Home > Philosophy > Probability and Determinism Vs. Free Will

Probability and Determinism Vs. Free Will

Trying to find new ways to explain why our monetary system is a disaster gets tedious, probably even more so for the reader than the author.  So I’m going to start peppering in some philosophy.  These will mostly be motivated by arguments I have had, largely with objectivists.  It all adds up to a sort of general theory of god and reality but we will work toward that a little at a time.  Today I will address the age-old debate over free will versus determinism but I must start by explaining the nature of probability.

Probability is among the most abused concepts developed by mankind.  The reason for this (as with many other such concepts) is the failure to distinguish between reality and theory.  The understanding most people have of probability is based on its function in a theoretical model.  Therefore I won’t go to too much trouble defining this function.  Its meaning in a model is what you think it is.  You can read about it here.  When we say that X occurs with probability .2, we are assuming that X is a random event.  The notion of randomness is a theoretical construct.  Essentially it implies that we (the modeller) have complete knowledge of the process taking place and all that this knowledge amounts to is that it will happen with probability .2.  Notice that in a model, the event X never actually happens or doesn’t happen.  The model must say what the result would be if either event happened.  These results can depend on the probability of X and this can be changed at will by the modeller and the results on the effects both when X occurs and when it does not can be evaluated.

The confusion arises when people use probability to describe real world events.  If you roll a fair die and ask your friend what the probablity of rolling a 3 is, there is a 90% chance he/she will say 1/6.  But this is not true in the same sense as when you make a model and say that the probability of a 3 occurring in the model is 1/6.  This is because the event in reality is not objectively random.  What I mean by this is that it isn’t true that any of the six supposed possibilities can happen.  One of them will happen.  Which one it is depends on the exact way in which the die is rolled and the physical characteristics of the surface on which it is rolled and the movement of the air in the room and the temperature and humidity and the position of the moon etc.  All of these things add up to some particular outcome.  In other words, the outcome is determinate.

When someone says that there is a 1/6 chance of rolling a 3 what they mean is that they don’t know what will happen and the best estimate that they can make with the knowledge they have is to treat it as a random event with probability 1/6.  If they had all of the information pertinent to the event (and knew how to process it), they would be able to tell you with certainty what number would come up.  If they had some of that information but not all, they may be able to do better than to guess 1/6 but still not know the outcome for sure (go to 4:40).  Notice that these different scenarios all assume the same event taking place, it is only the knowledge possessed by the person making the guess that changes.  Stating the probability of a real world event is only a way of quantifying one’s ignorance of what will happen.

When we want to connect the theoretical interpretation of probability with real world events we often say something like “if you rolled the die a large number of times, the proportion of rolls that come up a 3 will approach 1/6 as the number of rolls approaches infinity.”  This is true as long as the die is perfectly fair and the person rolling it has no ability to influence the roll by their throw.  And we choose things like dice and coin-flips to represent probabilistic outcomes because they are things that are very difficult to influence or predict.  But the fact remains that each individual roll is a unique event.  If you rolled the die an infinite number of times and all the factors that affect the roll of the die were literally the same, the outcome would be the same every time. It is only because we don’t expect them to be the same every time that if we imagine rolling it many times we imagine getting different outcomes.  There is no such thing, in the real world, as the same event taking place an infinite number of times.  And each unique event will result in a specific unique outcome.  Some are relatively easy to predict and some very difficult but this is different from the idea of probability in a theoretical model.

The same concept applies to the actions of people.  I have, in the process of explaining this point of view, pointed out that it is possible to predict people’s’ behavior.  As an example consider a poker game.  Let’s imagine that I have a bad hand and I think my opponent also has a bad hand but one which is slightly better than mine.  It is my bet.  Leading up to this point I have observed some sequence of events and actions by my opponent that have led me to the conclusion just described regarding his hand.  Now there are varying degrees of certainty which I may have about his hand.  I might think there is a 50/50 chance that my guess is wrong or I might feel like there is a 90% chance that it is right.  Additionally, I might be absolutely certain that my guess is right and not believe it is possible he could have something else.  Notice that in any actual situation only one belief can be right (this is different from rational).  If he has what I think and I am sure of it I am right.  If he doesn’t have that and I am sure he doesn’t then I am right (of course then it wouldn’t be what I think he has).  Any probability  I assign to it other than 1 or 0 is incorrect, although it might be rational given my degree of knowledge.

Now assume that he does have what I think and that I believe this with certainty (if it helps, feel free to imagine that I can see his cards in a mirror behind him or some scenario like that exists).  Still in order to make the correct move I must predict his behavior  given that hand.  Let’s narrow the range of options I face to just two.  I can either make a bet, or fold.  If I think he will call the bet I want to fold because he has a better hand than me.  If I think he will fold to my bet then I want to bet because I will win the pot.  This requires me to analyze the process going on in his mind.  There is some process going on in his brain that takes in data and leads to some action and there is some data going in.  If I can understand both the process and the data perfectly I can theoretically know exactly what he will do.  This is not easy.  However, now imagine I decide that he will fold if I bet, so I bet and he folds.  At this point I turn to my friend and proclaim “I knew he would fold.”  I predicted his behavior and I was right.  In a previous discussion, I described an analogous situation to this and was told that I couldn’t have known that because he could have done something else.  Therefore, the reality was that there was some probability of him folding and some probability of him calling and therefore it was incorrect of me to assign a probability of 1 to folding.  But what probability should I have assigned?  The answer of course is “it depends.”  It depends on how much information I had about his thought process.  But assuming there is a true probability between 0 and 1 is a mistake.  The only correct probability I could have assigned was 1.

Now take this quote by a certain brilliant (and handsome) blogger: “If you roll a fair die and ask your friend what the probability of rolling a 3 is, there is a 90% chance he/she will say 1/6.”  In saying this, said blogger predicts other people’s’ behavior.  The logic behind this statement is something like: if everyone on earth who could possibly stumble upon this blog carried out that experiment my best guess about the proportion of them who would receive the answer “1/6” is about 90%.  But if you added information, the estimate may change.  For instance, some people may answer this incorrectly because they don’t know basic probability.  So if I knew the reader were going to ask around the economics department at their college I might adjust the estimate upward.  If I knew they were going to ask in the sociology department I would have to account for the increased chance of people responding “probability is just an illusion  pushed on us by the bourgeoisie man, you gotta wake up!”  If I knew the person being asked and I had had the argument about probability with them ten times before, I might know “for sure” that they would say 1/6.  They could say something else but this possibility doesn’t make me wrong.  The only thing that would make me wrong is if they did say something else.

But if I know what someone is going to say or do in a certain situation does that mean that they don’t have a choice?  Obviously not, it just means that I know what they are going to choose.  The confusion over this seems to stem from assuming the converse, namely that if someone has a choice, I can’t know what they will do.  This is equally false.  So if you think of determinism as predictability (which I think is the only reasonable way to think of it since adding any additional meaning is purely arbitrary) then there is no reason why determinism and choice can’t exist simultaneously.  It is only a matter of perspective.  The more information (and understanding) one has the more deterministic the universe becomes.  This is completely independent from the concept of choice.  The notion of an omniscient god is simply the limiting case of this concept.

What’s more, the argument that the notion of choice implies an objective probability strictly greater than zero of all choices occurring is self-defeating.  In fact, the notion that there must be a probability strictly greater than zero of every possible choice occurring is not consistent with choice.  If I have the ability to choose between two options I must be able to choose one with certainty.  If there is a predetermined objective probability of me choosing A and B then this is not a choice it is a random process–the antithesis of choice.

*Note: I know physicists are convinced that on an atomic level the universe is probabilistic.  I’m not an expert on that but I don’t believe it changes the implications of this theory.  Obviously people don’t have enough information to see the universe as deterministic and it may very well be the case that it is theoretically (not just practically) possible for us to have that much information but that issue is independent from the concepts of choice and determinism.  If anyone wants to start a fight about this I will say more about it.

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  1. Frank Stein
    July 22, 2011 at 5:39 pm

    How do you define choice? If choice is having the *ability* to do otherwise, then in a purely deterministic universe there can be no choice since you don’t have the ability to respond to the same deterministic inputs in a different manner.
    Although unlike inanimate matter and lower lifeforms, being ‘aware’ introduces essentially infinite complexity and feedback loops – so that set of inputs A necessarily leads to action B, but set of inputs A + awareness of A is itself a different set of inputs, and could lead to action C. And (A + awareness) + awareness of that is again another set of inputs, etc. But in the end there’s still no choice to be found, just a system too complex to work out (and so free will is a reasonable model).

    So if you truly “know” what someone is going to do, then you know the outcome – and so that person does not have the choice to do otherwise. Unless they are aware that you know what they will do, but that just changes the set of inputs that affects them.

  2. Free Radical
    July 22, 2011 at 6:34 pm

    I agree with your definition of choice but I don’t see how this requires the ability to resond to the same deterministic inputs in a different manner. I’m not saying free will isn’t a reasonable model, In fact I’m saying that the distinction between the free will model and the deterministic model is only a matter of perspective. All those combinations (A, A +awareness, A++, etc.) lead to some outcome (of course they may be different) and of course we don’t have enough information to know all the connections. The point is that you can imagine having all of it, or at least imagine some kind of 3rd party observer having it (more on this later). In this case everything would be determinate from that perspective. But the point is that this does not contradict the notion of free will (I’m a free will kind of guy after all). From the perspective of any individual they still must make a choice. The two notions are not contradictory they are just different perspectives on the same thing. But on a moral level the point of this is basically to argue that you can believe in “fate” without shrugging off any personal responsibility for your actions. Just because the universe can be considered determinate from some imagined perspective doesn’t mean you don’t still find yourself in the middle of a different point of view where you must make a choice and accept the consequences of that choice. But people who already believe this aught to expend no effort trying to dispel the notion of fate either.

  3. Frank Stein
    July 22, 2011 at 8:48 pm

    I guess I would say that if some system can be completely determined from perspective X, then it is a deterministic system and there is no room for choice. If choice is the ability to take an alternative action given identical inputs (let’s say you rerun the same scenario like rewinding a movie), and perspective X is able to ‘see’ all the details of A and thus know what’s going to happen, then how could any agent in that system choose differently? It may be the case that agents in the system are self-aware and so believe they have a choice, but if the system is deterministic, then that can’t be true.

    I do agree that at our level of perspective it is as if there is such a thing as free will, and it is even useful to believe it, as both a moral foundation and for personal identity. But I just find it hard to believe it is *really* true, if in fact the universe is completely deterministic.

    But if the universe is not completely deterministic…what does that mean?

  4. Free Radical
    July 22, 2011 at 9:15 pm

    Well I guess I don’t see a way to imagine a non-deterministic universe, at least at some level. I can imagine a multidimentional universe. For instance, the physicists seem to believe that on some sub-atomic level the behavior of particles is random (indeterminate). I’m not an expert on this so I may be butchering it. But whatever is going on here, the only way I can understand this conclusion is as the conclusion that the information determining the behavior is not only beyond our current understanding but it is somehow logically beyond the possibility of ever understanding. However, each individual occurence only happens one time so there is still a thing that happens and a thing that doesn’t happen. To think of this as random simply means that the omniscient 3rd party perspective must be aware of multiple dimentions (I have heard of a theory in physics similar to this), one for each “possible” outcome. This is easy for me to comprehend because I make models for a living. So I can say to myself “at time t, individual i chooses to do A with probability x and B with probability 1-x. Then I have to keep track of what happens for each potential outcome, but I can do this. In this case the “reality” I create in my model is a tree which branches out at every random occurence (this could be a decision or the behavior of a particle or whatever). But what an actor operating within the model would observe would only be one path through the tree. Each other possible path would be experienced uniquely by some different version of each person.

    But my point is basically that the idea of this perspective existing doesn’t seem to me to refute the notion of choice. It is in fact the alternate position, namely that it is impossible to know with certainy (even in theory) what someone will do that contradicts the notion of choice because this seems to assume that our choices are bound by some cosmic dice roll over which we have no control.

    I’m gonna be away for a day or so but I think I need to complete the theory of god. I am basically hinting around it now. I will try to do that soon.

  5. littlefish
    July 29, 2011 at 10:13 pm

    So,let’s say a programmer makes a game and the game has many levels and each level has many obstacles/monsters/villains, and getting through each level requires making many choices. The player of the game starts out and promptly dies, but immediately goes in and tries again. With increased knowledge, the player makes different choices and gets further through the game. After many attempts, the player will have great knowledge and consistently make “good” choices that will allow him/her to advance. Eventually the knowledge will be great enough that the player can consistently make the choices needed to get all the way through the game.

    If you observe many players over time, you will be able to determine what choices they will eventually make and approximately how many attempts it will take for them to get there. So the outcome is determined by the programmer – but for the player, each choice is his/her own and the consequences are significant. So I guess I have to agree with you even though I’d rather not. I guess I just don’t care about the part that is pre-determined. I like the personal challenge of the game, and learning which moves will allow me to advance, and Hooray for the programmer. Game on!

    • Free Radical
      August 1, 2011 at 6:15 pm

      Yeah sort of but that’s not a perfect model because the programmer didn’t program the player. A better example is an NPC (non-player character) that is part of the program, or maybe a character in a book….. The author creates the character and decides what he/she will do in a given situation, but that doesn’t mean the charcter doesn’t agonize over the decision or that we don’t like or dislike the character or judge them morally
      because of what they choose.

      • littlefish
        August 2, 2011 at 3:10 am

        Good analogy.

  6. January 26, 2014 at 5:31 am

    This piece was cogent, werlewlitt-n, and pithy.

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