Bayesian Nights (Rationalist Story Time)

Tell us a story. A tall tale for King Solamona, a yarn for the folk of Bensalem, a little nugget of wisdom, finely folded into a parable for the pages.

 

The game is simple:

  1. Choose a bias, a fallacy, some common error of thought.
  2. Write a short, hopefully entertaining narrative. Use the narrative to strengthen the reader against the errors you chose.
  3. Post your story in reply to this post.
  4. Give the authors positive and constructive feedback. Use rot13 if it seems appropriate.
  5. Post all discussion about this post in the designated post discussion thread, not under this top-level post.

 

This isn't a thread for developing new ideas. If you have a novel concept to explore, you should consider making a top-level post on LessWrong instead. This is for sharpening our wits against the mental perils we probably already agree exist. For practicing good thinking, for recognizing bad thinking, for fun! For sanity's sake, tell us a story.

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This one comes from the "Dungeons and Discourse" system I'm gradually building and figures heavily as a location for one of the major campaigns

At the northern edge of the world, far and far from the comfortable lights of human habitation, beyond the Gulf of Inferential Distances and upon the shores of the steel-grey Frequen Sea, perched on a pillar of weathered stone there stands the Rational Bayesian Priory. There the Bayesian monks toil in their arcane researches, guided by the absolute leader of their sect, the Rational Bayesian Prior.

Few travelers ever come to the Priory, and this bothers the monks not at all, for they have a strange custom. When the guards spot a trader or missionary taking the long and tortuous road up the cliffs of Frequen Sea to the Priory, the monks speculate endlessly on what news he might bear of the outer world. When he arrives, they wine and dine him, getting as complete a report on the happenings in the far-off southern countries as possible.

And then, to the shock of the new arrival, as often as not their leader the Prior throws himself off the cliffs into the ocean. For it is longstanding tradition that if any mere monk should guess the traveler's news when the Prior can not, that monk becomes Prior, and the old Prior must take his own life in shame. Thus the inscription scrawled in an ancient tongue over the gates to the Priory: Priorem Mutamus Ex Novis Testimonium - "We Change Our Priors In Response To New Evidence".

But in these latter days, fewer and fewer the travelers who brave the cliffs, and fewer and fewer the southern folk who dare to approach the Priory at all. For a legend has arisen - whence no one knows - that the apocalypse is at hand, and that it is the Bayesians who will bring it. A legend that their arcane researches, delving too deep into forbidden mysteries, have awoken the Chaos God from his otherworldly slumber, and that he has possessed the Prior of the Rational Bayesian Priory.

And the legends say that no traveler shall catch the Prior possessed by the Chaos God unaware, and that he shall rule the Priory for a span of many years, consolidating his power and his hidden knowledge until he is without fear. And then he shall rain death and dark fire upon the world, burning its cities to rubble and its dreams to ashes, until all returns to the primaeval chaos from which it came.

And they will know him as the Prior of Maximum Entropy.

I want more output from the algorithm that generated this.

The Prior replacement doesn't make too much sense, insofar as a moderately large number of monks will have one correct guess by pure chance. The Prior gets to make one guess; the other monks get to make other-monk-quantity of guesses. It doesn't seem terribly rational to replace the Prior due to such random chance.

The monks making bad guesses for self-preservation is also a good point.

It sounds like solomonoff induction. The idea isn't that the one that got the right answer was obviously the best prior. It's that they're the one that matches the new evidence. It's just like how in solomonoff induction, you eliminate all the hypotheses that have been falsified, and leave the ones that just happen to match reality.

The wise monks would avoid correctly guessing the traveler's news (at least out loud), lest their lives depend upon repeating the performance.

Unless they expect that all other monks would think similarly, in which case they can take Priority without risk.

[Edit for my own memory: In game theoretic terms, they expect a large amount of utility if they decide to take Priority but others don't, while they expect a rather larger amount of disutility if they decide to take Priority and others also do. In other words, they experience a utility gain only if they decide to take Priority using an algorithm different from the one used by the other monks. That seems to imply a "contrarian" decision theory, which decides based on the decision theory held by the other monks... but the existence of more than one contrarian would negate the benefit of being a contrarian at all... Needs more thought.]

Currently, the Rational Bayesians are led by Prior Distribution III, who is becoming ever more frail and will surely end up on the rocks soon - when a traveler brought news of the Copenhagen army's victory at Heisen Mountain, he collapsed on the spot!

So, are you a contributor to http://dndis.wikidot.com/ , which google finds for Dungeons and Discourse?

This is awesome!

However, you might want to change the idea that the monks guess the traveler's news (i.e. a true/false judgment) to something about probabilities.

I would expect the monks to use some kind of log scoring, and the Prior kills himself if his total score is less than that of any other monk.

As already pointed out, that doesn't mend the perverse incentive that no one wants to be Prior and risk his life constantly. It would make more sense if the worst monk has to kill himself, and the best monk becomes Prior. This is an incentive to be the best and not be the worst.

(And of course, newbies are just 'novices', who aren't subject to the penalties or rewards. They practice until they feel confident they are good enough to compete - and if they aren't, the problem solves itself.)

That is assuming monks value a long life as a simple monk more than a short life as a Prior.

There was a certain invisible university with this problem.

But priors never change, only posteriors. But you're quite right not to base a story on that. Ew.

I liked the story.

Priorem Mutamus Ex Novis Testimonium

Would this sentence be improved by having the last word in plural ablative?

I don't know whether this really counts as a 'rationalist' story but I hope it will be interesting if it isn't educational. The following is "The Ones Who Walk Towards Acre" (Le Guin ref), a short story embedded in my perpetually incomplete novel Cloud Nine:


In the dusk, a tradesman dressed entirely in fuligin walked slowly through the lanes of that bright city. The many citizens gave him a berth, but not a wide one: death was a necessary craft too.

He entered the great hall in the center of the Mortaestrum, itself the center of the city. It was a cavernous hall, filled with art gifted by citizens, and consummate skill in stonework and all the arts of adornment were not least lavished on it than the objects within; in a city of beautiful buildings, the Mortaestrum was unique.

To one side of him were suspended cylinders. And each hung at a different height, held by oiled cords leading away into the depths. And upon each cylinder was inscribed a name. The merchant looked at one marked 'Sammael'. A man he had never met, and never would.

Into one of the holes by that particular cylinder, he dropped several heavy gold coins. Some time after their clinkings ceased to echo, the cylinder hoisted ever so slightly. Into the other hole he dropped a pouch containing: a parchment note listing a particular date, a fat coin in fee, and a stout lock.

He noted that the cylinder was noble silver where others were base bronze. To those knowledgeable in his profession, this spoke silently of days past; of old words being written on old papers, of old men conferring in even older buildings, and blind numbers senselessly increasing - the reward for the assassination would be redoubled by the Council.

Nothing would happen now. All that had happened was that some pieces of metal had innocently lifted other metal; nothing more. And that pouch would lie there in the dark for an unknowable span of days, and nothing would happen then, either. It is a mysterious trait of this world that the slightest cipher or symbol of which one is utterly ignorant can determine the days of one's life.

But the tradesman knew that this is how it would work, when that span of emptiness should come to an end: he knew that one day a messenger would come galloping up to the crowded gates of the city. The courier would be dusty all over from the stone roads, and weary from the haste of his travel, and he would beg to speak with the Council on a matter of some urgency, and to them deliver his message: that the one known as Sammael of Viron had died, had been cut down by the blade of a rogue on such and such a day.

And the Council and Magistrates would listen, and would go down into the depths to one door (locked doubly) and another (yet to be triply). Simultaneously they would take the keys entrusted them on their oath of office, and they would unlock the locks of the first door and open the contents whereof. The one correct 'prediction' of the date would be selected and the enclosed lock would seal the vault containing the reward. The magistrates and councilors would remove their own locks from that vault, allowing only the happy predictor the blood money. Through judicious use of an intermediary (the merchant of death), the predictor could make his prediction, pay the fee, and collect the reward while remaining unknown to all save one.

This custom had evolved over the ages and was their one great trick, whereby like a porcupine, they could remain prosperous and secure through the long years. They could not but be: the drifting scum of the world were at need their invisible army, for such rabble knew they had but to predict the day of death of the opposing general - or sovereign or miscreant official - and they would surely receive their reward. In a thousand years, not once had a predictor gone unpaid; Acre's reputation for honesty was without peer.

The wise men of that city had devised the practice when it became apparent to them that the endless clashes of armies on battlefields led to no lasting conclusion, nor did they extirpate the roots of the conflicts. Rather, they merely wasted the blood and treasure of the people. It was clear to them that those rulers led their people into death and iniquity, while remaining untouched themselves, lounging in comfort and luxury amidst the most crushing defeat.

It was better that a few die before their time than the many. It was better that a little wealth go to the evil than much; better that conflicts be ended dishonorably once and for all, than fought honorably time and again; and better that peace be ill-bought than bought honestly at too high a price to be borne. So they thought.

And the unfortunate tradesman - for such as he was: by lot, he and his were chosen for life - concluded his business and turned his slow steps homeward. Perchance there he would dream of a man he had never met, and never would. Or perhaps he would dream of the many lives ended. It is certain he would not dream of those spared.

OK! Now that a fair number have read & upvoted, quiz time!

How many realized that this story advocates assassination markets? How many read it, thought it was a good system, but react with horror to the bald idea of assassination markets?

Yes, I recognized this as a fantasy application of Jim Bell's "Assassination Politics." I think AP would work better in an Iron Age/fantasy setting than in a modern context where anyone with a computer and a 'net connection could donate anonymously to assassination jackpots. In an Iron Age setting, pretty much the only people famous and hated enough to garner significant jackpots would be despotic kings and priests, and their generals. Assassination itself would be as dangerous as the rulers could make it, so it probably would only happen when a king was genuinely tyrannical, or as a substitute for war. In other words, it would take a lot to provide incentive an assassin under those conditions. So, it would probably reduce the number of unjust or trivial assassinations, like a baker "betting" on the death of a rival baker.

In a modern situation where millions of people could easily and anonymously contribute small amounts to an assassination jackpot, it would (in my opinion) be too easy for a million people to, say, contribute a dollar each to a jackpot for some love-to-hate celebrity like Paris Hilton, Bill Gates, or the quarterback of an NFL team that's rival to theirs in the playoffs.

Also, an AP system could just as easily be used by the wealthy and privileged to fund the deaths of any upstart reformers as by any reform movements to target the powerful.

Not Always to the Swift

Captain Danae Andreadis glanced idly at the image of the Venture Free on one of the screens at her desk. Had she been looking out a window, it would have been a point of light not much brighter than the untwinkling stars. The Argos did not have any windows, since they would represent an unnecessary structural weakness and a breach in the ship's radiation shielding.

Venture Free was exactly like her own ship, the Argos, except for the company logo it bore. Manufactured by the same company according to the same plans. Three habitation rings two hundred meters in diameter rotating around a spindly-looking truss that mounted tanks of reaction mass, the ship's reactor, large heat radiators reminiscent of the giant fins on spaceships from the rocketpunk era of science fiction, and a VASIMR drive. A crew compliment of three thousand people plus equipment.

A chime sounded. "Acknowledge," Danae said. The image of the rival vessel was replaced by the face of Dr. Chandragupta, the biologist who headed the ship's life support team. He looked worried. Danae immediately gave him her full attention.

"Is there a problem, Doctor?"

"I'm afraid so, Captain. It's our soil nematodes. They're dying. If they die out, our life support ecosystem will collapse. We'll be out of oxygen before we reach Helium Diamond."

"Do you have any ideas on what's causing it?"

"I've chemically and genetically analyzed dead nematodes. The problem is an artificial polymer that's toxic to them. I've traced it to outgassing from the ecosystem's air cycling hoses."

"Why hasn't this happened before on any of the Mars missions or on Armstrong or Olympus Base?"

"The hose material is unique to the Deepspace Class ships. We and the Venture Free are the first of the class to go on long-term missions. It's a subtle problem, and it took longer than the Earth-to-Luna shakedown cruise to manifest."

"Is there something we can do about it?"

"I don't know yet, Captain. I have all my people working on it, and I suggest we contact the Venture and get their people working on it too. I'm close to certain they'll have the problem too."

"Is this a direct threat to the crew?"

"I have Medical checking, but the hoses in question are only in the greenhouses, and the polymer's lethality comes from the way it reacts to nematode biochemistry specifically. Can we still divert to Mars if necessary?"

Danae entered the parameters into the ship's navicomp. "Yes, but we'll have to make the go/no-go decision in five days. After that we won't have enough remass for orbital insertion. Do everything you can to find us a solution in that time. You have priority for supercomputer and comms time. If they have to divert too, we can still beat them to Helium Diamond if we get in line first at Phobos Station and get those hoses, and the nematodes replaced."

...

"I'm very sorry to hear that, Captain," Ray "Buck" Williams said. The hint of a sardonic smile and the way he casually leaned back into his command chair said otherwise. "Our little worms are doing just fine. You can still divert to Mars, can't you?"

"Yes," Danae said stiffly. "If your nematodes are immune, perhaps we could arrange to purchase a population of them?"

"I'm afraid not, Captain. It simply isn't in our interest. However much you might offer, it could hardly compensate us if you were to reach Helium Diamond ahead of us. And if you were to offer to split the claim with us, why should we accept, when we have a hundred percent chance of reaching it first after you divert to Mars?"
...

"I hate to break it to you Cap'n, but we've got it here too."

"I wouldn't worry too much," Captain Williams said. "Argos is going to have all the best minds on Earth trying to help them figure out how to save their worms. We can pick up all the transmissions coming back from Earth, so if Andreadis gets a solution, so do we. If she doesn't, we wait 'till she commits to Mars, then we raise Earth and keep 'em working on it.

"Helium Diamond is the richest, most concentrated source of He3 in the Solar System as far as anyone knows. It'll be worth trillions once we get it back to cislunar space. Every man jack on this ship will be a billionaire after we get our commission. Who wants to let a few dead microscopic worms get in the way of that? Not me, and not HQ. Sometimes you gotta go with your gut, and mine says we're all gonna live like kings."

...

"I've read the reports, Captain, and as far as I, or any of our science people can tell, the problem is intractable. But you and your crew are the ones on the scene, and we're not going to armchair-quarterback from Earth," the CEO of Argos Explorations said. "It's your call."

"Thank you, sir." Danae said. "Argos out." She looked to the grim faces of her officers, and sought their council one by one. Their prognoses were as grim as their expressions. Danae sighed. "What's true is already so. Owning up to it doesn't make it worse. Make ready to de-spin the ship for maneuvers. We're going to Mars."

...

Captain Danae Andreadis glanced idly at the image of the slowly tumbling icy comet nucleus on one of the screens at her desk. Had she been looking out a window, it would have been a point of light not much brighter than the untwinkling stars. As happy as she was for herself and her crew to be the first to reach Helium Diamond, she couldn't help but think of the comms that had come from the Venture Free as Captain Williams and his crew slowly suffocated. No human being would ever forget the mounting horror and pathos of those transmissions.

"Andreadis to Helm. Make ready to de-spin the ship for insertion maneuvers."

It's a well written story, but I don't think the error is a good one. What is the lesson? Don't be casual about your life? I don't think many people have that bias in situations roughly analogous to the one in your story.

I was trying to convey the Litany of Gendlin as the principle the story was based on. The lesson would be "Don't deny or ignore facts, even if there's lots of money in it for you, because the facts are still facts whether you like it or not." I think situations like climate change, peak oil, over-exploitation of aquifers and letting the FIRE sector run rampant over the real economy count as real-world examples.

I wrote this about a month ago for a game I help run. It is not specifically a rationalist story, but its moral is about as rationalist as it gets. Hopefully it'll stay reasonably accessible out of context.

The Fable of the Two Swords

Long ago, a band of the People grazed their herds on cursed and blighted land. With each season the plains withered, the blades of grass growing thin and crumpled like parchment cast into flames; and the band's cattle ate the grass, and starved, and bore no calves. At last the elders of the band called together its greatest hunters and sent forth them in all directions, each seeking new lands as yet unfounded.

The youngest among them was Sarai, and she rode to the east, taking with her the herdswoman Tamar, her friend since childhood; and her sword and her bow; and two good horses. They crossed many miles of wasted land, and many more of good land grazed by other bands with whom they were at peace. They rode beside pillars of stone, and over cracked expanses of unsown earth, and through copses of green trees. Yet for many days they found nothing.

A score of nights and a night they traveled, and at last they came to the fires of another band of the People. As they broke bread with the newcomers, Sarai asked its Wayfinder if there was land to be settled: a question already growing weary to the travelers, for they had asked the same of the last band and the one before. The old man shook his quilled and silvered braids, a gesture well-worn to Sarai; yet the guise of sorrow and fear came over his face as he said:

"Not far to the east there is a low place in the plains, girdled round with hills and dotted with mounds of hollow earth. And from ridge to ridge there are no campfires of the People, and neither are the stars obscured by the smoke of burning dung; yet do not rejoice, little sisters, for it is a cursed place.

"A tribe of demons dwells in the hollow mounds, children of the world's end of which our parents all have told, and they are without thought or mercy. Fire smolders in their hair and the manes of their horses; and hard and bony are their fanged faces; and fiery lashes they snap as they come ravening. Their chief carries a sword no man could wield, blazing with flames, and none dare stand against him.

"Ride no further, little ones. Even as close as we camp now, we are in danger; we dare not stray any closer, lest they rob us of our cattle and our children. So I have declared, for the safety of my band, and so do the elders agree."

Sarai fell silent at this, and thanked the Wayfinder for his counsel, and chose a place near the fire to sleep. Yet she remained awake, and as the moon rose she crept to the edges of the camp to gather her thoughts.

There, as she gazed into the tall grass beyond, she for a moment glimpsed a face like a horse's skull, limned in ruddy flame. Startled, she cried out, and a sentry hurried at her cry. But the specter was gone in the space of a breath, and when the man arrived nothing remained but bent grass and the smell of smoke.

She could not sleep for her fears, tossing and turning throughout the night. Yet the next morning, as the band gathered for the morning meal, she stood by the fire, and drew her sword, and spoke:

"Look at my sword.

"You do not see a warrior's birthright, nor a blacksmith's pride, nor a chieftain's comfort. You see an edge, a tool made only for cutting. I could perhaps use a longer sword, or a thicker, or a finer, but it makes no difference; whatever the blade, I must think only of cutting my enemy, or I will surely die at her hands.

"Wield your mind as you would a sword. Do not think of fears or hopes, of what has been or what may be; think only of cutting to the heart of what lies before you.

"Come with me to the east, and we will drive out these demons. Any man or woman of you who stands with me stands to gain an honored place in my Thousand Cranes Band, and the first choice of spoils in the hunts to come."

The Wayfinder turned away, making a sign against evil as he did so, and most of the band turned with him. But a scarce handful of hunters, the young or the foolish or the quick-thinking, raised their weapons and met Sarai's gaze.

And when the sun set, the small band rode for the hollow mounds.

They did not have far to ride. Soon they crested the first of the hills of which the Wayfinder had spoken; and soon after they were among the hollow mounds, buzzing in the twilight with web-winged insects. The band slowed there, and closed tightly about each other, and the demons at once were upon them.

The spirits were as the Wayfinder had said. Their horses were black and gaunt, and their tattered manes flickered with fire. Their faces were the skulls of cattle, and horses, and buffalo, and fire glittered in their long, loose hair. They were robed in black, and raised lashes of fire as they closed with a shrill, warbling cry.

Their leader was more terrible still: tall as a horseman’s spear, swathed in darkness, his head was the pale skull of a crocodile. Flames blazed from his sword, long and heavy as a barge’s oar, as he held it aloft and howled.

Sarai's band trembled, teetering for a moment on the verge of flight. Yet Sarai steeled herself and urged her horse forward, charging headlong at the fanged monstrosity.

Flames snapped at her from the demons' lashes, but she was not daunted. Soon she had broken through the ring of evil spirits; and soon after she had met their chief, who raised his flaming sword like a lance to meet her.

Steel clashed, scattering motes of fire. Sarai's coat charred, and her horse spooked and reared; yet she held firm, bringing her blade back to meet the cumbersome arc of the demon's sword a second and a third time.

On the fourth, the demon blade shattered.

The demon recoiled. Dropping the broken hilt, he drew a long dagger; but Sarai pressed her attack, striking two blows for each of the spirit's. At once the dagger spun to the ground with the demon's fingers, and Sarai drove the point of her sword with all her strength through the bony mask and into the eye beyond.

For a mask it was, shaped to accommodate the human face beneath and trailing strips of thin-beaten copper, which glinted in the flames of the pitch-coated blade. The man's height was true, yet his limbs were twisted and overgrown, and his baleful robe was but tattered cloth. And the sound he made as he died was not a demon’s ululation but a man’s mortal scream.

The false demons broke then, dropping their trickster's masks and charlatan’s chains as they fled. And in the shadow of the hollow mounds the new hunters of Thousand Cranes Band slept for the first time; and that night each man and woman of them resolved forever to reason as with a blade.

The story doesn't work terribly well for me because the "demons" turn out to be humans with a fairly clever means of holding their land who haven't done anything wrong except scare people.

It also isn't clear why they're using that method when people generally seem to be living very peacefully with each other.

"Scooby-Doo Rationality" may form a subset of rationality stories, aimed primarily at young children.

Sarai, and she rode to the east, taking with her the herdswoman Tamar

Your campaign uses biblical Hebrew names? Neat!

I've found that theft, when it comes to worldbuilding, is cheaper and more effective than making things up wholesale. Or at least less prone to producing apostrophe stew.

And you had the good taste to steal something that doesn't get stolen all that often.

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