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Author Topic:   Test your wits
Hyroglyphx
Member
Posts: 5692
From: Austin, TX
Joined: 05-03-2006
Member Rating: 1.4


Message 1 of 49 (477811)
08-08-2008 1:43 AM


A paradox, a dilemma, a riddle, an enigma... Insoluble? You tell me. I will post 2 questions that are intended to pose a dilemma. Can you solve them? Is it even possible to solve them, or will the result end in a stalemate?

1. Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

2. An eccentric billionaire places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life or have any lasting effects. The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. He emphasizes that you need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. All you have to do is intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin.

Edited by Nemesis Juggernaut, : No reason given.

Edited by Nemesis Juggernaut, : typo


“Tu ne cede malis sed contra audentior ito"
Replies to this message:
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Thugpreacha
Member
Posts: 12445
From: Denver,Colorado USA
Joined: 12-30-2003
Member Rating: 1.3


Message 2 of 49 (477812)
08-08-2008 2:23 AM
Reply to: Message 1 by Hyroglyphx
08-08-2008 1:43 AM


Phat Logic
1) It looks as if the best bet is for the prisoners to remain silent.

2) Am I missing something? It looks too easy. Take the money and don't drink the toxin.


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 Message 1 by Hyroglyphx, posted 08-08-2008 1:43 AM Hyroglyphx has responded

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Minnemooseus
Member
Posts: 3725
From: Duluth, Minnesota, U.S. (West end of Lake Superior)
Joined: 11-11-2001
Member Rating: 3.2


Message 3 of 49 (477814)
08-08-2008 2:47 AM
Reply to: Message 1 by Hyroglyphx
08-08-2008 1:43 AM


1) I would think that IF each knows each other AND have a very trusting bond, both will remain silent and take the 6 months. Otherwise, they would each betray the other an assure that they do not get the maximum penalty, and possibly will get off entirely.

2) The choice seems to be between not trusting the billionaire about getting the money and/or the effects of the toxin, and thus not promising intent to drink the toxin or...

...trusting the billionaire. Then to honestly get the money one must promise intent to drink the toxin and then to actually drink it. One can not honestly promise intent knowing that you are later going to withdraw said intent. Of course, I guess you could truly honestly promise and then later rethink it and refuse to drink the toxin. Early idealism followed by later pragmatism.

Personally, I think I would decline the offer.

Moose


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LucyTheApe
Inactive Member


Message 4 of 49 (477815)
08-08-2008 2:51 AM
Reply to: Message 1 by Hyroglyphx
08-08-2008 1:43 AM


1 - They're only suspects, not enough for a conviction.
2 - Take a serious painkiller with the intention of drinking the stuff.

Edited by LucyTheApe, : No reason given.


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Hyroglyphx
Member
Posts: 5692
From: Austin, TX
Joined: 05-03-2006
Member Rating: 1.4


Message 5 of 49 (477816)
08-08-2008 3:03 AM
Reply to: Message 2 by Thugpreacha
08-08-2008 2:23 AM


Re: Phat Logic
I'll give you some clues.

1) It looks as if the best bet is for the prisoners to remain silent.

Game theory... What does game theory advocate?

2) Am I missing something? It looks too easy. Take the money and don't drink the toxin.

Alright, second clue is freewill vs predestination. Have fun.


“Tu ne cede malis sed contra audentior ito"
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Hyroglyphx
Member
Posts: 5692
From: Austin, TX
Joined: 05-03-2006
Member Rating: 1.4


Message 6 of 49 (477817)
08-08-2008 3:15 AM


Great answers
Great answers so far. Some of them entail not playing the game. But in the first scenario, assume that it would not matter if they didn't have sufficient evidence.

In scenario 2, assume that you won't abstain from the game, or assume that you are a curious onlooker where someone else is playing the game and opts not to abstain.


“Tu ne cede malis sed contra audentior ito"
    
NosyNed
Member
Posts: 8842
From: Canada
Joined: 04-04-2003


Message 7 of 49 (477818)
08-08-2008 3:37 AM
Reply to: Message 5 by Hyroglyphx
08-08-2008 3:03 AM


Prisoner's Dilema
I think it has been strongly shown that if the prisoners are a population that may repeat interactions with each other then cooperators win out.

As I recall a game was played in a simulation. Different programs with different strategies were pitted against each other. Then the environment iterated with those doing well having more "babies". The wining strategy is:
Cooperate if not cheated.
Retaliate once if cheated and revert to co-opertation.

In other words be cooperative and forgiving. This wins against all comers.

In a single round there it is obviously best for both to remain silent. But the question is what is best for one to do? Unfortunately that may be to testify. Assuming you know nothing about the other person.


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Rrhain
Member (Idle past 45 days)
Posts: 6349
From: San Diego, CA, USA
Joined: 05-03-2003


Message 8 of 49 (477831)
08-08-2008 7:18 AM
Reply to: Message 1 by Hyroglyphx
08-08-2008 1:43 AM


The first question is a classic mathematical question called "The Prisoner's Dilemma."

The answer is to cooperate.

In extended competitions, the winning strategy is "tit-for-tat, with forgiveness, cooperate first." Whatever your opponent did the last time, you do this time. If it becomes apparent that you're both doing that, then forgive so you can both get back onto the winning strategy of mutual cooperation.

In more complex situations, game theory has means of coming up with strategies where you have multiple choices and the game need not be zero-sum.

The second question isn't a question of mathematics but rather a question of philosophy. As such, there is no "right" answer.

Edited by Rrhain, : See next two posts....


Rrhain

Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
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Percy
Member
Posts: 18498
From: New Hampshire
Joined: 12-23-2000
Member Rating: 2.9


Message 9 of 49 (477833)
08-08-2008 8:01 AM
Reply to: Message 8 by Rrhain
08-08-2008 7:18 AM


Rrhain writes:

The first question isn't a question of mathematics but rather a question of philosophy. As such, there is no "right" answer.

You mean the second question?

--Percy


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Rrhain
Member (Idle past 45 days)
Posts: 6349
From: San Diego, CA, USA
Joined: 05-03-2003


Message 10 of 49 (477834)
08-08-2008 8:07 AM
Reply to: Message 9 by Percy
08-08-2008 8:01 AM


Percy responds to me:

quote:
You mean the second question?

Yes...yes, I did.

I need an editor.


Rrhain

Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
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Modulous
Member (Idle past 277 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005


Message 11 of 49 (477838)
08-08-2008 9:42 AM
Reply to: Message 1 by Hyroglyphx
08-08-2008 1:43 AM


How should the prisoners act?

Betrayal.

Assuming that I'm socially short-sighted or just self-serving, if the other person cooperates my best response is to betray (I go free). If the other person betrays me, my best response is to betray them (Gives me a lesser sentence). No matter what they do, my best option is to betray them.

All you have to do is intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin.

Assuming the billionaire can detect intentionality, I drink the toxin and prepare myself for day of pain and consider my investment options. Can I intend to drink it knowing I don't have to? Yes, I simply make the decision to be honourable and keep my word. I can intend to keep my word, even if the rational thing to do would be to not, because matters of honour are not decided rationally - the human mind is capable of such acts irrationality.

If the billionaire cannot detect intentionality I just lie to to the crazy old guy.


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New Cat's Eye
Inactive Member


Message 12 of 49 (477840)
08-08-2008 10:10 AM
Reply to: Message 2 by Thugpreacha
08-08-2008 2:23 AM


Re: Phat Logic
2) Am I missing something? It looks too easy. Take the money and don't drink the toxin.

You wouldn't get the money because you never intended to drink the toxin in the first place.


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Deftil
Member (Idle past 2628 days)
Posts: 128
From: Virginia, USA
Joined: 04-19-2008


Message 13 of 49 (477841)
08-08-2008 10:22 AM
Reply to: Message 1 by Hyroglyphx
08-08-2008 1:43 AM


1. The good ol' Prisoner's Dilemma! It's classic and has been discussed in great detail in many places. Like here: Prisoner's dilemma - wikipedia and here: Prisoner's Dilemma - Stanford Encyclopedia of Philosophy. So I'll say no more about it.

2. This is an interesting one too. One thing that seems to be missing in the puzzle to me, is a surefire way for the billionaire to tell whether you actually intend to drink the toxin or not. I think people get the idea that you can just lie and tell him you do, then actually not drink it and keep the money. But the basic idea of the puzzle seems to be whether you can force yourself to actually intend to do something, knowing that you can change your mind later. If you know you can change your mind, how can you force yourself to actually intend to do it? Anyway, assuming I can't lie, and assuming I can't really intend to drink the toxin without actually drinking it, I would go ahead and drink it. I can't count on faking intention.
More about the puzzle here: Kavka's toxin puzzle - wikipedia and here: Dynamic Choice/ Autonomous Benefit Cases - Standford Encyclopedia of Philosophy.


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LucyTheApe
Inactive Member


Message 14 of 49 (477843)
08-08-2008 10:22 AM
Reply to: Message 1 by Hyroglyphx
08-08-2008 1:43 AM


RED?
I got up, grabbed my gun and headed out of my tent south.
About 4km out a sat down and had a cup of tea. I didn't see
anything worth killing for a meal.

I got up and walked about 6km to the east
to see if there was anything there I could hunt.

After a rest of about half an hour I got up and walked
4km north. Just about then I seen a bear ravaging through my
tent.

I shot him.

what colour was he?


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Modulous
Member (Idle past 277 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005


Message 15 of 49 (477845)
08-08-2008 10:32 AM
Reply to: Message 14 by LucyTheApe
08-08-2008 10:22 AM


Heh, nice one. Here's my spin on it.

A time traveller goes forwards in time 1 billion years looking for a suitable energy detector (aka a celestial thermometer). Not finding anything he then travels 5 light years in a random direction. No luck so he travels 40 light years in a direction at right angles to his previous direction. Here he finds a suitable celestial thermometer. He goes back in time 1 billion years and finds himself back where he started. What temperature is it?

yeah, it doesn't work quite as well as the bear one, but...well...nevermind.

Edited by Modulous, : No reason given.

Edited by Modulous, : No reason given.

Edited by Modulous, : No reason given.


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