Sophie's choice.

[weller2]

In the case presented, the mother is asked to choose which child she wants to live, and the Nazi says he will kill the other. If she does not choose, then both will be killed. Most people think it is not a sin to choose which child she wants to live.

Acually, even assuming a purely utilitarian POV (= maximizing the number of survivors), choosing a child is dumb. This is because there is no guarantee that the Nazi will do as he promises, because his motivation is unclear.

#1 If the Nazi wants some sick entertainment, then the logical thing for him to do is to shoot the child she wanted to save, just to see the other child jump at her throat shouting “You wanted to kill me!”. Expected number of survivors = 0 or 1. On the other hand, refusing to provide entertainment means that the Nazi will give up (3 survivors), get angry and shoot the woman (2 survivors), or shoot both children (1 survivor). However, shooting both children would be illogical, because it accomplishes nothing entertainment-wise.

#2 Further, it is possible that the entire situation is a bluff (nobody will be shot anyway). In such situation, it is better to call the bluff (3 survivors), because the alternate scenario (“You wanted to kill me!”) means 1 or 2 survivors.

#3 If the Nazi wants to demonstrate that he can force her to make a choice, then carrying out the threat (shooting both children) in case of non-compliance accomplishes him nothing. This means that the situation is likely a bluff (see #2). If it isn’t, then after she chooses the Nazi will shoot either in line with her choice, or opposite for entertainment (see #1). So if she chooses child A, there is 50% chance he will shoot child B and vice versa – so she can as well throw a coin. Her choice is meaningless.

Thus:

• it does not matter which child she chooses, the Nazi will shoot the child of his choice anyway
• if she flat out refuses, then there is a good chance that he will give up, or kill only her.

Refusal to make the choice is mathematically optimal.

 

[Tomdstone]

Acually, even assuming a purely utilitarian POV (= maximizing the number of survivors), choosing a child is dumb. This is because there is no guarantee that the Nazi will do as he promises, because his motivation is unclear.

#1 If the Nazi wants some sick entertainment, then the logical thing for him to do is to shoot the child she wanted to save, just to see the other child jump at her throat shouting “You wanted to kill me!”. Expected number of survivors = 0 or 1. On the other hand, refusing to provide entertainment means that the Nazi will give up (3 survivors), get angry and shoot the woman (2 survivors), or shoot both children (1 survivor). However, shooting both children would be illogical, because it accomplishes nothing entertainment-wise.

#2 Further, it is possible that the entire situation is a bluff (nobody will be shot anyway). In such situation, it is better to call the bluff (3 survivors), because the alternate scenario (“You wanted to kill me!”) means 1 or 2 survivors.

#3 If the Nazi wants to demonstrate that he can force her to make a choice, then carrying out the threat (shooting both children) in case of non-compliance accomplishes him nothing. This means that the situation is likely a bluff (see #2). If it isn’t, then after she chooses the Nazi will shoot either in line with her choice, or opposite for entertainment (see #1). So if she chooses child A, there is 50% chance he will shoot child B and vice versa – so she can as well throw a coin. Her choice is meaningless.

Thus:

• it does not matter which child she chooses, the Nazi will shoot the child of his choice anyway
• if she flat out refuses, then there is a good chance that he will give up, or kill only her.

Refusal to make the choice is mathematically optimal.

This brings in the additional element of whether or not you can trust the Nazi.
In the scenario I had in mind, the assumption was that the Nazi would carry out the orders exactly as stated. And proceeding from that assumption, the question of interest was what would be the least objectionable choice.
It is true of course that you can question the existing assumptions and subsequently add other conditions and assumptions, but then this would be a different scenario from the one I had in mind.

 

[Charlemagne_III]

Thus:

• it does not matter which child she chooses, the Nazi will shoot the child of his choice anyway
• if she flat out refuses, then there is a good chance that he will give up, or kill only her.

Refusal to make the choice is mathematically optimal.

When confronted with the requirement that we choose between a greater and a lesser evil, we are always right to choose the lesser evil (with the understanding that we have still chosen an evil). In this instance whether one or two children is killed, Sophie has killed neither.

 

[PolarGuy]

This brings to mind another scenario where a father can use violence to stop the imminent rape of his daughter but refuses to do so.

Tom, how come you never want to explain why you wouldn’t use force to stop the rape of your hypothetical daughter?