Economists in hell.
November 3, 2003 10:05 AM   Subscribe

Problems in infinite decision theory [pdf]. You are in hell and facing an eternity of torment, but the devil offers you a way out, which you can take once and only once at any time from now on. Today, if you ask him to, the devil will toss a fair coin once and if it comes up heads you are free (but if tails then you face eternal torment with no possibility of reprieve). You don’t have to play today, though, because tomorrow the devil will make the deal slightly more favourable to you (and you know this): he’ll toss the coin twice but just one head will free you. The day after, the offer will improve further: 3 tosses with just one head needed. And so on (4 tosses, 5 tosses, ….1000 tosses …) for the rest of time if needed. So, given that the devil will give you better odds on every day after this one, but that you want to escape from hell some time, when should accept his offer? More discussion here.
posted by monju_bosatsu (36 comments total) 1 user marked this as a favorite
The thing is, the devil cheats every time, so it doesn't matter.
posted by mecran01 at 10:14 AM on November 3, 2003

Don't you think that the offer of hope makes any torture more bearable? Would you spend eternity wondering whether you should have taken the offer, and it might have been genuine? Would you be in a fit state to contemplate anything? Does anyone care anymore? Should I shut up?

The problem would certainly give entertaining food for thought whilst your bowels were boiling.
posted by Saddo at 10:23 AM on November 3, 2003

It seems to me that just one day of the torture described would be enough to drive you permanently insane. So the offer should be taken immediately, being the only hope of a happy existence.
posted by Pretty_Generic at 10:52 AM on November 3, 2003

Five days. My own experience in tossing coins show that they end up tails four times out of five. And there's no hope in just hoping without doing.
posted by linux at 10:53 AM on November 3, 2003

I always suspected tossing would send me to hell.
posted by Pretty_Generic at 11:06 AM on November 3, 2003

On a Thursday?
posted by cryosis at 11:16 AM on November 3, 2003

This is really a fun paper. The math is a little funky in places (he briefly confuses convergence of an infinite sum with continuity, and I don't think any actual mathematicians use the word "superdenumerable"), but mostly pretty good. And interesting. And hilarious. Go, Roy!
posted by gleuschk at 11:17 AM on November 3, 2003

just accept the offer immediately. then if you lose, just kick the devil in the bollocks and run past him and out of the exit while he is incapacitated. that's what i would do. oh yeah then i would come back the next day with some mates with baseball bats and murder him.
posted by mokey at 11:21 AM on November 3, 2003

My own experience in tossing coins show that they end up tails four times out of five.

You need a new coin.
posted by Ynoxas at 11:23 AM on November 3, 2003

I imagine a Shawshank Redemption type of experience...

You are offered The Deal. "Yeah, right." you tell yourself after a few minutes of contemplation. Obviously, Satan is out to short change you somehow, so the deal is clearly flawed/faked/buggered in some way you simply can't see at the moment. So, you keep it in the back of your mind, but resolve to not give Satan the satisfaction of actually acting on it.

Then, years later, you are hanging out with another of the Damned. Over drinks (of burning fire?) you relate the story of the day the Evil One made you "The Deal", which you have ignored because it's only intent is to give Satan a few giggles. Your Damned friend says you should do it for laughs and when the head fails to come up, you should do something inexplicable, like dance for joy, just to confuse/annoy Lucifer.

"Ha ha, good one.", you think. You ring up old Pointy Ears and take him up on your now 600-some odd flips. He pulls out the coin, and starts flipping. Heads comes up on flip three. You are free to go, but wasted years in unimaginable torture (fire water? brr) in Hell for nothing. Oh, the humanity!!
posted by timbley at 11:30 AM on November 3, 2003

it's just a sort of joke, isn't it? unlike pascal's wager etc.

it's the nature of our world that "infinitistics" do not come into play except on paper.

that said, they play a big part in science fiction / speculation. how long will the human race last - a short time [few hundred years], a long time or an infinite time? if the human race has the option of infinite life [cheating the big crunch or heat death - or other currently unforseen universe-time limits - through superior intelligence & technology], this suggests rather strongly that we should devote as much effort as we can to making that a possibility... after all, that's what an individual would do if he had a slight chance to live forever.

another common problem involves the growing likelihood of unforseen events. the longer the human race sits around on earth scratching its ass, the more likely it is that something strange will happen: attack by a vastly superior alien force or comet or some weird multidimensional disaster or something.

and then there's the much discussed topic "an infinite universe implies alien life". the statistics issues here are profound. e.g. if the universe has infnite time, it is natural that gods could simply evolve from very ancient and technologically advanced aliens. if it has infinite space, and galactic dispersion outpaces spontaneous life formation, most likely any given newborn race will be effectively alone in the universe which nevertheless teems with life. etc.

at least these are a bit closer to reality than some stupid religious joke. what if, instead of starting you out at 50%, the devil starts the wager at 1%, and each year gives you another chance if you wish to wait, at which point he multiplies your chances by 101% [again, you would never reach perfect certainty of success], and not only that, each year you wait, he briefly takes on the form of a giant half-rat half-crayfish and rapes and kills a bunny or squirrel each day, and you must eat their remains over and over because your intestines loop on your nasal passages? bear in mind, you are in intense pain the whole time, and st. peter pities you and good christians mock you and you must respond to occasional ouija board house calls to answer questions like "is this house haunted", "what is your name, spirit", and the spca is on your ass about the bunnies, and the devil may change the rules at any time, so you shouldn't wait too long.
posted by mitchel at 11:44 AM on November 3, 2003

the devil will toss a fair coin

As fair as you can expect in a realm where a three-headed dog is a mascot.
posted by Smart Dalek at 12:13 PM on November 3, 2003

I took him up on the bet. Turned out to be a fair coin with tails on both sides.

Never bet with the devil. Especially if he's the same one that Maxwell wrote about, the tricky little bugger capable of keeping gases from mixing.
posted by kaibutsu at 12:31 PM on November 3, 2003

Okay, here is my new take on it:

This premise is like a Kafka story, and I tend to enjoy that mans writing, and think hes onto something there. All of his stories contain an element of this infinite regression business, and are loaded with anguish for the indecisive nature of a strict dialectician. So, Im thinking, maybe this little thought experiment is illustrative of the internal debate between that part of us that wants to pursue our dream lifestyle(potentially noble and fulfilling, though risky) , and that part of us that doubts that life will be better than,say, the current life on night shift in Kwik-e-mart (Hell). The people who are pedantic about the intricacies and exact nature of hell in this hypothetical situation are probably the very people who would not want to confront this kind of question, and keep their head in the sand.

C'mon people! Work with me here!

(I apologise for this post in advance)
posted by Saddo at 12:42 PM on November 3, 2003

Heads, this thread is good. Tails, it's great...

posted by moonbird at 1:37 PM on November 3, 2003

It does beg the issue of a Faustian deal, no? Assuming he is the prince of darkness as celebrated in song and prose (dude...I've seen you on my album covers...), then I'm not sure there is such a thing as a fair deal.

Then again, my concept of hell is infinitely closer to a rampant bureaucracy run amok than the Inferno version...must be all that time I've spent working on government contracts...
posted by dejah420 at 1:42 PM on November 3, 2003

... and run past him and out of the exit ...

Of course, in Hell, those exits would be well-marked in accordance with the latest building and fire (heh) code..
posted by ZenMasterThis at 1:51 PM on November 3, 2003

Do you care?
Whats the sense
Of such a trivial question
From such a famous scholar,
Who's always either up in the air
With thoughts of the sublime,
Or in the depths of despair,
Looking for essence
In the primeval slime?
posted by Saddo at 1:55 PM on November 3, 2003

When people are free.
Look what they want to be.
posted by Saddo at 1:57 PM on November 3, 2003

Why does everyone think Lucifer runs hell? Hell was created to punish him and his crew. Clearly he is running some con game. Not that you could consider any questions while burning.

An easy test: stick a lit cigarette in your left eye, while continuing to read with the right eye. Can you read like that, and think about the content? I thought not.
posted by Goofyy at 2:01 PM on November 3, 2003

Not at all. For me it's pure bliss
To have a subtly-reasoned discourse such as this.

A crazy gambler monkey? He'd really go
If a monkey could buy a ticket for the lottery.

(Thaks dejah)
posted by Saddo at 2:01 PM on November 3, 2003

I've wondered that myself, Goofyy. If Lucifer was cast from heaven into hell, where he resides over his own kingdom, why on earth--or, in this case why not on earth--would he spend eternity torturing people who would agree with him. Instead, they'd probably have wicked-cool parties and download illegal music.
posted by The God Complex at 5:54 PM on November 3, 2003

Isnt this just isomorphic to the St. Petersburg Paradox?
posted by vacapinta at 6:16 PM on November 3, 2003

The odds of the coin coming up heads are 50/50. It does not matter how many times you toss the coin, because the odds never change. Even if you toss the coin an infinite number of times, the odds are still 50/50 at each toss. You may as well take the offer on the first day and get it over with.

I think.
posted by dg at 6:25 PM on November 3, 2003


The probability for heads coming up once is actually:

1 - (probability for heads never coming up)
= 1 - (0.5^n)

where n is the number of trials.
posted by VeGiTo at 7:20 PM on November 3, 2003

Your best odds are to make reservations somewhere elsewhere for your afterlife.

Where is up to you. Some say there's only one alternative, but others claim there are several. Sheol. Valhalla. Shangrila. Purgatory. New Orleans. There appear to be as many afterlives as there are beliefs to describe them. Your Afterlife is a privilege, not a right: No harrassment. Curse only in the curse channel. No cheating. No idiocy. Do not intentionally linkdie.

Well I sympathise completely but there's nothing I can do. I am just a humble servant with a message here for you. Well I know you have good reasons and there's things you've got to do, but the boatman won't be waiting and he's leaving here with you, and you can't take it with you no matter what you do. No, you can't take it with you. Not the place you're going to.
posted by ZachsMind at 8:55 PM on November 3, 2003

Does it matter? I mean, you ended up in hell. You must have been naughty. So why in hell (agh) would the devil offer you a reprieve?

I always hated crap like this that doesn't make sense from the start. Like, "You're in a Yugo traveling 40 mph. If you jump out now, you'll probably get hurt, but if you wait and prepare yourself for the fall, you might not get as hurt. Except! the car keeps accelerating" -- like I would ever even get into a Yugo in the first place.

I don't understand why people find these kinds of win-win questions so interesting.
posted by Civil_Disobedient at 9:35 PM on November 3, 2003

Thanks CrayDrygu and VeGiTo (I think).
posted by dg at 9:40 PM on November 3, 2003

Does it matter? I mean, you ended up in hell. You must have been naughty. So why in hell (agh) would the devil offer you a reprieve?

Because it's not the devil's job to enforce God's ideals of right and wrong. Maybe he's sending the people back up to recruit more hell denziens. Don't you know anything about evil?
posted by The God Complex at 9:42 PM on November 3, 2003

I'm amazed at how people have got caught up in the philospophy of the dilemma. It's just a peg on which to hang the problem, people.

Imagine a different but similar situation with you trapped in a witches' spell which due to your schooling in wizadry, you know will leave you in essentially eternal torment until the spell is broken, unless you have a magic coin. By chance you have one on you, and you remember the Grand Wizard telling you that you have to flip it and if it comes down red crystal side up, and this will break the spell. The magic coin's power increases so that the more days you have it, after an initialising chant, the more coin tosses you get to use it before it uses up it's power and dissolves completely. How many days after the initialising chant do you hold on for before the first flip?
posted by Blue Stone at 10:37 PM on November 3, 2003

Due to your schooling in wizardry, wouldn't you know how long to hold on for?
posted by dg at 10:39 PM on November 3, 2003

Rational expectations/rational choice is the scourge of modern economics and perhaps the sole reason, when you get down to it, I never completed my PhD.

Economists should go back to actually trying to understand consumer/producer behavior and the underlying thought processes and psychology instead of trying to make everything a math problem. Economics is, first and foremost, a social science. It is not a natural science, no matter how many of the greatest minds on earth try to make it one.

A dollar is less than 100 dollars. If 100 dollars is all you have, it is not 100x more valuable than 1 dollar, it is INFINITELY more valuable than 1 dollar.

For some reason positioning things this way confounds even the greatest Chicago-trained economists and makes me sick of the entire thing. They will tumble around in their head in an endless cycle how then 1 dollar must be infinitely valuable to you because it is 1/100 of infinity.


The St. Petersburg paradox is no paradox at all, because risk aversion scales depending on the value of what is being risked.

It is so simple a child could answer it, yet it is tortured and twisted and molested because it doesn't fit their fancy mathematical models WHICH DON'T WORK ANYWAY.

You cannot measure utility. It is impossible.

Therefore anything predicated upon measuring utility (i.e. rational expectations/rational choice) is a foolhardy pursuit.

Of course, this is just my opinion and probably 95% or more of current economists would disagree with me, including multitudes of Nobel prize winners.

Consider beanie babies. $2 toys bought for $2000 by otherwise frugal, financially responsible, coupon clipping mothers. Beanie babies will destroy virtually any mathematical model you throw at it. It cannot be explained through mathematical gymnastics. But beanie baby fever most assuredly did happen, on an international scale, in probably 100's of millions of transactions.

Modern economics is more a religion than a science. If you happen to see behind the curtain, and your god isn't there, you loose all faith.
posted by Ynoxas at 6:37 AM on November 4, 2003

actually bluestone, the problem is by its nature quasi-mystical: it asks you how you would deal with a bunch of non-reality based concepts [infinite time and infinite choice, and pretend-infinite pain]. so you can frame it in wizard garb and it's still reeks of the unreal.
posted by mitchel at 7:12 AM on November 4, 2003

oh yeah then i would come back the next day with some mates with baseball bats and murder him.

I <3 mokey.
posted by moonbiter at 5:59 PM on November 4, 2003

Ynoxas: Very, very nicely put.
posted by Civil_Disobedient at 1:51 PM on November 5, 2003

Civil: if you happen to know of any graduate schools that teach heresy like what I mention, please let me know.

I didn't exactly fit in my last one.
posted by Ynoxas at 9:03 AM on November 6, 2003

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