### Re: decision theory papers

On 23-Apr-02, Wei Dai wrote: I think it's pretty obvious that you can't predict someone's decisions if you show him the prediction before he makes his final choice. So let's consider a different flavor of prediction. Suppose every time you make a choice, I can predict the decision, write it down before you do it, and then show it to you afterwards. Neither the infinite recursion argument nor the no fixed point argument work against this type of prediction. If this is actually possible, what would that imply for free will? If you are an AI, this would be fairly easy to do. I'll just make a copy of you, run your copy until it makes a decision, then use that as the prediction. But in this case I am not able to predict the decision of the copy, unless I made another copy and ran that copy first. The point is that algorithms have minimal run-time complexities. There are many algorithms which have no faster equivalents. The only way to find out their results is to actually run them. If you came up with an algorithm that can predict someone's decisions with complete accuracy, it would probably have to duplicate that person's thought processes exactly, perhaps not on a microscopic level, but probably on a level that still results in the same conscious experiences. So now there is nothing to rule out that the prediction algorithm itself has free will. Given that the subject of the prediction and the prediction algorithm can't distinguish between themselves from their subjective experiences, they can both identify with the prediction algorithm and consider themselves to have free will. So you can have free will even if someone is able to predict your actions. I think free will is an incoherent concept and useless as a basis for aruguments about how the world works. Most people would say that the existence of a deterministic algorithm which modelled and predicted one's decisions would contradict free will. On the other hand, they would not accept a randomness in the decision process as free will either. Both viewpoints neglect the fact that a person is in almost continuous interaction with their evironment and to regard them as isolated computers is only an approximation. I suppose that the brain's function is something close to deterministic chaos. One's behavoir is unpredictable, to some degree, because the brain has a large amount of stored information that interacts with the stream of new information that has provoked the need for decision. All most all of this is below the level on consciousness. Although the brain must be almost completely deterministic, it is certainly possible that quantum randomness could play a part. The more obvious fact that you can't predict your own actions really has less to do with free will, and more with the importance of the lack of logical omniscience in decision theory. Classical decision theory basically contradicts itself by assuming logical omniscience. You already know only one choice is logically possible at any given time in a deterministic universe, I don't understand logically possible. Decision theory at most provides a quantification that identifies a certain choice as logically optimum and this optimality is only probabilisitic. But the optimality is relative to some value system of the decider. The value system is not logically entailed by anything in decision theory. and with logical omniscience you know exactly which one is the possible one, so there are no more decisions to be made. But actually logical omniscience is itself logically impossible, because of problems with infinite recursion and lack of fixed points. That's why it's great to see a decision theory that does not assume logical omniscience. So please read that paper (referenced in the first post in this thread) if you haven't already. Brent Meeker Every complex problem has a solution that is simple, direct, plausible, and wrong. -- HL Mencken

### Re: decision theory papers

On Wed, Apr 24, 2002 at 04:51:18PM +0200, Marcus Hutter wrote: In A Theory of Universal Artificial Intelligence based on Algorithmic Complexity http://www.idsia.ch/~marcus/ai/pkcunai.htm I developed a rational decision maker which makes optimal decisions in any environment. The only assumption I make is that the environment is sampled from a computable (but unknown!) probability distribution (or in a deterministic world is computable), which should fit nicely into the basic assumptions of this list. Although logic plays a role in optimal resource bounded decisions, it plays no role in the unrestricted model. I would be pleased to see this work discussed here. I'm glad to see you bring it up, because I do want to discuss it. :) For people who haven't read Marcus's paper, the model consist of two computers, one representing an intelligent being, and the other one the environment, communicating with each other. The subject sends its decisions to the environment, and the environment sends information and rewards to the subject. The subject's goal is to maximize the sum of rewards over some time period. The paper then presents an algorithm that solves the subject's problem, and shows that it's close to optimal in some sense. In this model, the real goals of the subject (who presumably wants to acomplish objectives other than maximizing some abstract number) are encoded in the environment algorithm. But how can the environment algorithm be smart enough to evaluate the decisions of the subject? Unless the evaluation part of the environment algorithm is as intelligent as the subject, you'll have problems with the subject exploiting vulnerabilities in the evaluation algorithm to obtain rewards without actually acomplishing any real objectives. You can see an example of this problem in drug abusers. If we simply assume that the environment is smart enough, then we've just moved the problem around. So, how can we change the model so that the evaluation algorithm is part of the subject rather than the environment? First we have to come up with some way to formalize the real objectives of the subject. I think the formalism must be able to handle objectives that are about the internal state of the environment, rather than just the information the subject receives from the environment, otherwise we can't explain why people care about things that they'll never see, for example things that happen after they die. Then we would invent a universal decision algorithm for acomplishing any set of objectives and show that it's close to optimal. This seems very difficult because we'll have to talk about the internal state of general algorithms, which we have very little theory for.

### Re: decision theory papers

H J Ruhl wrote: In any event in my view your argument makes many assumptions - i.e. requires substantial information, isolates sub systems, and seems to allow many sub states between states of interest all of which are counter to my approach. Imo the assumption of a limited information exchange between an intelligent being and its environment (nearly isolated subsystem) is unavoidable, maybe even the key, to DEFINE (intelligent) beings. Of course the details of complete isolation in the intervals [t,t'] was just to illustrate the point. Hal Finney wrote: So I don't think the argument against predictability based on infinite recursion is successful. There are other ways of making predictions which avoid infinite recursion. If we want to argue against predictability it should be on other grounds. I don't talk about how to physically implement this infinite recursion, e.g. brute force crunching a particle-level simulation and I don't argue against predictability in general. But if you assume that a part of the brain can perfectly predict the outcome of the whole brain, then this is a mathematical recursion. The same holds if you take an external device predicting the brains behaviour and telling it the result beforehand. Then you have to predict brain + external device on a third level and so on. This is again a mathematical recursion. Before discussion how this recursion could physically be realized we have to think whether this recursion HAS a fixed point at all - and this is already not always the case. The free will-computability paradox has actually nothing to do with computability. You could also formulate it if you want to as free will - brain can be described by a mathematical function. Wei Dei wrote: I think it's pretty obvious that you can't predict someone's decisions if you show him the prediction before he makes his final choice. For me its pretty obvious too, but as this thread discussing this paradox got longer and longer I got the impression that it is at least not obvious to all members of the list. I liked the paper of David Deutsch, although his assumptions in deriving decision/probability theory from QM could have been a bit more explicit, mathematical and clearly stated. Although quite different it reminded me on the derivation of probability theory from Cox axioms. I scanned the article by Barton Lipman but I'm not much interested in rational decisions based on logic, because I think there is no necessity to refer to logic at all when making rational decisions. In A Theory of Universal Artificial Intelligence based on Algorithmic Complexity http://www.idsia.ch/~marcus/ai/pkcunai.htm I developed a rational decision maker which makes optimal decisions in any environment. The only assumption I make is that the environment is sampled from a computable (but unknown!) probability distribution (or in a deterministic world is computable), which should fit nicely into the basic assumptions of this list. Although logic plays a role in optimal resource bounded decisions, it plays no role in the unrestricted model. I would be pleased to see this work discussed here. There is also a shorter 12 page article of this 62 page report available from http://www.idsia.ch/~marcus/ai/paixi.htm and a 2 page summary available from http://www.idsia.ch/~marcus/ai/pdecision.htm but they are possibly hard(er) to understand. Best regards Marcus

### Re: decision theory papers

Dear Everyboy on the Everything list, After having followed the discussions in this list for a while I would like to make my first contribution: The paradox between computability and free will vanishes through careful reasoning: That a part of the universe is computable is defined as follows: Assumption 1: Given a box (part of the universe) in state s at time t we can compute the next (or some farther future) state s' at time t't IF there is no interaction of the box with the rest of the universe during time t...t'. Without this independence assumption in time-interval [t,t'] the possibility of correct prediction cannot be guaranteed! Assumption 2: Assume that the brain is computable. It gets input x at time t and computes action y at time t'. During the thinking period [t,t'] it is completely separated from the environment. After input x the brain B is in a state s and Assumption 1 applies, i.e. we can compute, say with algorithm A:X-Y, the brains decision y. We can't tell the brain in the period [t,t'] this decision without violating Assumption 2. Assume we allow this interaction, then the brain B' maps input (x,y) to an action y', which is possibly different from y. There is no contradiction, since A maps X to Y whereas B' maps X x Y - Y, so these functions have nothing to do with each other. Assume now that a part B2 of brain B=B1 can simulate B1. Since B2 is assumed to behave identically to B1 it must itself contain a part, say B3 which simulates B2, etc. We have an infinite recursion as already mentioned by Brent Meeker in this thread. The first question is NOT WHAT the output of B is and whether it is finitely computable but whether this infinite recursion has a value (is mathematically sound) AT ALL! What we need is a fixed point. Insert a function A into brain B (as a possible candidate for B2) and look whether B computes the same function. If yes, A (and B) is a fixed point of the recursion. If such a fixed point exists (and is unique) we may define the value of the infinite recursion as this fixed point value. Finally we would have to check whether this fixed point can be found by a finite algorithm. It is well known that not every recursion y=f(y) has a fixed point. The paradox in our case is just that we implicitly assumed the existence of a (unique) fixed point. The paradox resolves by noting that this fixed point simply does not exist. Sometimes fixed points can be found by iteration. You start with some value y1 for y and iterate y2=f(y1), ..., yn=f(y_n-1). If the limit y_\infty exists, then it is a fixed point. Assume our function B as act 1 if B2 predicts 0 and vice versa. This is the paradox discussed in this thread. In this case y_n=1-y_n-1 oscillates and y_\infty does not exist. (In the case of a binary decision this proofs that a fixed point does not exist). We are talking about non-existent fixed-points. We simply cannot construct a self-contradictory brain from Assumptions 1 and 2. Marcus Hutter P.S. I maintain the Kolmogorov complexity mailing list. Maybe you want to have a look at http://www.idsia.ch/~marcus/kolmo.htm Dr. Marcus Hutter, IDSIA Istituto Dalle Molle di Studi sull'Intelligenza Artificiale Galleria 2 CH-6928 Manno(Lugano) - Switzerland Phone: +41-91-6108668 Fax: +41-91-6108661 E-mail [EMAIL PROTECTED] http://www.idsia.ch/~marcus

### Re: decision theory papers

Dear Marcus: I have some basic issues with your post. The idea I use is that the basis of what we like to think of as our universe and all other universes is There is no information. This is not really an assumption in the sense that you can not extract anything from nothing as one usually extracts consequents [data snips] from the information in some assumption set. Rather it is more a principle that one attempts to sustain while building dynamic universes. To initiate this one can notice that no information has two simultaneous yet completely counterfactual expressions - all information and no information - and further that there must be a dynamic boundary between them - this latter part from the idea that no information requires no selection, that is both expressions must exist and the all information expression contains its counterpart in an infinite nesting with itself - this because it is the ensemble of all counterfactuals which must include both itself and the no information expression. One now simply explores the dynamic of this boundary [the dynamic comes from the need to avoid selection - no fixed boundary, and the dynamic is random for the same reason - no selected pattern] while sustaining the balance of counterfactuals. While this approach allows for no rationale for why we are in this particular universe why should there be one? Ours is just one of an uncountable set that contain large sub structures and can transition to a next state while sustaining most of them. In any event in my view your argument makes many assumptions - i.e. requires substantial information, isolates sub systems, and seems to allow many sub states between states of interest all of which are counter to my approach. Hal

### Re: decision theory papers

Welcome to the list, Marcus. I think your analysis is very good. For some predictions there might be a fixed point; for example, I can predict that I will not commit suicide in the next 5 minutes. Even knowing that prediction I will not try to contradict it. For other things there might not be a fixed point; for example whether I will order chicken or fish at the restaurant tonight. Knowing a supposed prediction I might choose to do the opposite. Another point is illustrated by your example of using iteration to find fixed points. That is that there are more ways of predicting the future than brute force crunching a particle-level simulation. In physics we can make many useful predictions without actually calculating things down to the particle level. For example there are conservation laws that can be used to put sharp constraints on possible future states of a system. It is possible that analogous laws in a deterministic universe might allow for predictions of some aspects of future states of a system without having to go through and calculate the system at a microscopic level of detail. This avoids the problem of infinite recursion since we are using higher level laws to make predictions. So I don't think the argument against predictability based on infinite recursion is successful. There are other ways of making predictions which avoid infinite recursion. If we want to argue against predictability it should be on other grounds. Hal Finney

### Re: decision theory papers

I think it's pretty obvious that you can't predict someone's decisions if you show him the prediction before he makes his final choice. So let's consider a different flavor of prediction. Suppose every time you make a choice, I can predict the decision, write it down before you do it, and then show it to you afterwards. Neither the infinite recursion argument nor the no fixed point argument work against this type of prediction. If this is actually possible, what would that imply for free will? If you are an AI, this would be fairly easy to do. I'll just make a copy of you, run your copy until it makes a decision, then use that as the prediction. But in this case I am not able to predict the decision of the copy, unless I made another copy and ran that copy first. The point is that algorithms have minimal run-time complexities. There are many algorithms which have no faster equivalents. The only way to find out their results is to actually run them. If you came up with an algorithm that can predict someone's decisions with complete accuracy, it would probably have to duplicate that person's thought processes exactly, perhaps not on a microscopic level, but probably on a level that still results in the same conscious experiences. So now there is nothing to rule out that the prediction algorithm itself has free will. Given that the subject of the prediction and the prediction algorithm can't distinguish between themselves from their subjective experiences, they can both identify with the prediction algorithm and consider themselves to have free will. So you can have free will even if someone is able to predict your actions. The more obvious fact that you can't predict your own actions really has less to do with free will, and more with the importance of the lack of logical omniscience in decision theory. Classical decision theory basically contradicts itself by assuming logical omniscience. You already know only one choice is logically possible at any given time in a deterministic universe, and with logical omniscience you know exactly which one is the possible one, so there are no more decisions to be made. But actually logical omniscience is itself logically impossible, because of problems with infinite recursion and lack of fixed points. That's why it's great to see a decision theory that does not assume logical omniscience. So please read that paper (referenced in the first post in this thread) if you haven't already.

### Re: decision theory papers

Explorations of the definitional basis of a universe and its effect on the idea of decisions: First examine a deterministic universe j such that [using notation from a post by Matthieu Walraet]: TjTj Tj Sj(0) Sj(1) Sj(2) Sj(i) An interpretation is that all the information needed to get from Sj(0) to Sj(i) is contained in Sj(0) and the rules of state evolution for that universe that is Tj. I see a problem with this interpretation. Suppose we write an expression for the shortest self delimiting program able to compute Sj(i) as: (1) Pj(i) = {Tj[Sj(i - 1)] + DLj(i)} computes Sj(i) where DLj(i) is the self delimiter. Compressing Sj(i - 1) it can be written as Pj(i - 1) and this short hand substituted into (1) to yield: (2) Pj(i) = {Tj[Pj(i - 1)] + DLj(i)} computes Sj(i) Note that Pj(i) is always longer than Pj(i - 1) because it contains Pj(i - 1) plus the Tj plus the delimiter so Sj(i) contains more information [using the program length definition of information] than Sj(i - 1) and thus more information than Sj(0). What kind of information is it? I see it as location record keeping information. The universe is at state i of the recursion and this extra information is the tag providing that location. The effect has several results: 1) This new information can never be removed from such a universe so its local time has an arrow. 2) New information can manifest as either a decorrelation of the bit pattern of and/or an increased length of the string representing Sj(i). The length of the string is interpretable as space [a fixed number of bits say x bits describe the configuration of a small region of that space and there are y regions requiring description so an increase in length of the string causes y to increase.]. Note that the effect increases as the recursion progresses since DLj(i) increases monotonically with i. Thus such a universe should see a long term acceleration in the rate of expansion of its space. 3) So how do we define a universe? Suppose many universes are following the same recursion some at earlier states and some at later states than universe j. It seems best to define such universes by the state they are in [which includes Tj and DLj(i)]. Where did the additional information come from? The additional information is not that a universe can follow the recursion but rather as stated above the location of a particular universe in the recursion. Since this information is not in Sj(0) or Tj it must have come from outside universe j. Universes that are not deterministic but have rules that allow external true to enter are easier to analyze in this regard since the current state seems the only reasonable definition. 4) For a deterministic universe is the additional information true noise? In at least one sense it is because a particular universe j is defined by its current state it can not tell which state including the current state was or is Sj(0) so there is no clue as to what the information means or if it is somehow even additional or new or which information is involved. This is the same as the situation for a universe whose rules allow external origin true noise. 5) This would seem to enhance the case against the idea of decision since noise [chance] of some sort seems to be everywhere. 6) Behavior similar to (2) is found in universes that are sufficiently well behaved so that it is possible to propose a prior state such that the universe's rules when stripped of their allowance for external true noise can deterministicly arrive at the universe's current state. This proposed prior state need not have been the actual prior state. Hal

### Re: decision theory papers

On 18 Apr 2002, at 20:03, H J Ruhl wrote: 5) I do not see universes as splitting by going to more than one next state. This is not necessary to explain anything as far as I can see. 6) Universes that are in receipt of true noise as part of a state to state transition are in effect destroyed on some scale in the sense the new state can not fully determine the prior state. The new state can not fully determine the prior state only means that the application that give the next state from the prior state is not bijective. Let's call S the set of all possible states of universes. T is the application that give the next state from a prior state. Without true noise T is an application from S to S T S S prior state next state If the application T is not bijective (There is no reason that it should be) then the new state can not fully determine the prior state. Now with the mysterious true noise, the prior state alone can not determine the next state. T is not an application from S to S. T is an application from SxN to S. T S xN -- S (prior state, noise)-- next state. In your system universes are sequences s(t) defined by a given initial state s(0) and a given application T. Without true noise the sequence follows the rule: s(t+1) = T(s(t)) But with the true noise, s(t+1) = T( s(t), noise(t)). What is noise(t) ? Is it true random ? I would like to know your definition of true random. I suppose noise(t) is an arbitrary sequence in the N set. Why choosing an arbitrary sequence of noise ? I prefer to consider the application T' from S to the set of subset of S. T'(s) is the union of { T(s,n) } for all n element of N. T' is the application that give all possible next state for a given prior state. This means that when we consider a starting state s(0) there is not only a sequence of successive states but a tree of all possible histories starting from s(0). In other words, true noise causes the universes to split. If you say your universes don't split and are affected by a true noise, you are choosing an arbitrary sequence of noise. This is a kind of physical realism. On this list, we are mathematic realist (some even think only algebra has reality), and we think physical reality is a consequence of math reality. Don't say again my system is too complex, I just tried to define clearly your system. Matthieu. -- http://matthieu.walraet.free.fr

### Re: decision theory papers

Dear Matthieu: At 4/19/02, you wrote: On 18 Apr 2002, at 20:03, H J Ruhl wrote: 5) I do not see universes as splitting by going to more than one next state. This is not necessary to explain anything as far as I can see. 6) Universes that are in receipt of true noise as part of a state to state transition are in effect destroyed on some scale in the sense the new state can not fully determine the prior state. The new state can not fully determine the prior state only means that the application that give the next state from the prior state is not bijective. I do not agree. You seem to have missed what I said. Post the true noise event there is no T that can determine [deterministically extract] the prior state from just the info in the current state [because the true noise has no identifying tags]. Let's call S the set of all possible states of universes. T is the application that give the next state from a prior state. Without true noise T is an application from S to S T S S prior state next state If the application T is not bijective (There is no reason that it should be) then the new state can not fully determine the prior state. All that seems to say is that some computational universes are also severed from their history when using a fixed T. Some other T may be able to make that link. Now with the mysterious true noise, the prior state alone can not determine the next state. T is not an application from S to S. T is an application from SxN to S. T S xN -- S (prior state, noise)-- next state. I see it as: T + N S(i) - S(i +1) In your system universes are sequences s(t) defined by a given initial state s(0) and a given application T. Without true noise the sequence follows the rule: s(t+1) = T(s(t)) I usually write my Type 1 [no internal rules allowing external true noise] more like T(i) acting on P(i) where P(i) is the shortest self delimiting program that computes S(i) [not necessarily from S(i -1) in fact there may be no S(i -1)]. This allows derivation of a cascade with naturally increasing information in the P(i) as i counts up. P(i + 1) always contains P(i) plus T(i) plus the self delimiter. T(i) may change given the requirement for true noise regardless of the nature of T But with the true noise, s(t+1) = T( s(t), noise(t)). I usually write my Type 2 [internal rules allow external true noise] as T'(i) acting on P'(i) where P'(i) is the shortest self delimiting program that computes S(i) from some S'(i - 1). S'(i - 1) is not necessarily the actual S(i - 1) but can be deterministicly proposed from S(i) using some deterministic T. What is noise(t) ? Is it true random ? I would like to know your definition of true random. I suppose noise(t) is an arbitrary sequence in the N set. I define it as new information from an external source [from the Everything/Nothing boundary]. The closest model I can think of in our universe is to attach a radiation counter to a computer input and use the event data to create strings that are then used in the computer's computations. Why choosing an arbitrary sequence of noise ? That is a little longer story and is addressed in my draft paper at: http://home.mindspring.com/~hjr2/model01.html I am still editing this work. The root reason is to avoid information generating selection in the Everything. I prefer to consider the application T' from S to the set of subset of S. T'(s) is the union of { T(s,n) } for all n element of N. T' is the application that give all possible next state for a given prior state. This means that when we consider a starting state s(0) there is not only a sequence of successive states but a tree of all possible histories starting from s(0). In other words, true noise causes the universes to split. As you can see I consider the process like one makes soup [the T'] and then right at the end adds a random sprinkle of salt. The result is one finished soup. No more is needed. If you say your universes don't split and are affected by a true noise, you are choosing an arbitrary sequence of noise. Well what other kind of true noise is there? This is a kind of physical realism. Actually I do not see a need for a physical reality. The S(i) strings can have more than one interpretation but these interpretations need not be physical On this list, we are mathematic realist (some even think only algebra has reality), and we think physical reality is a consequence of math reality. In that sense I see no need for anything mathematic, just a lookup table [a rather large but finite one in our case] active at each of a number of discrete cells plus some degree of external noise in some of them [a cellular automaton + some noise]. For example I suspect that our universe is a

### Re: decision theory papers

Your approaches seem incoherent to me. If the universe is defined by a complete computable description then that description includes you and whatever decision process your brain implements. To treat the universe as computable and your choices as determined by some utility function and decision theory is contradictory. Brent Meeker There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened. --- Douglas Adams On Thu, 18 Apr 2002, Wei Dai wrote: On Wed, Apr 17, 2002 at 08:36:29PM -0700, H J Ruhl wrote: I am interested because currently I find it impossible to support the concept of a decision. I was also having the problem of figuring out how to make sense of the concept of a decision. My current philosophy is that you can have preferences about what happens in a number of universes, where each universe is defined by a complete mathematical description (for example an algorithm with no inputs for computing that universe). So you could say I wish this event would occur in the universe computed by algorithm A, and that event would occur in the universe computed by algorithm B. Whether or not those events actually do occur is mathematically determined, but if you are inside those universes, parts of their histories computationally or logically depend on your actions. In that case you're in principle unable to compute your own choices from the description of the universe, and you also can't compute any events that depend on your choices. That leaves you free to say If I do X the following will occur in universes A and B even if it is actually mathematically impossible for you to do X in universes A and B. You can then make whatever choice best satisfies your preferences. Decision theory is then about how to determine which choice is best. That's the normative approach. The positive approach is the following. Look at the parts of the multiverse that we can see observe or simulate. How can we explain or predict the behavior of intelligent beings in the observable/simulatable multiverse? One way is to present a model of decision theory and show that most intelligent beings we observed or simulated follow the model. We can also justify the model by showing that if those beings did not behave the way the model says they should, we would not been able to observe or simulate them (for example because they would have been evolutionarily unsuccessful).

### Re: decision theory papers

On Thu, Apr 18, 2002 at 11:57:28AM -0700, Brent Meeker wrote: Your approaches seem incoherent to me. If the universe is defined by a complete computable description then that description includes you and whatever decision process your brain implements. To treat the universe as computable and your choices as determined by some utility function and decision theory is contradictory. Why is that contradictory? Please explain. Also, what alternative do you propose?

### Re: decision theory papers

On Thu, Apr 18, 2002 at 12:26:21PM -0700, Brent Meeker wrote: Perhaps contradictory is too strong a word - I should have stuck with incoherent. But it seems you contemplate having different wishes about the future evolution of the world and you want to find some decision theory that tells you what action to take in order to maximize desirable outcomes. But if the world is already determined, then so are you actions and your decision processes. Thus are actions and decision processes are supposed to be determined in two completely different ways - one at the level of physical processes of the universe, the other at the level of desires and decision theory. These two are not necessarily contradictory, but to avoid contradiction you need to add the constraint on the decision theory you follow that it agree with what your actions are as defined by the mathematical description of the universe. While you're contemplating a decision, you have no way, even in principle, of determining the action that agrees with the mathematical description of the universe. Therefore as a normative matter, adding the constraint on the decision theory you follow that it agree with what your actions are as defined by the mathematical description of the universe doesn't do anything. As a positive theory, decision theory is going to be wrong sometimes (e.g. not predict what people actually do), but it may be able to make up for that with conceptual elegance and simplicity.

### Re: decision theory papers

On Thu, 18 Apr 2002, Wei Dai wrote: On Thu, Apr 18, 2002 at 12:26:21PM -0700, Brent Meeker wrote: Perhaps contradictory is too strong a word - I should have stuck with incoherent. But it seems you contemplate having different wishes about the future evolution of the world and you want to find some decision theory that tells you what action to take in order to maximize desirable outcomes. But if the world is already determined, then so are you actions and your decision processes. Thus are actions and decision processes are supposed to be determined in two completely different ways - one at the level of physical processes of the universe, the other at the level of desires and decision theory. These two are not necessarily contradictory, but to avoid contradiction you need to add the constraint on the decision theory you follow that it agree with what your actions are as defined by the mathematical description of the universe. While you're contemplating a decision, you have no way, even in principle, of determining the action that agrees with the mathematical description of the universe. Therefore as a normative matter, adding the constraint on the decision theory you follow that it agree with what your actions are as defined by the mathematical description of the universe doesn't do anything. Exactly. So what does the assumption about the complete mathematical description add? As a positive theory, decision theory is going to be wrong sometimes (e.g. not predict what people actually do), but it may be able to make up for that with conceptual elegance and simplicity. Hmm. Maybe I misunderstood your objective. I thought it was to decide what action to take - not to predict what some person will do. Brent Meeker Imagine the Creator as a low comedian, and at once the world becomes explicable. -- HL Mencken

### Re: decision theory papers

On Thu, Apr 18, 2002 at 01:39:59PM -0700, Brent Meeker wrote: Exactly. So what does the assumption about the complete mathematical description add? It's so that your preferences are well defined. As a positive theory, decision theory is going to be wrong sometimes (e.g. not predict what people actually do), but it may be able to make up for that with conceptual elegance and simplicity. Hmm. Maybe I misunderstood your objective. I thought it was to decide what action to take - not to predict what some person will do. Did you not understand the distinction between positive and normative? A positive theory explains and predicts, a normative theory tells you what you should do. I'm interested in both.

### Re: decision theory papers

On Thu, 18 Apr 2002, Wei Dai wrote: On Wed, Apr 17, 2002 at 08:36:29PM -0700, H J Ruhl wrote: I am interested because currently I find it impossible to support the concept of a decision. I was also having the problem of figuring out how to make sense of the concept of a decision. My current philosophy is that you can have preferences about what happens in a number of universes, where each universe is defined by a complete mathematical description (for example an algorithm with no inputs for computing that universe). So you could say I wish this event would occur in the universe computed by algorithm A, and that event would occur in the universe computed by algorithm B. Whether or not those events actually do occur is mathematically determined, but if you are inside those universes, parts of their histories computationally or logically depend on your actions. In that case you're in principle Why are you in principle unable to compute your own choices? Do you refer to unable to predict or unable to enumerate or both? And do you mean with certainity or only probabilistically - It seems you can compute (in both senses) your choices probabilitically. Are you assuming that the algorithm describing the universe in deterministic or do you allow that it might have a random number generator? Brent Meeker unable to compute your own choices from the description of the universe, and you also can't compute any events that depend on your choices. That leaves you free to say If I do X the following will occur in universes A and B even if it is actually mathematically impossible for you to do X in universes A and B. You can then make whatever choice best satisfies your preferences. Decision theory is then about how to determine which choice is best. Brent Meeker Microsoft has done for software what McDonalds has done for the hamburger.

### Re: decision theory papers

On Thu, Apr 18, 2002 at 02:08:56PM -0700, Brent Meeker wrote: Why are you in principle unable to compute your own choices? Do you refer to unable to predict or unable to enumerate or both? I mean there is no algorithm which your brain can implement, such that given the mathematical description of a universe and your place in it, it always correctly predicts your decision. The reason is that the decision you actually do make is going to be affected by the prediction. Whatever prediction the algorithm makes, the rest of your brain can decide to do something else after learning about the prediction. And do you mean with certainity or only probabilistically - It seems you can compute (in both senses) your choices probabilitically. I mean with certainty. The meaning of probabilities isn't clear at this point. Probabilities only make sense in the context of a decision theory, which we don't have yet. What I'm describing is just the philosophical framework for a decision theory. Invoking probabilities at this point would be circular reasoning, because we want to justify the use of probabilities (or something similar) using more basic considerations. (This was one of the historical motiviations for classical decision theory.) Are you assuming that the algorithm describing the universe in deterministic or do you allow that it might have a random number generator? Deterministic.

### Re: decision theory papers

On Thu, Apr 18, 2002 at 04:15:48PM -0700, Brent Meeker wrote: I don't see this. You seem to be making a proof by contradiction - but I don't see that it works. There is no contradiction is assuming that there is an algorithm that correctly predicts your decision and then you make that decision. You only arrive at an apparent contradiction because you suppose the there is some left out part, the rest of your brain, that was not taken into account by the algorithm. This is what I meant by incoherent. All that really follows is that *if* there were such an algorithm you would necessarily do what it predicted. If the universe is deterministic and computable, such an algorithm must exist. The only conclusion I see is that if you executed this algorithm you would loose the feeling of free will (of course you would have predicted this). I think I stated the idea badly before. Let me state it differently: there is no algorithm which given the mathematical description of any universe and the location of an intelligent being in it, always predicts his decision correctly. Suppose this algorithm exists, then we can construct (the mathematical description of) a universe where someone runs the algorithm on himself and then does the opposite of what it predicts, which is a contradiction.

### Re: decision theory papers

On Thu, 18 Apr 2002, Wei Dai wrote: On Thu, Apr 18, 2002 at 04:15:48PM -0700, Brent Meeker wrote: I don't see this. You seem to be making a proof by contradiction - but I don't see that it works. There is no contradiction is assuming that there is an algorithm that correctly predicts your decision and then you make that decision. You only arrive at an apparent contradiction because you suppose the there is some left out part, the rest of your brain, that was not taken into account by the algorithm. This is what I meant by incoherent. All that really follows is that *if* there were such an algorithm you would necessarily do what it predicted. If the universe is deterministic and computable, such an algorithm must exist. The only conclusion I see is that if you executed this algorithm you would loose the feeling of free will (of course you would have predicted this). I think I stated the idea badly before. Let me state it differently: there is no algorithm which given the mathematical description of any universe and the location of an intelligent being in it, always predicts his decision correctly. Suppose this algorithm exists, then we can construct (the mathematical description of) a universe where someone runs the algorithm on himself and then does the opposite of what it predicts, which is a contradiction. Keeping to the idea of a deterministic universe - wouldn't the mathematical description of the universe include a description of the brain of the subject. And if the universe is computable it follows that the behavoir of the subject is computable. If the person, or anyone else, runs the algorithm predicting the subjects behavoir - an operation that will itself occur in the universe and hence is predicted - and *then the subject doesn't do what is predicted* there is indeed a contradiction. But the conclusion is only that one of the assumptions is wrong. I'm pointing to the assumption that the subject could then do the opposite of what it predicted - *that* could be wrong. Thus saving the other premises. Obviously the contradiction originates from assuming a deterministic universe in which someone can decide to do other than what the deterministic algorithm of the universe says he will do. Brent Meeker Time is the best teacher; Unfortunately it kills all it's students!