# The Saved and the Damned

Suppose God gives to each person the greatest equal probability of being saved. It is true, suppose, that there are two, and only two, groups of people. The members of one group will all be saved and the members of the other group will all be damned. The good news is that one of the groups is twice as large as the other. God gives each person the greatest equal probability of being saved only if he saves every member of the larger group. The epistemic probability that you are among the saved is then about .67 or 2/3.

Now suppose God offers to tell everyone whether she is in the larger group or the smaller group. Would it be rational to accept this information? If everyone learns which group she is in, then the greatest equal epistemic probability that each person is saved diminishes to .5 or 1/2. God must now flip a coin to decide which group is saved, the smaller or the larger. That is the only way to give each person the greatest equal probability of being saved. What should you do?

It is a strange problem since, if we refuse the information, many more people get saved! It is also strange since, you are already in one or the other of those groups. The information doesn’t affect which group you’re in.

"If everyone learns which group she is in, then the greatest equal epistemic probability that each person is saved diminishes to .5 or 1/2."

Mike, why is this? I'm having a hard time seeing why the new information changes the epistemic probabilities to .5 for everyone, rather than 1 for the saved and 0 for the damned.

Are we assuming here that nothing you do or believe determines which group you're in but that it's purely chance? If not, I think there will be complicating factors and a need to distinguish between this method of finding out you're saved and the ordinary one of seeing the evidence in your life that you are one of the faithful.

Suppose only one person accepts the information, and everyone else rejects it. This is sufficient for the change to coin flipping.

Mike, I think that would do it, provided that one's lifestyle and beliefs don't provide evidence of whether one is saved or damned.

If God simply flips a coin and the results will be that heads is saved and tails are damned then there is as you suggest a 50-50 chance of being saved. In the actually of flipping of the coin 67% of the flips turns out to be heads. God now knows that 67% are (not will be) saved, and who these people are. You now know that there is a probability of 1 that you will are saved if you got heads when your name came up for the coin toss and you got heads or damned if it came up tails. If God tells you that he choose the outcome for each of us by flipping a coin with heads being saved, etc., this assures us that there is a equal chance of being saved or damned. But once the flips are made there is no chance of the outcome being different then what it actually is. If God tells us that the actual outcome is 67/33 the outcome is a probability of 1 that we are in the group of 67 or 33 in so far as we are in one of these groups. If I am in the group that is damned there is no chance that I am also in the group that is saved.

If God decides to save and damn at a rate of 2 to 1 then yes we have a 67% chance of being saved before we are assigned a group. But once we are in a group then the probability that we are in that group is 1. That cannot change unless God is going to do the assignments all over. If he uses a flip of a coin then the chance of being saved or damned changes to 50-50. but again once we are in a group the probability that we are in that group is 1. Membership in the group we are in has nothing to do with what we know - our knowledge does not change the probability that we are in the group that we are in. Even if we know that God wants a certain result percentagewise, say 67-33, we do not know the outcome regarding which group we are in prior to the distribution actually being made.

I was assuming that the 'greatest equal probability' is 50-50. If that is the case then God has to use a mechinism for choosing that results in a 50-50 chance that I will be saved. He could line us up at random (I assume He wants to be fair)and have us call off by 2's with the 1's being saved and the 2's being damned. But that will result in a distribution at worse that is 51-49 (if there is an odd number of beings to be saved), not 67-33. Flipping a coin on the other hand gives us a 50-50 chance per flip that could result in a distribution greater then 51-49 depending on the actual outcome of all the flips. But that distribution is not knowable, predictable, foreseeable, prior to the flip, but dependant upon the outcome of the flips. This is true as long as I do not know if I am in in that group of people at the end of the flipping (whatever) where the effect does not change as the number of people yet to make a choice have been reduced to a point where the outcome cannot be changed. But it is not my knowledge that affects the outcome, it is the number of people left to make choices that affects the outcome.

What am I missing?

"After everyone is divided into the larger and smaller group it is true that (i) if you do not know which group you are in, then if God chooses the larger group, then you have a 2/3 chance of beng saved (ii) if you do know what group you are in, then if God chooses the larger group, then you have a 0 or 1 chance of being saved."

If God chooses the larger group and you are in that group you have a 100% chance of being saved. If I am already in the group that is saved there is no possibility that I am in the group that is damned therefore there is a probability of 1` that I am in the group that I am in. Once I am in the group that probability does not change even if from my epistemic perspective the chances appear to be different (I admit I know not understand how this could happen). If I am saved then I am saved, I must be saved or not saved, and I cannot be both saved and not saved at the same time. If I am already in a group it is established that I am what I am. My epistemic point of view does not affect the probability of which group I am in It makes no difference if I know which group I am in or not. I am already in the group I am in. That has already been settled.

I guess I do not understand what it is that you are trying to demonstrate by your thought experiment.

Mike: I agree that this is fun. I do enjoy our interactions on this blog. I hope I do not come across in any manner that suggests otherwise. If I do, then I apologize.

I wonder whether there is an argument that it is rational to accept the information, along the lines of Rawls's maximin argument for his difference principle. Someone may think, "If I turn out to be in the smaller group, I can raise the probability that I will be saved from 0 to 50-50 by accepting the information." I think that the plausibility of this argument depends on the relative size of the smaller group. Suppose, e.g, that out of a total population of 1,000,000, God decides to save everyone except one person. It doesn't seem reasonable to accept the information on the grounds that if you turn out to be the one unfortunate, you will increase the probability of your salvation.

I'm sorry, I know this is a dead thread, but I am just baffled by why this is a question of rationality.

Unless you think that you should maintain a belief that you are 2/3 likely to be saved instead of finding out whether you are saved, John is right.

Mike, you're right that your epistemic probability of being saved in the original scenario is 2/3. What I don't understand is why finding out whether you are in the large or small group will change your actual probability. Presumably, this is the fear. It would be irrational of you to seek out information that would lower your objective chance of being saved. But there is no reason to think that finding out whether you will be saved will change this. Your objective probability of being saved is either 1 or 0, because God has already decided.

If you find out, then you will have the epistemic probability of 1 or 0 that you will be saved. Because God is the most reliable source of information his telling you that you will or will not be saved is sufficient for your epistemic probability in regards to saving to be 1 or 0.

So, you have the option of matching your epistemic probability to the objective probability. There is a 1/3 chance that your epistemic probability will go from 2/3 to 0 and a 2/3 chance that your epistemic probability will go from 2/3 to 1.

Whether there is a rational choice to make here isn't clear to me.

Am I missing something? Perhaps I'm incorrectly assuming that group membership is fixed throughout the process?

Okay, I understand now. You are using Greatest Equal Probability to be Epistemic probability. So, in this case, finding out which group you're in would cause God to need to redistribute assignments to the groups to allow everyone equal belief that they are saved.

But in this case, it is obvious that it is irrational to find out which group you are in. Because, assuming you are randomly assigned, your first group assignment is more likely to be in the large group. And you have stipulated that the large group is the saved group under ignorance. Under knowledge of whether one is in the large group or not God is forced to re-assign destinations to the group in order to keep people ignorant about their salvation (in order to meet his obligation to give us all greatest equal Epistemic probability). So our chances of being saved have gone down.

But once this is clear, why would anyone seek out the information about whether she is in the large or small group. It is of no use whatsoever, because God needs you to not know if you are saved or damned. So you will never up your odds of being saved by finding out if you're in the large group or small group. You have a very small chance that you are in the small group and of causing the small group to be made the saved group by the coin toss. But this probability is much lower than the chance that you make the large group the damned group when you're in the large group.

Obviously you should not find out. The only reason this seems like a problem is the equivocation between Greatest Equal Probability and Greatest Equal EPISTEMIC Probability. Once this is clarified, it becomes obvious that finding out which group you are in yields no good information and only serves to decrease your chances of being saved.

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