Question for mathmeticians and ethical philosophers

[john330]

I have been thinking about this ethical dillemma for quite a few years now. Two men are in a room permanently, until death. They cannot leave the room. There is enough food for one man to eat and survive, but the two men cannot share the resource. One man (A)behaves according to the directives to survive (and the subset of directives that will allow his survival, such as to kill if need be to survive). The other man (B) behaves according to the same directives to survive, except he also has additional directives (he lives according to the Gospel: he is willing to love sacrificially, and thus will not kill someone in order to survive).

I believe the natural man, man A, wins this every time if each man behaves strictly according to his directives. Man A will win out for the resource because he is willing to do whatever it takes to earn it. I have been trying to come up with an equation to represent this dillemma mathematically, but I do not have the mathematics background to do so.

I thought that the men should perhaps be represented according to their instincts, with S representing the instinct to survive/thrive/reproduce, and S also representing the entirety of a subset of related instincts, such as the willingness to kill in order to survive. So Sa >Sb. Not only am I not sure if this is the correct way to transcribe the equation, but I am not sure how to indicate that man B’s instincts are lessened by his directives to obey the Gospel. I thought about dividing Sb’s original directives by his directives to obey the gospel such as:

S(survive, thrive, reproduce, kill, steal, hate, lie, cheat, etc.)
C(-kill,-steal, love, honesty, fair play)

So: Sa>Sb/C

Any nerds out there have any thoughts on this (haha)?

 

[Bob_Crowley]

I’m no mathematician either, but I don’t think you need the suffix “a” or “b”. For all intents and purposes, you are proposing the two men are equal, except that one of them has additional characteristics (scruples or C) which prevent him from being ruthless enough to survive.

So it’s just a case of S < S/c, or a man without scruples is more likely to survive than the same man with scruples. Or you could put it as S-C > S+C, in the sense that scruples (C) are a negative factor in survivability.

But on the other side of death the terms will be reversed is. S+C > S-C; or S+C > S, when the two of them face judgement. The natural man’s goose is eternally cooked in that scenario.

Saint Maximilian Kolbe faced a similar situation when he died in the concentration camp. He gave up his life for another man. The other man might be in heaven as well for all we know, but Maximilian Kolbe is now a saint, and the other man isn’t.

 

[colmywaykurtz]

I have been thinking about this ethical dillemma for quite a few years now. Two men are in a room permanently, until death. They cannot leave the room. There is enough food for one man to eat and survive, but the two men cannot share the resource. One man (A)behaves according to the directives to survive (and the subset of directives that will allow his survival, such as to kill if need be to survive). The other man (B) behaves according to the same directives to survive, except he also has additional directives (he lives according to the Gospel: he is willing to love sacrificially, and thus will not kill someone in order to survive).

I believe the natural man, man A, wins this every time if each man behaves strictly according to his directives. Man A will win out for the resource because he is willing to do whatever it takes to earn it. I have been trying to come up with an equation to represent this dillemma mathematically, but I do not have the mathematics background to do so.

I thought that the men should perhaps be represented according to their instincts, with S representing the instinct to survive/thrive/reproduce, and S also representing the entirety of a subset of related instincts, such as the willingness to kill in order to survive. So Sa >Sb. Not only am I not sure if this is the correct way to transcribe the equation, but I am not sure how to indicate that man B’s instincts are lessened by his directives to obey the Gospel. I thought about dividing Sb’s original directives by his directives to obey the gospel such as:

S(survive, thrive, reproduce, kill, steal, hate, lie, cheat, etc.)
C(-kill,-steal, love, honesty, fair play)

So: Sa>Sb/C

Any nerds out there have any thoughts on this (haha)?

Perhaps simply: S does not equal the result of S-C because “C” represents some undefined quantity like (x/0) …or somethimg like that. I’m obviously no mathatician, either.

 

[Mount_Carmel]

How is man A able to reproduce unless there are others - notably female; this is further assuming they are both fertile? How does the offspring survive, or indeed any future generations? We all need help from time to time, what happens if he gets ill or frail?

The nature of even selfish man is normally to know that their best survival chances are through some form of cooperation. We are ‘group animals’ - no healthy man is an island.

 

[john330]

The men will not reproduce with each other, obviously. Rather, the instinct to reproduce is part of a subset of instincts which is a function of his instinct for survival. Perhaps I should have explained this a little better. This is an ethical dilemma like the prisoner’s dilemma. Google prisoner’s dilemma or Hobbes game to find similar ethical dilemmas. The purpose of analyzing such scenarios is to try to understand how people will act in given situations. By studying these, we gain wisdom into economics, psychology, sociobiology, and human nature in general. So of course if such a scenario were to arise, there would be individuals who behaved according to an entire spectrum of values…that is why I custom tailor the experiment. One of the rules of the game is that they can’t share the resource. Like when two construction companies go after a single contract, say, to build a land grant university. One may use bribery to influence the politicians selecting the contractor, another company may not. As a result, the nefarious company receives the contract, and the honest company does not. In other words, we are trying to study how humans behave when a non- reusable resource is being sought by competing parties. And we want to know if there is any ability to predict outcomes in these scenarios. Hobbes predicts that humans will behave in very specific ways in these scenarios.

 

[john330]

I’m no mathematician either, but I don’t think you need the suffix “a” or “b”. For all intents and purposes, you are proposing the two men are equal, except that one of them has additional characteristics (scruples or C) which prevent him from being ruthless enough to survive.

So it’s just a case of S < S/c, or a man without scruples is more likely to survive than the same man with scruples. Or you could put it as S-C > S+C, in the sense that scruples (C) are a negative factor in survivability.

But on the other side of death the terms will be reversed is. S+C > S-C; or S+C > S, when the two of them face judgement. The natural man’s goose is eternally cooked in that scenario.

Saint Maximilian Kolbe faced a similar situation when he died in the concentration camp. He gave up his life for another man. The other man might be in heaven as well for all we know, but Maximilian Kolbe is now a saint, and the other man isn’t.

Yes, Maximilian Kolbe is an interesting case study in this. Thank you for bringing him into discussion.

Also, I thought of subtracting C from S as well, but I’m not sure if this is correct function.

What it all comes down to is the Resurrection. If man b has hope of his own resurrection, then he can choose to sacrificially love man a, as hard as that will be. This scenario is really all about the Cross and Resurrection of Jesus. It is also about a broken world, in which others will do evil in order to profit. Without the Cross, there is therefore no hope for mankind. I think that atheists would be loathe to examine the consequences of this dilemma.

 

[Gorgias]

The other man (B) behaves according to the same directives to survive, except he also has additional directives (he lives according to the Gospel: he is willing to love sacrificially, and thus will not kill someone in order to survive).

I believe the natural man, man A, wins this every time if each man behaves strictly according to his directives. Man A will win out for the resource because he is willing to do whatever it takes to earn it.

I don’t think that you can say that A wins every time. He might have a heart attack, or choke on a chicken bone, or meet an untimely demise in any number of ways.

Moreover, your construct says that B will not kill someone; however, he would still be a moral person, ‘living by the Gospel’, if he were to act in self-defense in order to fend off an unjust attack by A. In that case, if the attempt at self-defense incapacitated A – only because B was licitly defending himself – then B might prevail.

Just sayin’…

 

[Mount_Carmel]

john330 - I am well versed in the ‘moral dilemma’ scene, having waded through ‘decision making processes’ and ‘foundations of behaviour’ and having scored a rare 50:50 in the ‘Sheep and Goats’ test.

The truth is that without some form of consensus and cooperation humanity is ultimately doomed. I am more a Smith type person, feeling social interaction as positive, rather than Hobbes more negative take.

The scenario you write in your OP would have both perish one way or another, particularly mentally and emotionally if totally deprived of interaction. Would man A have access to outside interaction, would there be scope for pets?

Banged up in ‘solitary’ a type A man is mentally less likely to survive because his mental and emotional faculties and strategies would tend to be internally less able to access laterality and flexibility of thought and action. Food alone would not see him through, I hope the room is well padded - and sound proofed!

 

[john330]

Well put. I hope I didn’t seem uncharitable in my reply to your post. My apologies if I did.

The dilemma can be changed then to a scenario in which two men are in a room with a red button on the wall. The man who first pushes the button will live, the other man will die. The man who lives can return to normal life. Or you can remain in the first scenario, with the admendment that whoever earns the resource will have continual and repeated access to it. One thing that I thought was “who would want to win the game, given that the winner must remain in a room alone indefinitely.” And yes, both will die eventually. Another interesting variable is how a man’s values change when very hungry. Moral strength decreases as physical exhaustion occurs, thus a good man may become overpowered by instinct after a period of time without food or drink.

I do believe that the natural man, as defined by his directives, will act in a specific way.

 

[john330]

I don’t think that you can say that A wins every time. He might have a heart attack, or choke on a chicken bone, or meet an untimely demise in any number of ways.

Moreover, your construct says that B will not kill someone; however, he would still be a moral person, ‘living by the Gospel’, if he were to act in self-defense in order to fend off an unjust attack by A. In that case, if the attempt at self-defense incapacitated A – only because B was licitly defending himself – then B might prevail.

Just sayin’…

There is much wisdom in your post. I considered this scenario. The original scene that I came up with included a weapon in the room that either man may use against the other. So in order to decrease the probability of physical attack, I decided to remove this element from the scenario. This does not eliminate the possibility of physical attack, however. One thing that has to be taken into consideration is that by fighting back, man B is trying to win the game. Part of the definition of his directives is that he lives by sacrificial love. Jesus died on the cross and did not open his mouth towards his accusers. He also told us to offer the other cheek when struck. The Church teaches that we are entitled to self defense, but that is not how Jesus lived. I believe that the directive to sacrificial love precludes self defense in this scenario. I will be interested to hear your thoughts on that statement (haha).

 

[Peter_Plato]

I have been thinking about this ethical dillemma for quite a few years now. Two men are in a room permanently, until death. They cannot leave the room. There is enough food for one man to eat and survive, but the two men cannot share the resource. One man (A)behaves according to the directives to survive (and the subset of directives that will allow his survival, such as to kill if need be to survive). The other man (B) behaves according to the same directives to survive, except he also has additional directives (he lives according to the Gospel: he is willing to love sacrificially, and thus will not kill someone in order to survive).

I believe the natural man, man A, wins this every time if each man behaves strictly according to his directives. Man A will win out for the resource because he is willing to do whatever it takes to earn it. I have been trying to come up with an equation to represent this dillemma mathematically, but I do not have the mathematics background to do so.

I thought that the men should perhaps be represented according to their instincts, with S representing the instinct to survive/thrive/reproduce, and S also representing the entirety of a subset of related instincts, such as the willingness to kill in order to survive. So Sa >Sb. Not only am I not sure if this is the correct way to transcribe the equation, but I am not sure how to indicate that man B’s instincts are lessened by his directives to obey the Gospel. I thought about dividing Sb’s original directives by his directives to obey the gospel such as:

S(survive, thrive, reproduce, kill, steal, hate, lie, cheat, etc.)
C(-kill,-steal, love, honesty, fair play)

So: Sa>Sb/C

Any nerds out there have any thoughts on this (haha)?

Fundamentally, I think the problem with the way this dilemma is couched is that enduring a long solitary life in an enclosed room is not much of a payoff even for the “survivor.” It could be legitimately suggested that it might be just as rationally self-interested to let the other person have the food to be relieved of enduring “survival” alone in the room for the rest of one’s life.

The prisoner dilemma has a distinctively desirable payoff - a shortened prison sentence.

If A and B both betray the other, each of them serves 2 years in prison
If A betrays but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)

There is no truly desirable payoff in your version of the dilemma since solitude in an enclosed room is not much of a positive choice, unless, of course, a person finds their own company exhilarating.

What if you added some further conditions, more in line with the prisoner dilemma?

What if the room contained a year’s supply of food for one man (six months each for two), and only at the time when the food supply was completely consumed would only one man be released from the room?

Perhaps a trap door is triggered when the food is completely consumed allowing only one to escape.

The dilemma, then, becomes a more “chillingly live” one because cooperation, on some level, would seem to be necessary to shorten the time of captivity to six months or slightly longer (according to when the food is consumed,) but then is challenged not so much by simple survival, but, rather, a more compelling option, i.e., freedom.

This would be a more revealing “test” of Gospel values, if that is what you are looking for, since survival rules would point to only one man gaining freedom at the end while the other is either killed or overpowered and left to starve. Although, other options are possible.

Perhaps I missed it, but what exactly is this dilemma supposed to show? Is it something like Pascal’s Wager where the odds of the Gospel being true and a person who refuses to take the “survival” at all costs option has a probable chance of gaining a “better” reward that the survivor (as killer) won’t?

 

[john330]

Fundamentally, I think the problem with the way this dilemma is couched is that enduring a long solitary life in an enclosed room is not much of a payoff even for the “survivor.” It could be legitimately suggested that it might be just as rationally self-interested to let the other person have the food to be relieved of enduring “survival” alone in the room for the rest of one’s life.

The prisoner dilemma has a distinctively desirable payoff - a shortened prison sentence.

There is no truly desirable payoff in your version of the dilemma since solitude in an enclosed room is not much of a positive choice, unless, of course, a person finds their own company exhilarating.

What if you added some further conditions, more in line with the prisoner dilemma?

What if the room contained a year’s supply of food for one man (six months each for two), and only at the time when the food supply was completely consumed would only one man be released from the room?

Perhaps a trap door is triggered when the food is completely consumed allowing only one to escape.

The dilemma, then, becomes a more “chillingly live” one because cooperation, on some level, would seem to be necessary to shorten the time of captivity to six months or slightly longer (according to when the food is consumed,) but then is challenged not so much by simple survival, but, rather, a more compelling option, i.e., freedom.

This would be a more revealing “test” of Gospel values, if that is what you are looking for, since survival rules would point to only one man gaining freedom at the end while the other is either killed or overpowered and left to starve. Although, other options are possible.

Perhaps I missed it, but what exactly is this dilemma supposed to show? Is it something like Pascal’s Wager where the odds of the Gospel being true and a person who refuses to take the “survival” at all costs option has a probable chance of gaining a “better” reward that the survivor (as killer) won’t?

Thank you for your (name removed by moderator)ut. The dilemma is supposed to show mathematically and practically that the natural man has a survival and evolutionary advantage over the man of Christian values, simply from a worldly point of view. It intends to indicate that the Christian is able to experience heinous evil because of the hope of the Resurrection, whereas the natural man has no moral basis when it comes down to survival. It can be used as an instrument to indicate to non- believers that only Christian morality and grace will suffice to practice sacrificial love in the direst of circumstances. Above all, I believe that it is the beginning of a discussion on moral acts, setting up the necessity of the Cross and Resurrection. Christ commands us to love sacrificially, but how can we do so when we are placed in precarious economic situations? Such a precarious economic situation is what I was attempting to construct in this dilemma. Man B can never be man B unless he has the hope of Resurrection.

The worldly sociobiologist will interpret the dilemma as indication that the good man always loses, and therefore whatever he must do to survive is ethically right. The Christian philosopher will interpret this, as many on the page already have, as the possibility of sacrificial love as a result of faith in Jesus.

Again, thanks so much on the (name removed by moderator)ut! Will be eager to hear your thoughts on this. Any thoughts on the mathematics side of the discussion?

 

[john330]

As an addendum to my previous post, I would like to say that I intended to produce a scenario in which there were only two options, life or death, and in which cooperation was not possible.

Also, I think that whether you agree with the speculation about people, values, the broad spectrum of possible outcomes or not, that both the Christian and non-Christian can take something away from the scenario. Descartes’ method is useful to non- Christians, but his argument for the existence of God is not.

 

[Gorgias]

One thing that has to be taken into consideration is that by fighting back, man B is trying to win the game.

I think I’d disagree with this notion. In defending himself, B is neither ‘fighting back’ nor ‘trying to win the game’; rather, he’s simply defending himself against an unjust attack on his life.

He also told us to offer the other cheek when struck.

It’s important to recognize the context of this statement, though. In Matthew, we read,

“You have heard that it was said, ‘An eye for an eye and a tooth for a tooth.’ But I say to you, offer no resistance to one who is evil. When someone strikes you on (your) right cheek, turn the other one to him as well."

The reference to ‘an eye for an eye’ is critical to our understanding of this passage. Jesus is quoting from the Mosaic law: when one does you an injustice, you’re entitled to restitution – in this case, the application of the law means that the aggressor can be forced to give up what he’s taken from another. Jesus, then, isn’t making a statement about pacifism, but rather, about foregoing retribution through recourse to the law.

The Church teaches that we are entitled to self defense, but that is not how Jesus lived.

Jesus said to [the apostles], “one who does not have a sword should sell his cloak and buy one." (Lk 22:36)

“I have come to bring not peace but the sword.” (Mt 10:24)

Now… you were saying?

I believe that the directive to sacrificial love precludes self defense in this scenario.

Perhaps, but I’m not convinced. After all, if B allows A to effectively kill him in order to ensure his own survival, isn’t B (at least indirectly) contributing to A’s loss of salvation through sin? After all, “whoever wishes to save his life will lose it… what profit would there be for one to gain the whole world and forfeit his life?” (Mt 16:25-26)

By extension, then, if B allows A to kill him, then B gains eternal life at the very real potential of ensuring that A loses eternal life. Is that really an example of ‘sacrificial love’?

 

[Mount_Carmel]

Perhaps, but I’m not convinced. After all, if B allows A to effectively kill him in order to ensure his own survival, isn’t B (at least indirectly) contributing to A’s loss of salvation through sin? After all, “whoever wishes to save his life will lose it… what profit would there be for one to gain the whole world and forfeit his life?” (Mt 16:25-26)

By extension, then, if B allows A to kill him, then B gains eternal life at the very real potential of ensuring that A loses eternal life. Is that really an example of ‘sacrificial love’?

It could equally be argued that allowing A to survive longer might give him time to reflect and even perhaps change for the better - most type A folks minds still have that small voice of humanity and reasonableness that nags and taps and occasionally manages to get a hearing.

 

[Just_Lurking]

The Wikipedia article on Evolutionary Game Theory (see here) is a broad overview of this area of research.

For a particular example, the paper “Infanticide as an evolutionarily stable strategy” (see here) illustrates some of the mathematics that evolutionary biologist are using to analyze these types of questions.

 

[john330]

I think I’d disagree with this notion. In defending himself, B is neither ‘fighting back’ nor ‘trying to win the game’; rather, he’s simply defending himself against an unjust attack on his life.

It’s important to recognize the context of this statement, though. In Matthew, we read,

The reference to ‘an eye for an eye’ is critical to our understanding of this passage. Jesus is quoting from the Mosaic law: when one does you an injustice, you’re entitled to restitution – in this case, the application of the law means that the aggressor can be forced to give up what he’s taken from another. Jesus, then, isn’t making a statement about pacifism, but rather, about foregoing retribution through recourse to the law.

Jesus said to [the apostles], “one who does not have a sword should sell his cloak and buy one." (Lk 22:36)

“I have come to bring not peace but the sword.” (Mt 10:24)

Now… you were saying?

Perhaps, but I’m not convinced. After all, if B allows A to effectively kill him in order to ensure his own survival, isn’t B (at least indirectly) contributing to A’s loss of salvation through sin? After all, “whoever wishes to save his life will lose it… what profit would there be for one to gain the whole world and forfeit his life?” (Mt 16:25-26)

By extension, then, if B allows A to kill him, then B gains eternal life at the very real potential of ensuring that A loses eternal life. Is that really an example of ‘sacrificial love’?

I respect your thoughts, but still disagree with you on every point. Your ideas do help me to develop my own understanding.