Newcomb's Problem

[Gogf]

No, I was talking about the likelihood of him being continuing to be accurate. Statistically, it's around 99%. The fact that he has been 100% accurate in the past helps us in no way to predict any future outcomes.

These are contradictory statements.

The issue here is that if you would lose that, you would be doomed (the costs of losing would be significantly higher). This is a bonus, so you're not doomed if you lose.

If someone did offer you a $100 bill or a 0.1% chance at $1000000, you should logically choose the latter option since its expected value is 10 times the former's expected value.

I assume you are familiar with expected value... and I assume that a person would make the rational choice, not the "common-people" choice.

How is taking that kind of a gamble the "rational choice"? You're assuming that a choice's value is equal to its expected value until it has been chosen, and I don't think that's necessarily true.

It strongly suggests he will, certainly enough to counter the potential to win an extra $1000

But in this situation you've nothing to lose. People tend to act more rashly when there's nothing they earnt on the line.

Of course, and I think a problem with the original question is that there's too little money involved. My immediate reaction to a scenario like this is to ignore the $1,000 and try to maximize my chances of getting $1,000,000, but that doesn't mean that doing so will net me the most money possible. I presume getting the most money is the goal here, and (pre-Perf's solution) taking both boxes will ALWAYS get you more money than simply taking one.

 

[Defiant47]

Problem . loterries.

Lotteries in real life have negative expected values, so they're usually a bad idea. The cost isn't worth the potential benefit and its likelihood.

If there was a lotterry (you could buy only one) that costed $100 with a 0.1% chance of $1000000 , i wouldn't take it. If however if there was a lotterry where each participant won $1000000 and it costed $1000 i would take part in it. As would most humans.

Well, you should. The expected value is greater than the cost of the ticket. This means that on average, you stand to gain more if you partake in the lottery. The cost is worth the potential benefit and its likelihood.

I fail to see how Omega being correct %100 of the time changes the value of the boxes at the exact second that I choose. It is not trying to trick the alien or anything related. If you believe that your choice will influence the amount of money put in the boxes, choose box B. But otherwise, the money is already in there and will not change, and box B will have either the 1 million or nothing. Again, I'd fully expect to find 1,000 dollars when I choose both boxes, but I know that my choice didn't cost me one million dollars- the alien chose not to put the money in box B beforehand.

So the question instead becomes do you believe that reality changes as a result of your choice?

On the contrary, your choice is synonymous with reality. If you choose box B, then the money will have been there (not magically spawn), if you choose both boxes, then the money will never have been there. This is because Omega predicted your choice very well. If you were to suddenly change your mind and switch your answer, Omega would have likely predicted that as well.

These are contradictory statements.

Sorry for the confusion. This is what I meant:

The claim "Omega has been right 100 times out of 100 times. Therefore, he has had 100% success rate in the past." does not help us analyze the future at all; only the past. It would only be useful if we were to go back into the past and make decisions there(then).

The claim "Omega has been right 100 times out of 100 times. Using a statistical analysis based on the data, this shows that his success rate is most likely 99% or greater." actually helps us make predictions about the future; about what his success rate will continue to be.

Thus, it's irrelevant that he's had 100% success rate in the past, since that's not the number we need. Rather, it relevant that he will likely have 99% or greater success rate in the future, since that's the number we use to analyze the situation (especially for creating expected values).

How is taking that kind of a gamble the "rational choice"? You're assuming that a choice's value is equal to its expected value until it has been chosen, and I don't think that's necessarily true.

That is true (other than the second part which I don't really get): a choice's value is equal to its expected value. A 10% chance of gaining $10 has a value of $1 for analytical purposes.

Would you spend 1$ for a 99% chance of gaining $100? What about spending $10? $20? $50? $99? $99.50?

Every cost up to $99 given you a positive expected value, making you on average wealthier. Every cost beyond $99 gives you a negative expected value, and the opposite is true (thus it's a bad idea).

Of course, and I think a problem with the original question is that there's too little money involved. My immediate reaction to a scenario like this is to ignore the $1,000 and try to maximize my chances of getting $1,000,000, but that doesn't mean that doing so will net me the most money possible. I presume getting the most money is the goal here, and (pre-Perf's solution) taking both boxes will ALWAYS get you more money than simply taking one.

See my previous post where I analyzed the expected value. Taking both boxes will sometimes get you more money, and on average get you much less money.

 

[Darth_Pugwash]

I fail to see how Omega being correct %100 of the time changes the value of the boxes at the exact second that I choose. It is not trying to trick the alien or anything related. If you believe that your choice will influence the amount of money put in the boxes, choose box B. But otherwise, the money is already in there and will not change, and box B will have either the 1 million or nothing. Again, I'd fully expect to find 1,000 dollars when I choose both boxes, but I know that my choice didn't cost me one million dollars- the alien chose not to put the money in box B beforehand.

So the question instead becomes do you believe that reality changes as a result of your choice?

This argument misses the crux of the issue. From the moment the boxes are created, their contents do not change - this isn't disputed. Neither do they pop in and out of existence as you ponder your decision. Indeed, as you suggest, it isn't your choice at all that puts money in the box - it's the alien's choice; whether he has chosen to categorize you as a one-boxer or a two-boxer.

The crux of the argument is the suggestion - backed up by the alien's 100/100 track record - that the alien can predict your decision with a high degree of accuracy, possibly even 100% accuracy. For the purposes of the question, we can assume a very high probability that the alien knows what you are going to do before you do it - even before you decide to do it. How? High tech scanner? Simulation? Time travel? Doesn't matter, but, hey, who are you to call his bluff?

So for a one boxer, reality isn't changing according to their choice at all. In fact, they may as well not be making a choice - the 'problem' here really is one of free will vs determinism, and since the very premise of the question suggests a deterministic scenario, one-boxing is the only smart way to go. If you one-box, the mil will always have been there, if you two-box, it will never have been there, since the alien will have known wheather you would one or two box when he created the boxes.

Defiant47 actaully explains this better than me and if I was an omni-mega alien I would send him a cookie

 

[Perfection]

Well, I think my RealYou versus SimYou explination works with free will.

 

[Nike Zeus]

I fail to see how Omega being correct %100 of the time changes the value of the boxes at the exact second that I choose. It is not trying to trick the alien or anything related. If you believe that your choice will influence the amount of money put in the boxes, choose box B. But otherwise, the money is already in there and will not change, and box B will have either the 1 million or nothing. Again, I'd fully expect to find 1,000 dollars when I choose both boxes, but I know that my choice didn't cost me one million dollars- the alien chose not to put the money in box B beforehand.

So the question instead becomes do you believe that reality changes as a result of your choice?

Actually, it is indeed possible for your actions to determine the presence of money in the box.
Suppose the aliens make a perfect computer simulation of you (I think this violates the uncertainty principle or something...?) and gives that simulation the two box choice. If the simulation takes one box, money is placed in box B when you play, if the simulation takes box A too, box B will be empty. The only way that the perfect simulation will pick box B is if you will too, so you can never get the extra $1,000. Your decision, made through your simulation, is made before the boxes are filled with money, and therefore can influence the amount of money in box B.
My point is that if we accept aliens who can predict the future somehow, your choice can determine the presence of money in the boxes, even if you pick a box after the money is put in.
Eh, Perfection said it first and better.

 

[Darth_Pugwash]

Haha, at first I didn't quite grasp how that works, but it is actually quite brilliant.

 

[El_Machinae]

Perfection, I think your idea was a really clever one. I especially like the assumption that a SimYou would think that it's you.

 

[warpus]

Well, if I understood the OP correctly then you're supposed to know about the results of the other descisions when you make your descision, so you would need to include the people off to the side.

If you had to make the choice blind though, without knowing about the other results or the alien/omega/flying toaster's uncanny predictive powers, then two boxing would be the smartest move, because you wouldn't have any reason to believe that two-boxing results in an empty box b.

I don't understand how anyone can not understand that you picking two boxes is not going to affect what's in them. Whatever is in there before you make your decision is not going to magically dissappear!

There are two scenarios here:

A) Box B is empty
B) Box B contains a million dollars

This is predetermined before you make your decision.

You making your decision will not affect what's in the boxes. Picking both boxes is the smartest move.

You are all just getting sidetracked and confused by the 100 people standing off to the side. They do not matter, unless the alien is cheating and changing what's in the box after you have made your decision.

In this case, picking 1 box only would be smarter. But if the alien isn't cheating, pick 2 boxes. Your decision isn't going to alter what's already in there.

 

[El_Machinae]

With 100 people on the side, I'm willing to bet that the alien is cheating.

 

[warpus]

With 100 people on the side, I'm willing to bet that the alien is cheating.

Yes exactly!.. I forget if we're told in the OP whether the alien is cheating or not.. too lazy to check.

I would pick only one box if I thought that he was (cheating). Maybe he's cheating by looking into the future? If he can do that - I'm picking one box only.

No cheating = both boxes.

 

[scy12]

Lotteries in real life have negative expected values, so they're usually a bad idea. The cost isn't worth the potential benefit and its likelihood.



Well, you should. The expected value is greater than the cost of the ticket. This means that on average, you stand to gain more if you partake in the lottery. The cost is worth the potential benefit and its likelihood.



On the contrary, your choice is synonymous with reality. If you choose box B, then the money will have been there (not magically spawn), if you choose both boxes, then the money will never have been there. This is because Omega predicted your choice very well. If you were to suddenly change your mind and switch your answer, Omega would have likely predicted that as well.



Sorry for the confusion. This is what I meant:

The claim "Omega has been right 100 times out of 100 times. Therefore, he has had 100% success rate in the past." does not help us analyze the future at all; only the past. It would only be useful if we were to go back into the past and make decisions there(then).

The claim "Omega has been right 100 times out of 100 times. Using a statistical analysis based on the data, this shows that his success rate is most likely 99% or greater." actually helps us make predictions about the future; about what his success rate will continue to be.

Thus, it's irrelevant that he's had 100% success rate in the past, since that's not the number we need. Rather, it relevant that he will likely have 99% or greater success rate in the future, since that's the number we use to analyze the situation (especially for creating expected values).



That is true (other than the second part which I don't really get): a choice's value is equal to its expected value. A 10% chance of gaining $10 has a value of $1 for analytical purposes.

Would you spend 1$ for a 99% chance of gaining $100? What about spending $10? $20? $50? $99? $99.50?

Every cost up to $99 given you a positive expected value, making you on average wealthier. Every cost beyond $99 gives you a negative expected value, and the opposite is true (thus it's a bad idea).



See my previous post where I analyzed the expected value. Taking both boxes will sometimes get you more money, and on average get you much less money.

Lotteries in real life have negative expected values, so they're usually a bad idea. The cost isn't worth the potential benefit and its likelihood.

Actually lets compare the one loterry in real life with the other one.

In real life i have either the choice of buying a ticket which is - 100 or not buying it which is 0

In Alien land i have either the choice to get 100 or to not.



It's a pretty simple equation really. You either choose it being represented as having no negative loss of income. Or you consider it like buying a lotterry ticket from an Income + 100 .

I consider losing 100 on an extremely small luck of gaining more as losing $100 from an income which unexpendedly appeared as having $100 more.



Let's say you got an $100 donation. If you buy a ticket will you consider it an $100 loss or no loss being made ?

So i consider this buying a lottery ticket with your 100$ donation money. Bad investment.

Well, you should. The expected value is greater than the cost of the ticket. This means that on average, you stand to gain more if you partake in the lottery. The cost is worth the potential benefit and its likelihood.

I consider losing free money is a cost worth just as much as losing any other money. The potential value is not worth the cost because the probability of it happening is very small and the value of the ticket is very costly. So you have a very very high probability to be throwing your money to the fire. That is an atrocious investment.


However if the alien allows you to buy multiple tickets the investment may become more probable.

If by just one $100 ticket you have an 0.1% probability of winning , if you buy all 1000 of each ticket you would be guaranteed to win. That would cost you only $100000 which is $900000 cheaper than the one million. So you will earn $900000

And this is indeed one amazing investment.

Stupid aliens.

 

[scy12]

Yes exactly!.. I forget if we're told in the OP whether the alien is cheating or not.. too lazy to check.

I would pick only one box if I thought that he was (cheating). Maybe he's cheating by looking into the future? If he can do that - I'm picking one box only.

No cheating = both boxes.

The alien could be cheating if there is no prediction involved. (And he says there is). The boxes would simply have a mechanism when you select either B or both boxes somehow. (One way is having selection buttons for both boxes where you can select and reselect a box and an OK button that confirms your choice at Box B). Then if you choose B you have a million , if you choose both you get the one thousand. But you don't need an alien with a fancy name like Omega to do this.

 

[Perfection]

I think we operate under the assumption that Omega doesn't cheat, if he did the solution would be quite obvious.

Penn & Teller could definitely pull it off.

 

[warpus]

I think we operate under the assumption that Omega doesn't cheat, if he did the solution would be quite obvious.

Penn & Teller could definitely pull it off.

Well, let's assume that he doesn't cheat, and that he's very very good at predicting people's behavioural patterns.

Case 1 Let's say that he predicts that I'm going to take both boxes. And thus, he does not put the million dollars in box B.
If this happens, and I pick box B only, I get nothing. If I pick both boxes, I get $1,000.

Case 2 Let's say that he predicts that I'm going to take one box. So, he puts the million dollars into box B.
If this happens, and I pick box B only, I get $1 million dollars. If I pick both boxes, I get $1,001,000

In both cases, picking both boxes is more profitable. There is no way around that conclusion.

 

[Perfection]

Well, I think there's a flaw in that argument in that you don't know who you are.

 

[Defiant47]

Well, let's assume that he doesn't cheat, and that he's very very good at predicting people's behavioural patterns.

Case 1 Let's say that he predicts that I'm going to take both boxes. And thus, he does not put the million dollars in box B.
If this happens, and I pick box B only, I get nothing. If I pick both boxes, I get $1,000.

Case 2 Let's say that he predicts that I'm going to take one box. So, he puts the million dollars into box B.
If this happens, and I pick box B only, I get $1 million dollars. If I pick both boxes, I get $1,001,000

In both cases, picking both boxes is more profitable. There is no way around that conclusion.

Well, I think there's a flaw in that argument in that you don't know who you are.

Actually, the problem is that a full statistical analysis of the possibilities yields better results for choosing one box.

Your argument is spawned from the (unconscious) assumption that his prediction rate is exactly useless: i.e. he is as likely to be wrong as he is to be right about your decision - thus both boxes yields $1000 more in both cases. Fact of the matter is that it isn't that simple.

 

[Defiant47]

*snip*

Apologies, but I had problems trying to get your point.

So would you participate in a lottery that provides you with a positive expected value?

So would you try to go for the extra $1000 given that the chances of that happening (getting $1001000) are infinitesimal, and you stand to lose much, much more?

 

[Perfection]

Actually, the problem is that a full statistical analysis of the possibilities yields better results for choosing one box.

Your argument is spawned from the (unconscious) assumption that his prediction rate is exactly useless: i.e. he is as likely to be wrong as he is to be right about your decision - thus both boxes yields $1000 more in both cases. Fact of the matter is that it isn't that simple.

Here's the rub though, this sort of reasoning implies backwards causality; that you can "choose" the prediction Omega will make. My argument dispenses with both backwards causality, and provides the solution that is the proven money winner.

 

[scy12]

Apologies, but I had problems trying to get your point.

So would you participate in a lottery that provides you with a positive expected value?

So would you try to go for the extra $1000 given that the chances of that happening (getting $1001000) are infinitesimal, and you stand to lose much, much more?

So would you try to go for the extra $1000 given that the chances of that happening (getting $1001000) are infinitesimal, and you stand to lose much, much more?

Are you referring to me ?

Apologies, but I had problems trying to get your point.

So would you participate in a lottery that provides you with a positive expected value?

I don't think i was a quite complicated point the one i made.


The choice of either gaining 100$ or trying my luck on an extremely hard to win lotterry is the same as buying an $100 ticket by the money i just received from a donation. And that is not a good investment. I would only participate in a lottery which gave me good odds at winning and a low cost at participating. I think that is the most logical way for one to act.

i also mentioned what if , i had the choice of buying multiple tickets. And as by buying one ticket i have 0.1 chance of winning. If i buy all 1000 ones i would win , no matter what. That would cost me $100000 and as a result i would make an $900000 profit as the prize money is $1000000.

 

[Mise]

If I were to to comone across Omega I would note that Omega has demonstrated a profound accuracy rate. I would presume that he has a sort of simulated version of me. This simulation would be just as capable of making choices as me, taking into the same things into account as me. In a lot of ways, the simulation is me.

Isn't this just a restatement of the fact that Omega's predictions are always correct?

Also, isn't this kind of thinking a self-fulfilling prophecy?

I.e. it's ALWAYS preferable to pick Box B. Therefore I predict that you will pick Box B. I don't need any kind of advanced simulated Perfy to predict that -- it's just the only logical conclusion!