Newcomb's Paradox

Great Debates
121

Indistinguishable has it right. I was only talking about one criterion for causation. This is the point that I was making when I wrote in that post “(3) The criterion for causation above is not the only one that I would accept, but I claim that it applies in this case.” (I probably should have emphasized this even more. Perhaps I should have always used the word “criterion” instead of “definition”.)

At any rate, the criterion I gave was a sufficient, but not a necessary, condition. I acknowledge other criteria that also suffice to imply that causation is occurring. These include criteria that allow us to talk about causation in the absence of willful agency.

But I don’t need these other criteria to establish that causation is happening in the Newcomb scenario. They only expand the class of situations that can serve as evidence of causation. They do nothing to exclude anything that meets the criterion that I gave.

For the purposes of this discussion, all that matters is that all the prior rounds of the game that I observed count as “relevantly similar” to my own round. If they are relevantly similar, then what happened in them counts as inductive evidence for what will happen in my round.

If you disregard the “willfully” bit and the “relevantly similar” bit, then, yes, all that remains is correlation. But notice that it is correlation in all possible worlds. (But, of course, you shouldn’t disregard the “willfully” and the “relevantly similar” bits.)

You anticipated my reply when you wrote to Indistinguishable that

However, I will point out that the kind of cause that I defined was only the kind where my action causes an event of a certain sort. So take you light bulb, for example, and suppose that the only possible situation in which it can turn on is one in which you flip the switch. To apply my definition, you would have to formulate this as follows: “Whenever I perform the act of turning the bulb on, the switch is flipped. Therefore, my act of turning the bulb on caused the switch to be flipped.” Indeed, by hypothesis, flipping the switch was part of my act of turning the bulb on. So I don’t see a problem here, as long as you are willing to consider events to be among their own effects in a trivial sense.

Nonetheless, I admit that causal loops are possible under my definition. Indeed, in the Newcomb scenario, I would say that my choosing only one box causes the predictor to place $1,000,000 in it, and the predictor’s placing $1,000,000 in one of the boxes causes me to choose it. But, again, I think that we deny causal loops only on the basis of empirical evidence. We should adjust our beliefs if there is enough countervailing evidence.

Right. The literature is vast and full of mutually exclusive accounts. That’s why I was wondering which account you subscribe to.

122

I like the line that Gorsnak quoted.

I don’t see how there can be a paradox unless you assume two alternate views of how the predictor works.

If rational actors make rational choices to maximize gain, and the predictor is rational, it is impossible for the predictor to ever put money in Box B[sup]*[/sup]. No paradox because the rational choice is to take both boxes, and you get $1000. The million dollars is a phantom that cannot exist.

It’s no more complicated than this:

Me: If France has never lasted more than a year in a war, I’ll give you a million dollars.

You: The French don’t do that well in wars.

Me: Sorry, no million dollars.

[sup]*[/sup] I don’t mean this in reference to my earlier glib statement about the predictor’s money; this simply means the predictor predicts rational behavior.

But if the predictor analyzes behavioral patterns, or previous events, or a time-portal window, then why must we stick with the idea that you must choose rationally? In this case, there isn’t really a “rational choice” because we are not dealing in the realm of rational actors.

Not necessarily, anyways. A perfectly empirical predictor, when faced with a slew of rational actors assuming it to be rational as well, will consistently leave Box B empty, even if it doesn’t know one bit of logic. I suppose there’s a bit of strangeness in that a rational actor pitted against an unknown entity may do better by assuming the entity to be irrational, but now we’re dealing with incomplete information and more behavioral analysis. It’s just one more step away from the wholly rational player realm.

But the Pasadena game (in which the rational strategy fails merely due to observed behavior) isn’t considered a paradox, is it? It just means that the world is not made up of rational actors, which is hardly a surprise.

123

I suppose I lack (well, have consciously shed) the intuition that the past is determined in a way which the future is not. To me, the unknowns of the past are just as indeterminate as the unknowns of the future, and the knowns of the future are just as determinate as the knowns of the past, and so on.

I think it’s easy but misguided to adopt the view that the past is necessarily closed, fixed, determined, whatever, while the future, in contrast, is a great big open indeterminate free mystery. If we just start off with the past as being “those states of the world with lower time coordinates” and the future as being “those states of the world with higher time coordinates”, there’s a perfect symmetry between the two until we adopt some symmetry-breaking principle. And while various symmetry-breaking principles do seem attractive as truths of our universe, we should always keep in mind their contingency, and be willing to discard them when evidence arises which is better explained without them.

I think it’s attractive to say the past is already determined and the future is a great big open mystery because one thinks of everyday examples where one has (near) certain knowledge of the past but very little knowledge of the future. For example, because I have a memory right now of John having eaten cereal for breakfast, I am very confident that John did, in fact, have cereal for breakfast in the past. However, I do not have evidence before me right now which allows me to state confidently whether or not John will eat cereal for breakfast tomorrow. Because I see smoke right now, I am confident there was a fire here earlier (“where there’s smoke, there was fire”). But I don’t know if there will be fire here again later.

Very well. There are laws which allow us to determine information about the past from information about the present. But the situation is symmetric. The contrapositive of every such law is one which allows us to determine information about the future from information about the present. Because John isn’t eating cereal today, I am confident that I won’t later on remember him as having eaten cereal today. Because there is no fire here right now, I am confident that there won’t be any smoke here later today. The same techniques that would allow us to get certain knowledge about the past would also allow us to obtain certain knowledge about the future. So the presence of determinateness, in that sense, is not unique to the past, but rather found in both the past and the future.

And the presence of indeterminateness, I would say, is not limited to the future. True, given the particular system of constraints on the history of the universe which I consider to be the physical laws, I have no way of knowing today what the result of a coin flip conducted tomorrow will be. But we can also suppose that a coin was flipped yesterday, with no one watching and leaving no record of its outcome in any way. I have the same difficulty knowing the outcome of this past flip as I have of knowing a future flip. The presence of indeterminateness is thus not unique to the future, but rather found in both the past and the future. The dual of the random generation of information tomorrow is the erasure of information yesterday.

Now, as a matter of contingent fact, I guess we tend to believe that physical laws are such that a large proportion of the information about the past is recoverable from the information about the present but only a small proportion of the information about the future is recoverable from the information about the present. (I.e., there is a lot of random generation of information but not so much erasure of information). Very well. But this is not, I would say, part of the essential nature of the past or the future.

From my perspective, when faced with the ultra-accurate predictor and his boxes, I have to ask myself “What do I know?”. I know that the contents placed in the boxes in the past correlate in a particular way with the actions I take in the future. Beyond that, I know nothing; beyond that, the past is as indeterminate to me as anything in the future can be. If asked, then, which action I would like to take regarding the boxes, I would be stupid not to reply with the action which I know, as a result of my confidence in the ultra-accurate predictor, to result in the greatest gain for me.

Anyway, this is just some sort of peek into the perspective I’m coming from.

124

Oh, also, I guess I want to say that I see the sort of correlation we would call ultra-accurate prediction as just as good as backwards causality. If one wants to, for some reason, refuse to describe it that way, very well, but this reluctance with terms would not be good grounds upon which to modify one’s actions. If some actions are rational in a situation with backwards causality as the source of the predictor’s accuracy, then they would be just as rational, I want to say, in a situation where the predictor is just as accurate but this accuracy is attributed to any other mechanism.

125

I don’t have any particular views on causality, nor have I done any substantial reading in the field. At first blush the Lewisian counterfactual account appeals more to my philosophical intuition, but that’s worth no more than the contents of the opaque box when it’s my turn to choose.

Frankly, this whole side discussion is missing the point of the problem. The problem as presented is interesting to people studying game theory and rational choice for two reasons, neither of which has anything to do with backwards causation. The first reason is that a great many people react to the problem with a very strong inclination to choose the single box (to the point of arguing for crazy stuff like backwards causation and indeterminacy of the past! :wink: ) This is interesting because it runs counter to one of the most basic principles in game theory, and becomes more interesting as you learn that it’s extremely difficult to convince people that they’d be better off taking both. So there’s something interesting going on in psychological terms - given the prevalence and tenacity of this one-box inclination it can’t be passed off as a simple careless sort of irrationality, but there must be something about the way people actually reason when making decisions about what to do that works for them in real world situations but screws up in this odd hypothetical. So how do people actually reason when they make this sort of decision?

The second reason is the question of whether it can be rational to behave irrationally (in which case is it actually irrational?) In rational decision theory, by definition the rational choice is the one with the greatest expected utility (utility here being presented as dollars as a shortcut, as is usually the case in these hypotheticals). So how can we explain how it can be rational to adopt a course of action that will make one worse off.

This question also comes up in conjunction with a hypothetical known as “Centipede”, which hasn’t any possible connection to backwards causation. In Centipede (so-called not because of any relation to Chilopoda, but because of the way the game is diagrammed) a benefactor places $100 on the table in singles. Two players, ideal rational agents both, take turns. Each turn consists of taking either $1 or $2. If the player takes $1, the game continues and the other player takes a turn. If the player takes $2, the game ends and the benefactor takes any remaining money.

So what do ideal rational agents do in this situation? The first player takes $2 on the first move, and the game ends. WTF? Why on earth wouldn’t the players cooperate by taking $1 each the whole way through? They’d both be better off! Ah, but on the next to last move, with only $2 left on the table, player A is going to take both dollars, coming out with $51 to player B’s $49. (Remember, dollars are substituting for utility here, so no complaining about player A wanting to be fair, etc, that’s all supposed to be factored in to utility.) Knowing that A is going to take the last $2 if faced with that decision, B will take $2 when there are $3 left on the table, leaving B with $50 to A’s $49, and more importantly leaving B better off than if he takes just $1. Knowing that B will take $2 given the chance at the $3 point, A will take $2 the prior turn. And so on, right down to the very first turn.

Here again, an “irrational” agent could do much better, spinning the game out long enough to get half or nearly half of the available money. These questions are of interest because they illuminate potential issues with the basic presumptions of game theory and its conceptualization of rational agents.

So, that said, if you tell me with 100% certainty that backwards causation is going on in the Newcomb problem, I tell you that the Newcomb problem is now completely uninteresting from the point of view of rational decision theory, because it’s then just a straight choice between $1000000 and $1000. It’s only an interesting problem if we have ordinary, garden-variety prediction going on.

126

I wouldn’t say a single “irrational” agent would do any better in the centipede game, since his “rational” opponent would just take two bucks at first opportunity and end the game, same as before (at least, as long as his “rational” opponent is constantly acting on the assumption that everyone else will make “rational” decisions at every future opportunity). Two irrational players, though, yeah, they might do much better, which is somewhat interesting. But you’d also do alright with two rational agents with the ability to form a cooperative contract. Seems to me, when we say that two irrational players can do much better than two rational ones, we’re just noting that, with all their unpredictable irrationality, they might as well as anything else stumble upon the same solution that two contracting rational agents would. What’s going on isn’t really a failure of “rationality”, even with the scare quotes, but a failure of lack of ability to cooperate, a Prisoner’s Dilemma type thing.

127

A single irrational agent paired with a rational agent both do fine, because the rational agent knows the irrational agent isn’t rational, and so will spin the game out for a while, gambling that the irrational agent will continue to take $1 at a time.

There is a bit of cooperation stuff going on, but unlike Prisoner’s Dilemma scenarios, the “problem” in Centipede doesn’t go away when you iterate the game. If you iterate PD indefinitely, other strategies besides straight defection become rational (Tit for tat, most famously). The actual “answer” to why the results of Centipede are counterintuitive lie in the presumption of common knowledge of rationality (i.e., each player knows the other is an ideal rational agent) which under orthodox game theory prevents the players from using “irrational” moves to signal the other player to cooperate. It’s ultimately kind of tedious and technical, and purely an artifact of the characterization of ideal rational agents. However it does force one to think about the value of the specifics of that characterization.

My point in bringing it up is just to help illustrate the point of the Newcomb Paradox.

128

Ah, ok, the rational agent knows the irrational agent isn’t rational. Like I said, I’d been assuming the rational agent constantly assumed everyone else would make “rational” decisions at every future opportunity.

Just a minor terminological point, but I’m used to “common knowledge of” X denoting not just that everyone knows X, but also everyone knows that everyone knows X, everyone knows that everyone knows that everyone knows X, etc. I assume that’s what you meant, though.

Interesting stuff, to be sure. The discussion of idealized rationality and its complications does offer one perspective on “the point” of Newcomb’s Paradox, but I would say there are other aspects of Newcomb’s Paradox worth discussing as well. But, I guess, yeah, I do take the perspective that the problem ends up becoming some trivial thing, where one would be stupid not to take the one box, because of effects in play at least functionally equivalent to backwards causality. I would say ultra-accurate “garden-variety” prediction is such an effect, though.

129

For the sake of discussion, let’s suppose we turned Newcomb’s Paradox around. There are two boxes, capable of being wired directly up to your bank account, and you can choose to either activate both or just the first one. The day after your choice, someone decides to assign money to the boxes; he’ll definitely put a small amount of money in the second box, and he’ll put a large amount of money in the first box if and only if he thinks you won’t activate the second box. He is generally extremely accurate at determining what people’s past choices were, though it’s not specified what his methods for doing so are.

In terms of choosing boxes to activate, what should you do? If you feel the situation differs significantly from its (almost exactly) time-reversed dual, what is the nature and source of this difference?

130

I realized a flaw in the causation criterion I gave back in post #85. I don’t think it affects the discussion of Newcomb’s paradox, though. My original criterion was this:

This criterion has the unfortunate consequence that an inevitable event is caused by anything I do. For example, my brushing my teeth causes the Sun to rise the next day because, in all relevantly similar situations in which I brush my teeth, the Sun rises the next day. Note that this problem doesn’t affect the application of my criterion to the Newcomb scenario. This is because the placement of the $1,000,000 in the second box isn’t inevitable—sometimes it happens and sometimes it doesn’t. Nonetheless, I think I can deal with inevitable types of events by adding a clause to the effect that, in some relevantly similar situation in which the action is not performed, no event of that type happens. So the revised criterion is now as follows.

I say that I cause a D-event if I willfully perform an action A such that, (1) in all relevantly similar situations (real or merely possible) in which A is performed, a D-event occurs, and (2) there is a relevantly similar situation in which A is not performed and no D-event occurs.

Of course, one naturally begins to suspect that more and more counter-examples will force me to add more and more conditions until the criterion sinks under its own weight. But for now I don’t see any problems.

131

This seems like too narrow a definition of “rational”. Altruism, in which both players agree to be nonselfish and work for the greater good, could be considered “global” rationalism, in that it can see outside the boundries of the game itself and arrive at a cooperative strategy that is “irrational” if you consider only the logic of the game itself. The situation described occurs if one or the other players is so greedy that they’ll sabatoge the game in a futile attempt to gain a short term advantage.

132

There’s absolutely nothing said one way or the other about altruism by the standard definition of rational in use here. If an actor places value on the good of others (i.e., is altruistic), then the good of others factors in to what constitutes utility to her. Then it becomes the case that by maximizing her own utility she’s actually working towards the good of others. If you like, rational choice theory is content-neutral with regards to ends, and speaks only of how to rationally adopt means towards whatever ends you have.

This is why it’s important in discussing Centipede to be clear about whether the dollars on the table are standing in for utility, or are actually just dollars. If they’re actually just dollars and I’m an ideal rational agent playing against my friend who is likewise an ideal rational agent, we can clean out the benefactor - because part of my utility is that I have a preference that my friends do well, and part of my friend’s utility is a preference that I do well. As soon as we place any amount of value on each other coming out ahead, it’s trivially simple for ideal rational agents to cooperate in Centipede.

133

The difference is that you lose the condition in the original scenario that “the boxes already have the money in them, or they don’t, and nothing the predictor can do can change that when you make the decision.” As that condition was the basis for the “choose both boxes” argument, there is now no contradiction, and all rational agents will choose only the single box.

To me, with my background in logic, a paradox shows that there is a flaw in the premesis, in the basic scenario as presented. Newcomb’s Paradox is a argument that perfect prediction is impossible.

134

Why do you take that route instead of saying the existence of the paradox shows that the “dominance strategy” is wrong, or that it shows that the other strategy (I forget what it’s called) is wrong?

-FrL-

135

But Newcomb’s Paradox doesn’t mention a perfect predictor. It only mentions a predictor who has been right so far. And even that isn’t necessary: nothing changes if the predictor was wrong once, or even several times, as long as he has been right most of the time. He could be flipping a coin for all we know; he’s just gotten really lucky so far. (Or maybe he does this on millions of planets at once–as soon as he’s wrong, that planet never hears from him again; on the planets he goes back to, he always has a perfect record.)

ETA: Yeah, and what Frylock said. There’s nothing impossible here–just two apparently logical arguments that reach opposite conclusions.

136

The paradox only occurs if the selector seriously believes that the predictor is perfectly accurate, to the degree that waffling deliberation on the subject now can “change” the predictor’s actions in the past. If the selector has no such belief, then they rationally would have to choose both boxes, since if they ponder the situation and convince themselves to just grab one, that’s not going to put money in it that wasn’t there anyway.

137

Okay so, what you may have missed somehow is, lots of people–smart people, who have thought this through–think you’re wrong that it’s “obvious” that one should take both boxes. And lots of people–smart people who have thought this through–think you’re right.

Again, it’s a bit problematic to call this a “paradox” but if there’s something like a paradox involved here, it is in that very fact–that everybody thinks one answer or the other is “obvious,” even after seeing and understanding very well constructed arguments from those with whom they disagree.

-FrL-

138

No, that is the paradox. Everyone who has made the rational decision so far has received less money (utility) than everyone who has made the irrational decision. So is the irrational decision now more rational?

139

Yah, and how many of those arguments on either side are actually waffling about whether the predictor is perfectly accurate (as in, your current choice directly effects the previously-determined contents of the boxes)? If it is perfectly accurate, you pick one box. If it’s not, you pick both. Simple.

140

Very few. It is understood by people who argue both sides of the issue that the predictor is not necessarily perfect, and uses only natural means of prediction.

-FrL-

(Well, the problem has been stated in different ways at different times, but the standard way of stating it is as I’ve just specified, and smart people who have thought it through have taken that way of stating the problem as their starting point. It is taken as a given that the predictor is not a supernatural or perfect predictor. And people still think it’s “obvious” that you should take both boxes. I myself think you should take both boxes, though I clearly no longer think it’s “obvious.”)