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.
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.
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!
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.)
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?
Nah, mine is better.
Hah :D Fair enough.
It is, you know. You have only to read his guide or read the campaign or listen to the songs to know.
But priors never change, only posteriors. But you’re quite right not to base a story on that. Ew.
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.
I liked the story.
Would this sentence be improved by having the last word in plural ablative?