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# Rational choice theory

Helen Thomas
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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?

Helen Thomas
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You, a rational agent, are in Purgatory, for good it seems. Things could be worse - you�ve heard horror stories about hell, but they could be better - you hear great things about heaven. These two possibilities seem to be equally valuable, in opposite directions. You�d be indifferent between your current state of affairs and a gamble with a 50% chance of a day in heaven and a 50% chance of a day in hell. (Purgatory is a lot like earth, so this kind of gambling is highly encouraged.)

One day an angel appears with a nice offer. God will give you some time in heaven for good behaviour. But He decided to play a little game to figure out how much time you�ll get. He wrote down two numbers, x and 2x, on slips of paper, and dropped them into identical envelopes. You will get one of the envelopes, it�s your choice which, and the slip will be good for the number of days in heaven that is written on it. The angel doesn�t know which envelope is which, and he doesn�t know what x is, except that it�s over 10. (They don�t send angels down for smaller missions than that.)

So you pick an envelope, and are about to see how long you�ll get in heaven when�

The angel makes you an offer. If you�ll do a day in Hell to cover for a friend of his that got caught up in a little scandal, he�ll give you the other envelope. He argues that this must be a good deal, as follows. Let y be the number written on your slip. The other envelope has either 2y or y/2 written on it. Each is equally likely, so your expected number of days in heaven if you switch envelopes is 0.5 * 2y + 0.5 * y/2 = 1.25y. So the expected gain from swapping is 1.25y - y = y/4. Since we know y > 10, y/4 > 2.5, so this is more valuable to you than a day in Hell.

The reasoning starts to sound attractive, until you worry about what other offers the angel has in mind if you accept. So you ask for some time to think about it. �It�s purgatory,� says the angel, �take all the time you want.�
[ July 13, 2004: Message edited by: Helen Thomas ]

Thomas Paul
mister krabs
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As long as you can endure the suffering of hell?

Helen Thomas
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Posts: 1759
Originally posted by Thomas Paul:
As long as you can endure the suffering of hell?

You could accept that you deserve to be there and refuse to play the game.

The following may help or not. Just how long is eternity, again ?

Good intro

Or look for a more philosophical solution.
[ July 13, 2004: Message edited by: Helen Thomas ]

Warren Dew
blacksmith
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When do I take the Devil's deal? Depends on my discount rate ... and on whether I trust the Devil, which seems unlikely.

The Angel, however, gets reported to God (they have whistleblower rules in heaven, right?)

I've never found the St. Petersburg 'paradox' to be at all paradoxical. If you take the actual amount of money that the house has as a limit to what it can actually pay you, the value of the bet ends up being small.

And even if it weren't, using some form of arctan as one's utility function - or, indeed, any bounded utility function - fixes things.

John Smith
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Posts: 2937
HT: The angel makes you an offer. If you�ll do a day in Hell to cover for a friend of his that got caught up in a little scandal, he�ll give you the other envelope. He argues that this must be a good deal, as follows. Let y be the number written on your slip. The other envelope has either 2y or y/2 written on it. Each is equally likely, so your expected number of days in heaven if you switch envelopes is 0.5 * 2y + 0.5 * y/2 = 1.25y. So the expected gain from swapping is 1.25y - y = y/4. Since we know y > 10, y/4 > 2.5, so this is more valuable to you than a day in Hell.

This is an example where one has to start with the intuition first, followed by logic, to make the right decision. If you reverse the two appraches, you end up with a paradox. So, here is the decision process:

1. The angle is essentially asking you to pay one day in hell for the choice that you can make for free in the first place (choose any envelope). Something is rotten here!

2. Let's verify the intuitive thinking with an example. Suppose the two envelopes contain 20 days and 40 days, respectively. If you switch, you stand a 50% chance of gaining 20 days, and a 50% chance of losing 20 days. Thus, your expected gain is 0.5 * 20 + 0.5 * (-20) = 0. That is, you gain nothing by the switch.

3. Generalize. The two envelopes contain x and 2x days, repectively. If you switch, you stand a 50% chance of gaining x days, and a 50% chance of losing x days. Thus, your expected gain is 0.5 * x + 0.5 * (-x) = 0. That is, you gain nothing by the switch.

4. Verify by actually playing the game.

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.

This one is a little more difficult, and that's because any math fails miserably here, since no matter how small the probability of losing the game, and no matter how you play it, your expected result is always an eternity in hell (eternity * probablility of all tails = eternity). This seems a rather unfortunate shortcoming in math that leaves you unprepared to make an important decision. What you've got to do is to use the concept of eternity against itself: if you accept the devil's deal and wait for a year before the 365 coins are tossed, you end up in heaven. That's because the probability of 365 tails is so small that it will take the devil an eternity to come up with this series of tosses.

Helen Thomas
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You'd also have to make one hell of an assumption that the devil tosses a fair coin.

But that was very convincing analysis , John Smith.

Helen Thomas
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Posts: 1759
Gambling on God A paper that refers to the first problem.

Pascal's Wager is a prudential argument for cultivating a belief in
God's existence. An undogmatic atheist must admit that there is at least a
small chance that God exists. However, God assigns believers infinite bliss
and unbelievers infinite blitz. Thus the expected value of theism is
infinite. So however much finite good accrues from secular living, the
religious life is the best bet.

[ July 14, 2004: Message edited by: Helen Thomas ]

Jeroen Wenting
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Posts: 5093
1) the devil is the father of deceit and lies, why trust him to indeed toss a fair coin (or even if the coin is fair to not corrupt the result of the toss)?
Seeing that you have nothing to loose and should postpone taking him up on the offer until your suffering becomes unbearable. Even then, impartial arbitration might be called for if any impartial observers can be found willing and capable of entering hell.
2) gambling is itself immoral so the gamble the angel offers you may well add enough sin to your soul to condemn you to hell immediately while refusing the gamble could lift you to heaven.
Therefore refusing the bet at worst costs you nothing and at best gets you to heaven.

These things remind me of the Incarnations of Immortality series by Piers Anthony.

Jeroen Wenting
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Posts: 5093

Pascal's Wager is a prudential argument for cultivating a belief in
God's existence. An undogmatic atheist must admit that there is at least a
small chance that God exists. However, God assigns believers infinite bliss
and unbelievers infinite blitz. Thus the expected value of theism is
infinite. So however much finite good accrues from secular living, the
religious life is the best bet.

Interesting quote, but problematic in the existence of more than one religion.

Seeing as there are many mutually exclusive religions and the predicted penalty for not believing at all is for all or most of them less than that for believing in a false religion it becomes better to not believe in any of them.
If they're all incorrect and there are/is no god(s) you loose nothing, if there is a god you get a lesser punishment than all those who believed in another god.

Thus the expected result of theism in the actual scenario is a higher chance of eternal damnation than that of enlightened atheism (meaning the non-belief in any deity but not actually preaching their non-existence).

This gets even more pronounced as there are religions that don't predict punishment for those who don't believe in their gods UNLESS those unbelievers believe in false gods.

A good example of this is the Roman era where many religions lived peacefully side by side as long as all respected all others.
Christians (contrary to church teachings) were NOT persecuted for their belief in a different god (what's one more when you have a hundred) but for their denial that any other god could exist (which was sacrilege against the deitic entity of the emperor which of course amounted to high treason).
People who didn't actively revere the emperor as a god were not persecuted (though they might not be able to achieve high public office) as long as they didn't speak out agains the deitic nature of the emperor.

Thomas Paul
mister krabs
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If they're all incorrect and there are/is no god(s) you loose nothing, if there is a god you get a lesser punishment than all those who believed in another god.

Can you name a single religion that works this way?

Jeroen Wenting
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Christianity makes a clear distinction between heretics (those who believe in other gods) and unbelievers.
Unbelievers can be converted (in the case of Mormons even post-mortem), heretics can never be redeemed (which led in the past to them being burned at the stake to show one's own dedication to god).

The only religion that does the reverse is Islam and then only in the specific cases of Jews and Christians which it considers followers of their own god but in a misguided way.

Jeroen Wenting
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Posts: 5093
And even if not, if I as a nonbeliever are not elligible for either heaven or hell because for me they don't exist I've lost nothing and gained all the "volluntary" donations to the church and a lot of time not spent in sermons

Helen Thomas
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Posts: 1759
It's the devil who made the offer but he happily abides by God's final decision regardless if the coin toss results in a head. God decides who goes where and the devil tortures the ones in hell for ever afterwards enthusiastically.

So why even bother making a deal with the devil he cannot be trusted other than to torture thos who fall to him ?

Unless it has been recorded somewhere ( the Bible ?) of a trustworthy devil honouring his end of a bargain , in which case one might accept such a deal.
[ July 14, 2004: Message edited by: Helen Thomas ]

Helen Thomas
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Posts: 1759
Originally posted by Warren Dew:

I've never found the St. Petersburg 'paradox' to be at all paradoxical. If you take the actual amount of money that the house has as a limit to what it can actually pay you, the value of the bet ends up being small.

And even if it weren't, using some form of arctan as one's utility function - or, indeed, any bounded utility function - fixes things.

Vann McGee : �An airtight dutch book� . The surprise ending I believe is that if you were completely rational in the economic sense of the term- maximizing your expected utility- an eternity in hell would be the sure outcome.

Thomas Paul
mister krabs
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Posts: 13974
Originally posted by Jeroen Wenting:
Christianity makes a clear distinction between heretics (those who believe in other gods) and unbelievers.
Unbelievers can be converted (in the case of Mormons even post-mortem), heretics can never be redeemed (which led in the past to them being burned at the stake to show one's own dedication to god).
I think you have that wrong. Christianity (at least a strict interpretation) says that no one can be saved unless they have been baptized. Heretics were burned because they were a danger to society not because they can't be redeemed. If the king is claiming to be king by the will of God, what would it mean if you are claiming that his God is not the real God! There is no reason that a heretic can't confess their sin and be redeemed.

Christianity does not make a distinction between atheists and heretics as far as the final result goes.

Note: Technically there is a distinction but all go to hell...

Apostate - a Christian who renounces Christianity for another, non-Christian religion

Heretic - a Christian who abandons one Christan sect for another

Infidels - someone who has not been baptized

Warren Dew
blacksmith
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Helen Thomas:

The surprise ending I believe is that if you were completely rational in the economic sense of the term- maximizing your expected utility- an eternity in hell would be the sure outcome.

Ah, but it's an infinitesimal amount of time compared to the subsequent eternity I get to spend in heaven.

John Smith
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Posts: 2937
TP: Note: Technically there is a distinction but all go to hell...
Heretic - a Christian who abandons one Christan sect for another

Let me try to understand this. A Christian who was a catholic and becomes a protestant is a heretic and he goes to hell? How about a protestant who becomes a catholic? Or do you mean to say that it's OK to switch sects as long as both of them are Christian?

Thomas Paul
mister krabs
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Posts: 13974
Let me try to understand this. A Christian who was a catholic and becomes a protestant is a heretic and he goes to hell?

Correct.

How about a protestant who becomes a catholic?

Depends on the sect. Calvin was very strict and actually burned a fellow Protestant to death because they differed on the status of infant baptism. The amusing thing (well, not if you were the guy who got toasted) was that the heretic has just escaped from the clutches of the Catholic Church. He made the big mistake of stopping in Geneva to see his old firend Calvin.

Or do you mean to say that it's OK to switch sects as long as both of them are Christian?

Are we talking about today or in the past? Things are different today as the Catholic Church teaches a concept called "infallible ignorance" so even if you aren't a believer you can still claim ignorance and get to heaven.

Mohanlal Karamchand
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Posts: 189
when you go to heaven you get plenty virgins . in hell you are the virgin

Mohanlal Karamchand
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Posts: 189
but not for long

P. Sagdeo
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Posts: 67
Ok, here's the thing:

I'm afriad we're all in for some pain.

Jeroen Wenting
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Posts: 5093
Originally posted by John Smith:
TP: Note: Technically there is a distinction but all go to hell...
Heretic - a Christian who abandons one Christan sect for another

Let me try to understand this. A Christian who was a catholic and becomes a protestant is a heretic and he goes to hell? How about a protestant who becomes a catholic? Or do you mean to say that it's OK to switch sects as long as both of them are Christian?

According to a catholic no other Christian sect is the True Faith and any adherents are the worst sort of heretics.
Same to many strict protestant groups.
Bloody religious wars in history have been fought in Europe over the pronunciation of the name of Christ and the puncutation of a few sentences in the bible (which is indeed all that distinguishes some of the Christian groups here).
There are many Christians who will accept a mosque next to their church before accepting a church of another Christian sect.

Jeroen Wenting
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Posts: 5093
Originally posted by Warren Dew:
Helen Thomas:

The surprise ending I believe is that if you were completely rational in the economic sense of the term- maximizing your expected utility- an eternity in hell would be the sure outcome.

Ah, but it's an infinitesimal amount of time compared to the subsequent eternity I get to spend in heaven.

We'll expand your eternity in hell by a factor of Alef 2 for that heretic reasoning.

Christopher Docherty
Greenhorn
Posts: 4
"So you pick an envelope, and are about to see how long you�ll get in heaven when�

The angel makes you an offer. If you�ll do a day in Hell to cover for a friend of his that got caught up in a little scandal, he�ll give you the other envelope. He argues that this must be a good deal, as follows. Let y be the number written on your slip. The other envelope has either 2y or y/2 written on it. Each is equally likely, so your expected number of days in heaven if you switch envelopes is 0.5 * 2y + 0.5 * y/2 = 1.25y. So the expected gain from swapping is 1.25y - y = y/4. Since we know y > 10, y/4 > 2.5, so this is more valuable to you than a day in Hell."

At the risk of sounding incredibly simplistic, a bird in the hand is worth two in the bush.

No ???

Mohanlal Karamchand
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Posts: 189
if saintly lady dies and goes to heaven, of what use to her is a covey of virgins ?

Jeroen Wenting
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Posts: 5093
Originally posted by Mohanlal Karamchand:
if saintly lady dies and goes to heaven, of what use to her is a covey of virgins ?

she's probably used to having servants at her disposal to do things like cooking and cleaning, laying out clothes, etc. etc.