You need to do EV for all conditions to compare them. Give me actual numbers for each outcome and we can run the numbers. Maybe start at the actual problem of a near perfect predictor.
Possible outcomes are now:
Less than ten fingers went one box was correctly predicted, got a million.
Less than ten fingers went two box, correctly predicted, got 1000.
Less than ten fingers went one box, incorrectly predicted, and got nothing.
Less than ten fingers went two incorrectly predicted and got 1.001M.
Ten fingers went one box, was correctly predicted, got a million.
Ten fingers went two box, correctly predicted, got 1000.
Ten fingers went one box, incorrectly predicted, and got nothing.
Ten fingers went two, incorrectly predicted, and got 1.001M.
If you want EV for less than ten vs ten you look at EV for the first four added up vs the last four added up. You need numbers for all outcomes to do that.
Actually no we don’t. More to the point they are both caused by the same thing.
Imagine I as predictor can know by profiling who thinks that CDT is always the right method and who is EDT in their decision making process. From this thread those cognitive approaches do seem to be very strongly held! Few who are one are able to be convinced that the other makes more sense.
That information will cause me as predictor to:
For the CDT folk - place nothing in the opaque box and cause those CDT folk to pick taking both boxes, my prediction being correct.
For the EDT folk - place a million in the opaque box and cause those CDT folk to just take that box, them getting a million, my prediction correct.
Yup and there is a causal between being CDT type person and not getting a million, and a casual relationship between being a CDT type person and taking two boxes. But that doesn’t mean there’s a casual relationship between taking two boxes and not getting a million, that’s a fallacy.
Suppose we are in the alternative reality when the “Type A” hypothesis is correct. In this reality all of those experiments carried out in the first half of the 20th century showed conclusively there was no casual relationship between smoking and lung cancer. e.g. if you are a type A person who starts smoking later in life, you have no elevated chance of lung cancer after you start smoking compared to before (statsicially considering how chances of cancer increase with age). Carcinogens cannot time travel the relationship must be correlation NOT causation. So should the government put warning labels on cigarettes saying they cause cancer? Of course not! Just because being a particular type of person causes two different things, it doesn’t mean those two things are causally related
And as you don’t have those numbers you can only consider the EVs of those things separately. And the EV increase caused by chopping off your finger is much greater than the EV increase of leaving box A.
Neither is good advice. Just because the EV maths is correct it doesn’t make it anything more than a meaningless number.
Walking into a room with Elon Musk might make your average net worth suddenly billions of dollars, and that is undeniably the correct way to calculate a mean, but that doesn’t make it anything other than a meaningless number (it will also mean you may have to talk to Elon Musk which makes cutting off your finger seem preferable;) )
EV analysis don’t work like that. If I don’t have those numbers I cannot do a comparison of EVs. Period.
Really beating a horse that was never alive here. But still consider a population in which 90% of the population is missing at least one finger. Roughly 90% of those winning a million dollars are missing at least one finger. Roughly 90% of those winning 1000 are also. And?
In terms of the rest, we are repeating ourselves.
But let’s emphasize what we can agree on: in this thought experiment those who would have their own device pick the opaque box only will likely get a million and those who would pick two boxes will likely get a thousand. If at the last minute an opaque only person was coerced, threatened with violence to self or loved ones say, to take both boxes, they would get 1.001M and if the person who was the two box person was similarly coerced to just take the opaque box they would leave with nothing.
If you were a person that the predictor had predicted to be one box taking the additional thousand would gain you more money, but if you are someone who would do that the predictor would have classified you as two box. So those who do that will only get a thousand.
If you do take only one box the odds are great that the predictor had predicted you were going to take one box, and you will get a million. Even if you had been a late converter to that thought process.
Your choice is not causing the outcome but functionally there is little difference.
It’s the premise of the thought experiment. However much proof is needed to convince you that there is no trick, just a very good predictor, has been provided to you.
There’s no way for someone predicted as a two box person to win. And there is no casual relationship between being predicted as a two box person and taking the first box
You may or may not be a two box person. But when your in the room take the good damned 1000 dollars! There is no downside!
By all means do other stuff to be predicted as a one boxer, like publicly announcing you are leaving your change on the counter every time. That might make you be predicted as one boxer. Leaving the first box will absolutely definitely not do so.
Positions in this thought experiment having been well expressed by now, let’s modify the experiment.
We do not trust the set up. The host says there is no trickery involved but we are, understandably, not convinced.
We do believe that the previous contestants were real people, randomly selected, not confederates. Each of them picked, close to 50 50, one or both boxes. And were told that the predictor got it right. Got a thousand or a million respectively. Maybe one not? Over a thousand players before you. But this prediction bit? You are cynical.
I’d do what I said previously: take one box. 1,000 in a row is only possible by shenanigans or precognition. Either way, the game ensures that choosing one box gives the most $$$.
That seems very small amount of evidence to start considering a super natural explanation, especially when the thing being predicted is “will someone refuse to take a guaranteed, real, 1000 dollars they can see in front of them, when there is no downside to taking it”. 1000 out of 1000 seems a lucky but not preposterous result, given you don’t know what those other 1000 people were told and how many (if any) left box A. You also don’t know who those 1000 people were, what if they were chosen from the poorest areas of Lagos where 1000 bucks is more money than they have seen in their life?
Shenanigans is always an option of course, there are countless conjurers tricks that could be used to fill or empty box B after the choice is made. But they are extremely unlikely to cheat in order to give you a million dollars, rather than vice versa!
I’m not sure what the difference between this and the OP. But the answer is the same. Let’s consider this from the point of view of the host. What is his decision matrix?
Subject chooses to take box A. They can…
Give them a 1000 bucks. They lose 1000. But keep their 100% record intact (we don’t know how much value this has to them but obviously some)
Cheat and take away a million bucks. Same as first option. They could do this but why would you even risk it? Why not just never put a million bucks in the box?
Cheat and give them a million bucks. This would mean they lose a million and their record. Obviously this will not happen.
Subject chooses to leave box A. They can…
Give them an empty box. The don’t lose any money. But they lose their 100% record.
Cheat and take away a million bucks. Again, same as first option. They could do this but why would you even risk it? Why not just never put a million bucks in the box?
Cheat and give them a million bucks. This would mean they lose a million dollars but keep their record. This could be worth their while, but only if keeping their record (dishonestly) is worth a million bucks. This seems unlikely.
So viewing the hosts options, it’s clearly you should take box A, take the 1000 bucks. In all likelihood you are never getting the million bucks whatever you choose. Not because of some deep philosophical nature of the universe and predestination. But because people don’t like giving away a million dollars!
I’m more likely to take the single closed box in this situation. If i believe the thousand people are not confederates and each got what was promised, i think the odds are excellent that i will, too. And if I’m wrong, oh well, i get a nice souvenir box.
What’s the definition of “confederate”? If I’m not buying the prediction. Then I’m not buying 50% of one boxers, if they are not in some way coached and in league with the host.
100% prediction seems entirely plausible, if lucky. Getting even close to 50% of people to voluntarily leave 1000 dollars they can see in front of them, knowing it will make no difference the outcome, seems far more suspicious to me.
Again it’s all well and good discussing this as a thought experiment but when people are in the room and it’s “take this 1000 you can see in front of you, or not. And there’s no downside to taking it.”. An overwhelming number of people are taking the box.
Fundamentally I have no reason to think that whatever caused those people to leave the box and the host to give them a million dollars, applies to me. It might do, but is it worth a 1000 dollars to find out? I’m not so sure. I am basically betting 1000 dollars in the fact that this is a crazy multi billionaire willing to give away millions of dollars to anyone, not a scam of some kind.
The question is not “what makes you special” it’s “what makes those 500 people (compared to the other 6 billion people on the planet, who have not received a million dollars from the host) special”
This is fascinating to me. How about making it less fantastical: $10 or $10,000. Game show level. Strange game show but still. American game show audience that you are part of.
Seeing nearly every person who took the one box getting the big prize and nearly every person who took the open box also get the small prize. Would you still go with both boxes?
To @puzzlegal my point then continues … by what we have observed the two circumstances are functionally the same. In fact for you they are the same - you already refuse to trust that the predictor is not cheating somehow no matter how much evidence is offered; it is in too much discordance with what should be possible by your models of the universe. If this universe predictable and consistently behaves the same as if there was causation by the choice made, then there is no pragmatic difference between the circumstances.
Though that changes both of our cost/reward matrix. I’m now betting 10 dollars someone is legitimately giving away 5 million, by giving anyone who wants to leave 10 bucks 10000 dollars. Thats a different bet to betting 1000 dollars someone is legitimately giving away 500 million by giving anyone who wants it 1000000.
The first bet i’m probably taking. Sure it’s probably a scam and I’m not getting 10000. But it’s 10 bucks who cares? Second bet probably not. 1000 bucks is not life changing but it’s still 1000. I’d take the guaranteed 1000 over maybe getting a million if this isn’t a scam.
