The Narrow Path Ministries

Rational Choice

You are taken into a room with two boxes labelled “A” and “B”.
Bill, a truthful person whom you trust tells you that in Box A, there is either a million dollars or nothing. In Box B, there is a thousand dollars.

You must make either of the following choices:
1. Open Box A only, and keep the contents.
2. Open BOTH boxes and keep the contents.

Bill tells you that a seer is consulted before a person makes his choice. The seer has already predicted the choice of around 5000 people, and he was always right. It is also the case that whenever a person chose to open both boxes, there was always nothing in Box A, but whenever a person chose to open only Box A, there was always a million dollars in it.

What do you believe is the rational choice for you?

Will you choose to open both boxes?
Or will you choose to open Box A only?

Please state your choice and explain why you made that choice.
If you are unwilling or unable to provide a reason, please state your choice anyway.

Okay, I'll bite.

I'll open both boxes becasue the seer's prediction or past choices won't change the contents of the box, and I'll receive what's in both of them.

I asked my 14 year old and she chose both as well. Great minds think alike!

I will over-think this

I'll assume that the previous 5,000 people were given the same instructions that Bill gave me

I was also going to assume that the previous 5,000 people did not have the information about the seers predictions

IF that had been the case, none of the 5,000 would have rationally chosen to only open box A. They all would have chosen to open both boxes (why not?)

BUT since you insinuated that the seer sometimes correctly predicted the opening of only box A, I must assume that at least some of the previous 5,000 people did have a reason to only open box A. What could that reason have been? Either they were made aware of the seers success in predicting OR they were made aware of the previous results OR both.

If they were aware only of the seers predictions, this raises logical questions. What contestant number was the first to become aware? Certainly number 1 could only have been made aware of the seers prediction about himself. But that would have given him no reason to not open both boxes. Indeed, knowing the seers prediction is meaningless without also knowing the previous results. Given this reality, it seems logically impossible that the only thing the contestants were aware of was the seers predictions.

If they were aware only of the previous results, this raises statistical questions. At what point does it become rational to pick only box A. Nobody, in this scenario, would bother picking just box A until statistics accumulated that nobody was getting $1,000,000 under box A when picking both boxes. At some point, someone would likely, noting the trend of failure, take a chance and pick only box A. The very next contestant would have noted the success of that adventure. But it would still have been a risk, at that point, to pick only A (it could have just been lucky, even foolish, for the previous contestant to pick only A). So maybe a few subsequent contestants go back to picking both and getting $1,000 only. Before too long, someone is bound to think the guy that chose only box A took a worthwhile risk. They'll do the same. Now twice it has worked out well for the person picking only box A. This creates all the more incentive to choose only box A. After this happens 2, 3, 4, 5 times... the contestants would surely come to think, for good reason, that something about the contest is rigged to favor the person who only picks box A.

If they had information about the seers predictions AND the results, the seers predictions wouldn't be all that interesting. The results are what matter. They would ignore the seers predictions and focus on the results, which make it rationally justified to pick only box A.


SO... what is the rational choice for me?

1. If given ONLY the choice, I obviously pick both boxes
2. If given the choice AND the information about the seer always being right... what good does that do me? I could be just as perfect a seer by predicting that everyone will choose to open both boxes! Why wouldn't they? I will still choose to open both boxes and I'll assume everyone else has as well and I'll assume some have come away with $1,001,000 while others with only $1,000.
3. If given the choice AND the results, I'll choose to only open box A. That would be the rational choice. But I am lucky to be contestant 5,001. The later you are a contestant in this game, the better your rational justification for choosing to only open box A.
4. If give the choice AND the seers predictions AND the results... I only care about the results. And the results lead me to choose to only open box A.

I'm sorry.

Quite the thorough analysis, Matt.

This question has been given to thousands of university students. Their responses were almost equally split between those who would choose both, and those who would choose only Box A. And whichever choice they made, ALL were very adamant that they had made the rational choice.

I believe that the rational choice is to pick both for the reason that Steve F stated.

The past history and/or the seer's predictions don't matter at all, since they don't affect the contents of the box. The million is either in Box A, or it isn't. My choice will not affect that fact. Therefore the rational choice is to open both.

Paidion wrote:Quite the thorough analysis, Matt.

This question has been given to thousands of university students. Their responses were almost equally split between those who would choose both, and those who would choose only Box A. And whichever choice they made, ALL were very adamant that they had made the rational choice.

I believe that the rational choice is to pick both for the reason that Steve F stated.

The past history and/or the seer's predictions don't matter at all, since they don't affect the contents of the box. The million is either in Box A, or it isn't. My choice will not affect that fact. Therefore the rational choice is to open both.

I think the seers predictions are irrelevant for the reasons I stated. But I don't think the results are irrelevant. They indicate that the game had been rigged.

I suspect the seer

Please tell me how it would be possible to rig the game. Perhaps it just happened that the seer was always right and that all who chose Box A only found a million in it, while those who chose both found nothing in it.
No one could have KNOWN in advance what choices the participants would make. Though it seems highly improbable that this could have happened by chance (and hence your suspicion of rigging), it is theoretically possible, just as it is theoretically possible to throw a fair die 1000 times and have it turn up as 6 every time, though it is practically highly improbable. And just as it is theoretically possible that some people will in their next stage of existence reject God forever, though it is practically impossible (because "forever" is infinite).

Paidion wrote:Please tell me how it would be possible to rig the game. Perhaps it just happened that the seer was always right and that all who chose Box A only found a million in it, while those who chose both found nothing in it.
No one could have KNOWN in advance what choices the participants would make. Though it seems highly improbable that this could have happened by chance (and hence your suspicion of rigging), it is theoretically possible, just as it is theoretically possible to throw a fair die 1000 times and have it turn up as 6 every time, though it is practically highly improbable. And just as it is theoretically possible that some people will in their next stage of existence reject God forever, though it is practically impossible (because "forever" is infinite).

I don't know HOW they rigged the game. And, of course, it is theoretically possible that they didn't. But, practically, it is HIGHLY LIKELY that these results are best explained by some sort of manipulation... especially given the fact that money is involved... not to mention a spiritual element, which are also subject to human manipulation).

We do seem to have some consistent disagreements about conclusions that can be drawn from dice games

I feel very confident in saying that the most rational conclusion to this scenario is that the game has been rigged.

I choose nothing because I refuse to be involved with the occult.

KAPOW!

I think the most logical choice is to open both boxes because at least I will receive $1000 if box A is empty.

Bill tells you that a seer is consulted before a person makes his choice. The seer has already predicted the choice of around 5000 people, and he was always right. It is also the case that whenever a person chose to open both boxes, there was always nothing in Box A, but whenever a person chose to open only Box A, there was always a million dollars in it.

With this result it is Possible that the game might be rigged as Matt mentioned

If the game is not rig then those who chose box A only and received a million dollars were extremely lucky and those who chose both boxes and did not receive million dollars were extremely unlucky.