troubles not only lovestruck baboons, but ants, minnows, bats, and even viruses. Here the payoff is denominated not in years of jail time, nor in dollars, but in reproductive fitness and number of potential offspring - so evolution will certainly take note.

Most people, when they hear the rational arguments in favor of defecting every single time on the iterated 100-crime Prisoner's Dilemma, will feel some kind of emotional resistance. Thoughts like “Well, maybe I'll try cooperating anyway a few times, see if it works”, or “If I promised to cooperate with my opponent, then it would be dishonorable for me to defect on the last turn, even if it helps me out., or even “Bob is my friend! Think of all the good times we've had together, robbing banks and running straight into waiting police cordons. I could never betray him!”

And if two people with these sorts of emotional hangups play the Prisoner's Dilemma together, they'll end up cooperating on all hundred crimes, getting out of jail in a mere century and leaving rational utility maximizers to sit back and wonder how they did it.

Here's how: imagine you are a supervillain designing a robotic criminal (who's that go-to supervillain Kaj always uses for situations like this? Dr. Zany? Okay, let's say you're him). You expect to build several copies of this robot to work as a team, and expect they might end up playing the Prisoner's Dilemma against each other. You want them out of jail as fast as possible so they can get back to furthering your nefarious plots. So rather than have them bumble through the whole rational utility maximizing thing, you just insert an extra line of code: “in a Prisoner's Dilemma, always cooperate with other robots”. Problem solved.

Evolution followed the same strategy (no it didn't; this is a massive oversimplification). The emotions we feel around friendship, trust, altruism, and betrayal are partly a built-in hack to succeed in cooperating on Prisoner's Dilemmas where a rational utility-maximizer would defect a hundred times and fail miserably. The evolutionarily dominant strategy is commonly called “Tit-for-tat” - basically, cooperate if and only if your opponent did so last time.

This so-called "superrationality” appears even more clearly in the Ultimatum Game. Two players are given $100 to distribute among themselves in the following way: the first player proposes a distribution (for example, “Fifty for me, fifty for you”) and then the second player either accepts or rejects the distribution. If the second player accepts, the players get the money in that particular ratio. If the second player refuses, no one gets any money at all.

The first player's reasoning goes like this: “If I propose $99 for myself and $1 for my opponent, that means I get a lot of money and my opponent still has to accept. After all, she prefers $1 to $0, which is what she'll get if she refuses.

In the Prisoner's Dilemma, when players were able to communicate beforehand they could settle upon a winning strategy of precommiting to reciprocate: to take an action beneficial to their opponent if and only if their opponent took an action beneficial to them. Here, the second player should consider the same strategy: precommit to an ultimatum (hence the name) that unless Player 1 distributes the money 50-50, she will reject the offer.

But as in the Prisoner's Dilemma, this fails when you have no reason to expect your opponent to follow through on her precommitment. Imagine you're Player 2, playing a single Ultimatum Game against an opponent you never expect to meet again. You dutifully promise Player 1 that you will reject any offer less than 50-50. Player 1 offers 80-20 anyway. You reason “Well, my ultimatum failed. If I stick to it anyway, I walk away with nothing. I might as well admit it was a good try, give in, and take the $20. After all, rejecting the offer won't magically bring my chance at $50 back, and there aren't any other dealings with this Player 1 guy for it to influence.”

This is seemingly a rational way to think, but if Player 1 knows you're going to think that way, she offers 99-1, same as before, no matter how sincere your ultimatum sounds.

Notice all the similarities to the Prisoner's Dilemma: playing as a "rational economic agent" gets you a bad result, it looks like you can escape that bad result by making precommitments, but since the other player can't trust your precommitments, you're right back where you started

If evolutionary solutions to the Prisoners' Dilemma look like trust or friendship or altruism, solutions to the Ultimatum Game involve different emotions entirely. The Sultan presumably does not want you to elope with his daughter. He makes an ultimatum: “Touch my daughter, and I will kill you.” You elope with her anyway, and when his guards drag you back to his palace, you argue: “Killing me isn't going to reverse what happened. Your ultimatum has failed. All you can do now by beheading me is get blood all over your beautiful palace carpet, which hurts you as well as me - the equivalent of pointlessly passing up the last dollar in an Ultimatum Game where you've just been offered a 99-1 split.”

The Sultan might counter with an argument from social institutions: “If I let you go, I will look dishonorable. I will gain a reputation as someone people can mess with without any consequences. My choice isn't between bloody carpet and clean carpet, it's between bloody carpet and people respecting my orders, or clean carpet and people continuing to defy me.”

But he's much more likely to just shout an incoherent stream of dreadful Arabic curse words. Because just as friendship is the evolutionary solution to a Prisoner's Dilemma, so anger is the evolutionary solution to an Ultimatum Game. As various gurus and psychologists have observed, anger makes us irrational. But this is the good kind of irrationality; it's the kind of irrationality that makes us pass up a 99-1 split even though the decision costs us a dollar.

And if we know that humans are the kind of life-form that tends to experience anger, then if we're playing an Ultimatum Game against a human, and that human precommits to rejecting any offer less than 50-50, we're much more likely to believe her than if we were playing against a rational utility-maximizing agent - and so much more likely to give the human a fair offer.

It is distasteful and a little bit contradictory to the spirit of rationality to believe it should lose out so badly to simple emotion, and the problem might be correctable. Here we risk crossing the poorly charted border between game theory and decision theory and reaching ideas like timeless decision theory: that one should act as if one's choices determined the output of the algorithm one instantiates (or more simply, you should assume everyone like you will make the same choice you do, and take that into account when choosing.)

More practically, however, most real-world solutions to Prisoner's Dilemmas and Ultimatum Games still hinge on one of three things: threats of reciprocation when the length of the game is unknown, social institutions and reputation systems that make defection less attractive, and emotions ranging from cooperation to anger that are hard-wired into us by evolution. In the next post, we'll look at how these play out in practice.

New "Best" comment sorting system

25 matt 02 July 2012 11:08AM

Way back in October 2009 Reddit introduced their "Best" comment sorting system. We've just pulled those changes into Less Wrong. The changes affect only comments, not stories.

It's good. It should significantly improve the visibility of good comments posted later in the life of an article. You (yes you) should adopt it. It's the default for new users.

See http://blog.reddit.com/2009/10/reddits-new-comment-sorting-system.html for the details.

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Nash Equilibria and Schelling Points

41 Yvain 29 June 2012 02:06AM

A Nash equilibrium is an outcome in which neither player is willing to unilaterally change her strategy, and they are often applied to games in which both players move simultaneously and where decision trees are less useful.

Suppose my girlfriend and I have both lost our cell phones and cannot contact each other. Both of us would really like to spend more time at home with each other (utility 3). But both of us also have a slight preference in favor of working late and earning some overtime (utility 2). If I go home and my girlfriend's there and I can spend time with her, great. If I stay at work and make some money, that would be pretty okay too. But if I go home and my girlfriend's not there and I have to sit around alone all night, that would be the worst possible outcome (utility 1). Meanwhile, my girlfriend has the same set of preferences: she wants to spend time with me, she'd be okay with working late, but she doesn't want to sit at home alone.



This “game” has two Nash equilibria. If we both go home, neither of us regrets it: we can spend time with each other and we've both got our highest utility. If we both stay at work, again, neither of us regrets it: since my girlfriend is at work, I am glad I stayed at work instead of going home, and since I am at work, my girlfriend is glad she stayed at work instead of going home. Although we both may wish that we had both gone home, neither of us specifically regrets our own choice, given our knowledge of how the other acted.

When all players in a game are reasonable, the (apparently) rational choice will be to go for a Nash equilibrium (why would you want to make a choice you'll regret when you know what the other player chose?) And since John Nash (remember that movie A Beautiful Mind?) proved that every game has at least one, all games between well-informed rationalists (who are not also being superrational in a sense to be discussed later) should end in one of these.

What if the game seems specifically designed to thwart Nash equilibria? Suppose you are a general invading an enemy country's heartland. You can attack one of two targets, East City or West City (you declared war on them because you were offended by their uncreative toponyms). The enemy general only has enough troops to defend one of the two cities. If you attack an undefended city, you can capture it easily, but if you attack the city with the enemy army, they will successfully fight you off.



Here there is no Nash equilibrium without introducing randomness. If both you and your enemy choose to go to East City, you will regret your choice - you should have gone to West and taken it undefended. If you go to East and he goes to West, he will regret his choice - he should have gone East and stopped you in your tracks. Reverse the names, and the same is true of the branches where you go to West City. So every option has someone regretting their choice, and there is no simple Nash equilibrium. What do you do?

Here the answer should be obvious: it doesn't matter. Flip a coin. If you flip a coin, and your opponent flips a coin, neither of you will regret your choice. Here we see a "mixed Nash equilibrium", an equilibrium reached with the help of randomness.

We can formalize this further. Suppose you are attacking a different country with two new potential targets: Metropolis and Podunk. Metropolis is a rich and strategically important city (utility: 10); Podunk is an out of the way hamlet barely worth the trouble of capturing it (utility: 1).



A so-called first-level player thinks: “Well, Metropolis is a better prize, so I might as well attack that one. That way, if I win I get 10 utility instead of 1”

A second-level player thinks: “Obviously Metropolis is a better prize, so my enemy expects me to attack that one. So if I attack Podunk, he'll never see it coming and I can take the city undefended.”

A third-level player thinks: “Obviously Metropolis is a better prize, so anyone clever would never do something as obvious as attack there. They'd attack Podunk instead. But my opponent knows that, so, seeking to stay one step ahead of me, he has defended Podunk. He will never expect me to attack Metropolis, because that would be too obvious. Therefore, the city will actually be undefended, so I should take Metropolis.”

And so on ad infinitum, until you become hopelessly confused and have no choice but to spend years developing a resistance to iocane powder.

But surprisingly, there is a single best solution to this problem, even if you are playing against an opponent who, like Professor Quirrell, plays “one level higher than you.”

When the two cities were equally valuable, we solved our problem by flipping a coin. That won't be the best choice this time. Suppose we flipped a coin and attacked Metropolis when we got heads, and Podunk when we got tails. Since my opponent can predict my strategy, he would defend Metropolis every time; I am equally likely to attack Podunk and Metropolis, but taking Metropolis would cost them much more utility. My total expected utility from flipping the coin is 0.5: half the time I successfully take Podunk and gain 1 utility, and half the time I am defeated at Metropolis and gain 0.And this is not a Nash equilibrium: if I had known my opponent's strategy was to defend Metropolis every time, I would have skipped the coin flip and gone straight for Podunk.

So how can I find a Nash equilibrium? In a Nash equilibrium, I don't regret my strategy when I learn my opponent's action. If I can come up with a strategy that pays exactly the same utility whether my opponent defends Podunk or Metropolis, it will have this useful property. We'll start by supposing I am flipping a biased coin that lands on Metropolis x percent of the time, and therefore on Podunk (1-x) percent of the time. To be truly indifferent which city my opponent defends, 10x (the utility my strategy earns when my opponent leaves Metropolis undefended) should equal 1(1-x) (the utility my strategy earns when my opponent leaves Podunk undefended). Some quick algebra finds that 10x = 1(1-x) is satisfied by x = 1/11. So I should attack Metropolis 1/11 of the time and Podunk 10/11 of the time.

My opponent, going through a similar process, comes up with the suspiciously similar result that he should defend Metropolis 10/11 of the time, and Podunk 1/11 of the time.

If we both pursue our chosen strategies, I gain an average 0.9090... utility each round, soundly beating my previous record of 0.5, and my opponent suspiciously loses an average -.9090 utility. It turns out there is no other strategy I can use to consistently do better than this when my opponent is playing optimally, and that even if I knew my opponent's strategy I would not be able to come up with a better strategy to beat it. It also turns out that there is no other strategy my opponent can use to consistently do better than this if I am playing optimally, and that my opponent, upon learning my strategy, doesn't regret his strategy either.

In The Art of Strategy, Dixit and Nalebuff cite a real-life application of the same principle in, of all things, penalty kicks in soccer. A right-footed kicker has a better chance of success if he kicks to the right, but a smart goalie can predict that and will defend to the right; a player expecting this can accept a less spectacular kick to the left if he thinks the left will be undefended, but a very smart goalie can predict this too, and so on. Economist Ignacio Palacios-Huerta laboriously analyzed the success rates of various kickers and goalies on the field, and found that they actually pursued a mixed strategy generally within 2% of the game theoretic ideal, proving that people are pretty good at doing these kinds of calculations unconsciously.

So every game really does have at least one Nash equilibrium, even if it's only a mixed strategy. But some games can have many, many more. Recall the situation between me and my girlfriend:



There are two Nash equilibria: both of us working late, and both of us going home. If there were only one equilibrium, and we were both confident in each other's rationality, we could choose that one and there would be no further problem. But in fact this game does present a problem: intuitively it seems like we might still make a mistake and end up in different places.

Here we might be tempted to just leave it to chance; after all, there's a 50% probability we'll both end up choosing the same activity. But other games might have thousands or millions of possible equilibria and so will require a more refined approach.

Art of Strategy describes a game show in which two strangers were separately taken to random places in New York and promised a prize if they could successfully meet up; they had no communication with one another and no clues about how such a meeting was to take place. Here there are a nearly infinite number of possible choices: they could both meet at the corner of First Street and First Avenue at 1 PM, they could both meet at First Street and Second Avenue at 1:05 PM, etc. Since neither party would regret their actions (if I went to First and First at 1 and found you there, I would be thrilled) these are all Nash equilibria.

Despite this mind-boggling array of possibilities, in fact all six episodes of this particular game ended with the two contestants meeting successfully after only a few days. The most popular meeting site was the Empire State Building at noon.

How did they do it? The world-famous Empire State Building is what game theorists call focal: it stands out as a natural and obvious target for coordination. Likewise noon, classically considered the very middle of the day, is a focal point in time. These focal points, also called Schelling points after theorist Thomas Schelling who discovered them, provide an obvious target for coordination attempts.

What makes a Schelling point? The most important factor is that it be special. The Empire State Building, depending on when the show took place, may have been the tallest building in New York; noon is the only time that fits the criteria of “exactly in the middle of the day”, except maybe midnight when people would be expected to be too sleepy to meet up properly.

Of course, specialness, like beauty, is in the eye of the beholder. David Friedman writes:

Two people are separately confronted with the list of numbers [2, 5, 9, 25, 69, 73, 82, 96, 100, 126, 150 ] and offered a reward if they independently choose the same number. If the two are mathematicians, it is likely that they will both choose 2—the only even prime. Non-mathematicians are likely to choose 100—a number which seems, to the mathematicians, no more unique than the other two exact squares. Illiterates might agree on 69, because of its peculiar symmetry—as would, for a different reason, those whose interest in numbers is more prurient than mathematical.

A recent open thread comment pointed out that you can justify anything with “for decision-theoretic reasons” or “due to meta-level concerns”. I humbly propose adding “as a Schelling point” to this list, except that the list is tongue-in-cheek and Schelling points really do explain almost everything - stock markets, national borders, marriagesprivate property, religions, fashion, political parties, peace treaties, social networks, software platforms and languages all involve or are based upon Schelling points. In fact, whenever something has “symbolic value” a Schelling point is likely to be involved in some way. I hope to expand on this point a bit more later.

Sequential games can include one more method of choosing between Nash equilibria: the idea of a subgame-perfect equilibrium, a special kind of Nash equlibrium that remains a Nash equilibrium for every subgame of the original game. In more intuitive terms, this equilibrium means that even in a long multiple-move game no one at any point makes a decision that goes against their best interests (remember the example from the last post, where we crossed out the branches in which Clinton made implausible choices that failed to maximize his utility?) Some games have multiple Nash equilibria but only one subgame-perfect one; we'll examine this idea further when we get to the iterated prisoners' dilemma and ultimatum game.

In conclusion, every game has at least one Nash equilibrium, a point at which neither player regrets her strategy even when she knows the other player's strategy. Some equilibria are simple choices, others involve plans to make choices randomly according to certain criteria. Purely rational players will always end up at a Nash equilibrium, but many games will have multiple possible equilibria. If players are trying to coordinate, they may land at a Schelling point, an equilibria which stands out as special in some way.

Can the Chain Still Hold You?

108 lukeprog 13 January 2012 01:28AM

Robert Sapolsky:

Baboons... literally have been the textbook example of a highly aggressive, male-dominated, hierarchical society. Because these animals hunt, because they live in these aggressive troupes on the Savannah... they have a constant baseline level of aggression which inevitably spills over into their social lives.

Scientists have never observed a baboon troupe that wasn't highly aggressive, and they have compelling reasons to think this is simply baboon nature, written into their genes. Inescapable.

Or at least, that was true until the 1980s, when Kenya experienced a tourism boom.

Sapolsky was a grad student, studying his first baboon troupe. A new tourist lodge was built at the edge of the forest where his baboons lived. The owners of the lodge dug a hole behind the lodge and dumped their trash there every morning, after which the males of several baboon troupes — including Sapolsky's — would fight over this pungent bounty.

Before too long, someone noticed the baboons didn't look too good. It turned out they had eaten some infected meat and developed tuberculosis, which kills baboons in weeks. Their hands rotted away, so they hobbled around on their elbows. Half the males in Sapolsky's troupe died.

This had a surprising effect. There was now almost no violence in the troupe. Males often reciprocated when females groomed them, and males even groomed other males. To a baboonologist, this was like watching Mike Tyson suddenly stop swinging in a heavyweight fight to start nuzzling Evander Holyfield. It never happened.

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The Gift I Give Tomorrow

28 Raemon 11 January 2012 04:02AM

 

This is the final post in my Ritual Mini-Sequence. Previous posts include the Introduction, a discussion on the Value (and Danger) of Ritual, and How to Design Ritual Ceremonies that reflect your values.

 

I wrote this as a concluding essay in the Solstice ritual book. It was intended to be at least comprehensible to people who weren’t already familiar with our memes, and to communicate why I thought this was important. It builds upon themes from the ritual book, and in particular, the readings of Beyond the Reach of God and The Gift We Give to Tomorrow. Working on this essay was transformative to me - it allowed me to finally bypass my scope insensitivity and other biases, so that I could evaluate organizations like the Singularity Institute with fairness. I haven’t yet decided what to do with my charitable dollars - it’s a complex problem. But I’ve overcome my emotional restistance to the idea of fighting X-Risk.

 

I don’t know if that was due to the words themselves, or to the process I had to go through to write them, but I hope others may benefit from this.

 


 

I thought ‘The Gift We Give to Tomorrow’ was incredibly beautiful when I first read it. I actually cried. I wanted to share it with friends and family, except that work ONLY has meaning in the context of the Sequences. Practically every line is a hyperlink to an important, earlier point, and without many hours of previous reading, it just won’t have the impact. But to me, it felt like the perfect endcap to everything the Sequences covered, taking all of the facts and ideas and weaving them into a coherent, poetic narrative that left me feeling satisfied with my place in the world.


Except that... I wasn’t sure that it actually said anything.

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Expecting Short Inferential Distances

107 Eliezer_Yudkowsky 22 October 2007 11:42PM

Homo sapiens' environment of evolutionary adaptedness (aka EEA or "ancestral environment") consisted of hunter-gatherer bands of at most 200 people, with no writing.  All inherited knowledge was passed down by speech and memory.

In a world like that, all background knowledge is universal knowledge.  All information not strictly private is public, period.

In the ancestral environment, you were unlikely to end up more than one inferential step away from anyone else.  When you discover a new oasis, you don't have to explain to your fellow tribe members what an oasis is, or why it's a good idea to drink water, or how to walk.  Only you know where the oasis lies; this is private knowledge.  But everyone has the background to understand your description of the oasis, the concepts needed to think about water; this is universal knowledge.  When you explain things in an ancestral environment, you almost never have to explain your concepts.  At most you have to explain one new concept, not two or more simultaneously.

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