Comments (19)

• Keith

• Quote from the article: "... we cannot say with any certainty that a Prisoner's Dilemma has ever existed."

  I think this is the basic problem most libertarians would have with this scenario. Why are only the choices of the prisoners considered? Why aren't the police/prosecutors/jailers also considered players? How were the possible jail times for the prisoners set? Etc. Its all arbitrary and contrived.

  I'm reminded of a saying: All models are bad, but some models are useful. I'm not sure this meets the second criterion.
  

• Published: June 16, 2006 8:55 AM

• Randy Holcombe

• Mr. Crovelli is completely wrong in his analysis of the prisoners' dilemma, because it does not require any interpersonal utility comparisons. It merely looks at the incentives facing each prisoner, one at a time, and assumes that a higher payoff is preferred to a lower payoff. Each prisoner, acting by himself, decides that no matter what the other prisoner does, his best strategy is to not cooperate. There is no interpersonal utility comparison involved. The result is that everyone gets a lower payoff than if they all chose to cooperate. While it is reasonable to question the example's applicability to international relations, as Mr. Crovelli does in his first paragraph, the interpersonal utility comparison problem Mr. Crovelli discusses is not relevant to the prisoners' dilemma.

• Published: June 16, 2006 9:53 AM

• Richard Garner

• Interesting. I was wondering how an Austrian approach to Axelrod's argument may go. I was thinking of emailing Walter Block on it, because I was wondering about the issue of scales of preference, that it involves. However, I think the quote from Axelrod in the article answers that. It is pretty much true that I prefer somethings to others, and that is all that is needed.

  I agree with the previous poster. Interpersonal utility comparisons are irrelevant to the prisoners' dilemma. No so comparisons are needed by any party to the dilemma. Of course, there is the completely true problem that unless you can be certain of people's subjective preferences you cannot tell whether or not people are faced with a prisoners' dilemma, and given that in this world of non-psychics, only revealed preference gives us anything approaching an idea of people's preferences, and revealed preference would not reveal prisoners' dilemmas, empirical testing is pretty much impossible.

  But, again, that is irrelevant. I can still postulate prisoners' dilemma scenarios and then ask what may happen in them, even if I can't empirically show that any such scenarios actually exist or occur.

  On a different point, Axelrod's proof also shows that peaceful arbitration between private protection agencies under market anarchism is the rational strategy: In this case, the player using Tit For Tat starts off, not co-operating, but offering arbitration.

• Published: June 16, 2006 10:43 AM

• Tim Swanson

• I'll leave everyone else to argue about "Prisoner Dilemma's" but I thought this quote was of interest:

  But, how would it be possible to measure the utilities of two different people relative to each other without a constant unit of measurement for each individual, i.e., an absolute scale for each individual? Indeed, without a constant unit of measurement for each individual, the two utility scales are completely incommensurable.

  Exactly, a utili-meter. I got one at Walmart for a pretty good deal last spring, I think it's on isle 7.

  In all seriousness though, I agree with that statement (as noted in "The Bowl Championship Series: A Case Against Subjectively Aggregated Statistics"). By the very nature of how internal rank-order preferences operate, it is impossible to aggregate or in any way objectively compare them.

  My two-thumbs-up for the movie Serenity is not the same as another person's two-thumbs-up. Nor is my four-and-a-half-star rating for the Ritz Hotel the same as another patron's rating. Sure, we might all use a superficially similar name to label our rank, but there is no objective mechanism (i.e. equalizer) that can comparatively gauge our internal druthers.

  The same goes for GPA's:

  What makes these remotely valid? How can you rank heterogeneous, dissimilar institutions? A 3.8 GPA at one school is not at all comparable to a 3.8 at another. Each instructor has their own subjective evaluation of a student, course work is different in each department at each institution, resources available to students are different, student-body diversity/dynamic is different, so how can these be aggregated let alone objectively quantified?
  In a vain attempt to show transparency and impartial legitimacy, both letter and number scores are used to quantify student assessment. Can the 93 you received on your term paper for English 101 from Professor Smith in 1991 at a small rural liberal-art academy be legitimately weighted the same against pupils in other sections with different instructors at a substantially larger urban school years later? The scale methodology is flawed if nothing else for the fact that you cannot use a subjectively assessed interval aggregation system to compile a nice round number.

  QED.

• Published: June 16, 2006 11:05 AM

• Joshua Katz

• To expand on Tim's comment:

  Many instructors now are dropping objective considerations in grading papers, and instead ranking the papers (which they prefer over which they don't prefer) and then assigning grades in that order - this is what the process of curving is supposed to accomplish, I believe. So the grade you receive is largely dependent on the makeup of the class. How useful is that?

  But, on the other hand, as an employer, maybe there still is some use to it (if the classes taught things worth knowing, and required students to think in a way worth thinking, highly questionable premises.) All else being equal, don't I want students who came from the top of their class? It's true that I can't compare the 3.8 from one school to the 3.8 from another, but as a rough estimate, the 3.8 from the first school seems likely to be more intelligent/thinking/etc. than the 2.0 from the otehr school. Of course, once the assumptions are changed to reflect the real university, and we acknowledge that being on top of the class means agreeing with the stupid ideas of the professor, this value is lost entirely.

• Published: June 16, 2006 12:00 PM

• quincunx

• "Exactly, a utili-meter. I got one at Walmart for a pretty good deal last spring, I think it's on isle 7."

  Exactly, a utili-meter. I couldn't find one on aisle 7.

  Tsk Tsk, you should've told the truth Mr. Swanson, now we both can't increase our utility over time.

  ---

  This was a great article, btw.

• Published: June 16, 2006 12:41 PM

• Randy Holcombe

• quincunx says "This was a great article," but the essence of the article is wrong! (See my comments above for the reason.)Axelrod's application of the prisoners' dilemma can be criticized on many grounds, but the criticism expressed in this article is just plain incorrect.

• Published: June 16, 2006 1:13 PM

• averros

• As much as I dislike misapplication of mathematics in the economics and social sciences, this is indeed the case when the criticism is actually wrong.

  As was pointed above, the P.D. does not involve interpersonal utility comparison. The criticism about not knowing the structure of the utility function is only partially correct - any kind of decision-making can be represented as evaluation of some scalar utility function with the selection of the action yielding the best utility score.

  The hidden assumption in the iterative P.D. games is that the individual utility functions are stationary, at least to the extent that they do not change sufficiently to alter the outcome. This can be a pretty good assumption in some real-life cases.

  It is hard to argue that there are no some commonalities between people - otherwise we'd be unable to understand each other at all! The cardinal sin of game-theory economisis and sociologists is not that they try to explore whatever commonalities there are but rather in the oversimplification of the models to the point of complete irrelevancy.

  In fact, it can be argued that even the simple games, if done iteratively with actors capable of creating behavioral models of other actors, yield essentially unpredictable results in the long run, just like the evolution, (and unpredictable results in the short run due to unknown state of the inobservalbe internal models).

  When the utility functions are simple (i.e. genetics) the game theory can (and does) yield good quantitative predictions.

  So I'd propose to stop bashing game theory - it is not wrong, and is useful. What should be done is exposing misapplication of the theory and the irrelevance of oversimplified models to the real life situations.

• Published: June 16, 2006 4:40 PM

• Mark Crovelli

• Allow me to clarify my argument. Professor Holcombe is absolutely correct to state that the prisoner's dilemma does not require interpersonal utility comparisons when it is considered in a purely formal and theoretical manner. (As I state in the article, "We might be able to hypothesize, in a purely formal manner, that it might be possible for two men's preferences to approximate the Prisoner's Dilemma at a specific point in time.")

  My article, however, is not concerned with the purely theoretical version of the prisoner's dilemma-- and neither is Axelrod's treatment solely concerned with the formal version. My article aims at the problem of measuring and comparing utilities in the real world of acting men, (hence, "The Prisoner's Utilities Cannot be Measured or Compared"). In the real world, it is impossible to construct a scale of measurement that would allow us to measure the prisoner's utility and compare it to the utility of the other prisoner in a two-by-two matrix. Since we cannot measure the prefereces of the two prisoners, we can never know whether a prisoner's dilemma exists-- even the prisoner involved can never know the preferences of his opposite!
  This is the essence of my article; that we cannot know whether a prisoner's dilemma has ever existed. With the above clarification in mind, Dr. Holcombe, would you agree with the article? Without being able to say that a prisoner's dilemma has ever existed, wouldn't you agree that the idea of the prisoner's dilemma is of virtually no value for the study of real men?

• Published: June 16, 2006 5:13 PM

• George Weinberg

• Well, I think in some cases you can be pretty confident what the order of other peoples' preferences are likely to be. In particular, in the story behind the prisoners dilemma, I think each criminal is being perfectly reasonable in assuming the other criminal would prefer a short sentence to a long one.

  Although you can never be certain what another's preferences are, it seems reasonable that your initial assumption should be that fundamentally they aren't all that different from your own. Certainly that's more sensible than assuming they differ in some particular arbitary way.

• Published: June 16, 2006 6:07 PM

• cynical

• The hardest assignments in game theory were when the professor asked us to "find a real world example of a type of game". One never knew if a particular game applied to a particular situation, whether multiple games applied, etc. I would agree with the author that you can just never know. (To be clear, all the students in my game theory class, with the full knowledge of the teacher, just found examples of situations and argued that a particular game applied to the situation -- not very useful for real life applications... unless you are training to be a courtroom lawyer).

• Published: June 16, 2006 9:21 PM

• L. Ron Rothbard

• To measure Utility you can use the U-meter:

  The U-meter is a skin galvanometer, similar to those used in giving lie detector tests. The subject holds in his hands two tin soup cans, which are linked to the electrical apparatus. A needle on the apparatus registers changes in the electrical resistance of the subject's skin. The auditor asks questions of the subject, and the movement of the needle is apparently used as a check of the Utility of the subject. According to complex rules and procedures set out in Governmentology publications, the auditor can interpret the movements of the needle after certain prescribed questions are asked, and use them in diagnosing the Utility of the subject.

• Published: June 17, 2006 3:28 AM

• Allen Weingarten

• The article includes "Axelrod argues that cooperative strategies...can "invade" areas that are dominated by "mean" strategies, because just a few players employing a cooperative strategy can benefit from each other enough to allow the strategy to spread throughout the "mean" area over time."

  I can see that criminal gangs with a sense of loyalty (to never rat on one another) could be more survivable than others. So perhaps in time there will evolve such gangs. Perhaps not, but how does an absolute scale of utility measurement pertain?

  In other words, I do not follow why the absolute scale is pertinent for either side of the argument.

• Published: June 17, 2006 5:17 AM

• Richard Garner

• Mark,

  First off, it is possible to make pretty good guesses as to people's preferences in some cases: If it were not, we wouldn't give each other presents.

  Further, though, even if we could never know if a prisoners' dilemma occurred, this doesn't mean that they don't occur, could not occur, or that it would even be wrong to postulate the possibility of them.

• Published: June 17, 2006 6:00 AM

• Mark Crovelli

• Again, I am not claiming that it is impossible for prisoner's dilemmas to occur in the real world. Indeed, for all I know, they occur constantly. The point is, that without being able to know other people's preferences (until they act) we can never know with certainty that a prisoner's dilemma has ever occurred.

  Suppose that I were to claim that aliens sometimes come to Earth and occupy people's bodies without anyone ever being able to tell the difference. We might be able to hypothesize, in a purely formal manner, that such a scenerio is possible, but without being able to demonstrate that the scenerio has or has not actually occurred, my claim remains a useless, trivial, and hypothetical mind game.

  The same is true of the Prisoner's Dilemma. Because we can never know if it has ever applied to the world we live in, it remains a trivial, and hypothetical mind game.
  
  My readers are free to believe that Prisoner's Dilemmas actually occur in the real world, and they are free to believe in aliens or that Luther was one of God's messengers.

  I remain unconvinced of all these things.
  

• Published: June 17, 2006 7:24 AM

• Andy Feldman

• Are you suggesting that game theory has no predictive power under any situation?
  
  
  
  In your hypothetical case of alien mind control, even if I had a magic device that would tell me who was under control, it would be of zero value by definition: the alien's chosen behavior is indistinguishable from the person's ordinary behavior, so it is irrelevant whether I believe in the mind control or not.
  
  
  
  However, I would think a magic device that tells you when you are in a prisoner's dilemma with another entity would be quite useful indeed. It would tell you that the other person prefers to 'defect' (or lower prices, or any other binary decision) no matter what you do, but that they also prefer the case where neither of you 'defect' to the case where you both do. Although it doesn't tell you how much they prefer these outcomes, and certainly not how much "utility" (whatever that means) they get compared to you, it still gives you some information that has an effect on your expectation of their future behavior. (Because you can never have perfect information, your estimate of other people's behavior is always a probability that can be lower or higher but never 100%.)
  
  
  
  Let me ask another question: would the sentence "Because we can never know if it has ever applied to the world we live in, it remains a trivial, and hypothetical mind game" apply to anything we can't *know* has ever happened, or is there something else special about game theory?

• Published: June 17, 2006 11:39 PM

• Tullock

• You are really unconvinced that prisoners' dilemmas occur in the real world? Yes, we can't measure utils, but no one is seriously claiming that we can. All it takes is for a decision maker to be able to rank outcomes ex ante, not a very restrictive assumption. Even Rothbard uses downward-sloping demand curves.
  

• Published: June 18, 2006 3:44 PM

• Phil Manger

• I have not read Axelrod's book (or all of your article, for that matter), but I think your differences with him are based on a misreading of a statement he makes in the book. In one of your paragraphs you quote him:

  "There is no doubt that Axelrod is aware of this problem, and he addresses it specifically: 'The payoffs of a player do not have to be measured on an absolute scale. They need only be measured relative to each other.'[3] But, how would it be possible to measure the utilities of two different people relative to each other without a constant unit of measurement for each individual, i.e., an absolute scale for each individual? Indeed, without a constant unit of measurement for each individual, the two utility scales are completely incommensurable."

  It is the "payoffs of a player", not the payoffs of all the players that are to be measured relative to each other. I do not get the sense from that quote that Axelrod is in any way talking about comparing the utilities of two different individuals. The most fundamental assumption underlying utility theory (and consumer theory in economics) is that utility is ordinal, and therefore interpersonal comparisons of utility cannot be made. The assumption of cardinal utility is sometimes made to facilitate analysis, but in this case it is well-understood that "utility" is a dimensionless variable -- sort of like the "z" in the Gaussian probability distribution, which has a mean of zero and a variance of one. The cardinal utility function is valid only for a single individual; in fact, there are many cardinal utility functions that would be valid for that same individual -- any function that preserves his/her ranking of commodity bundles/states-of-nature would be a valid utility function. Which is why her/his "utility" cannot be compared with another's.

  As for real-world examples of the prisoner's dilemma, just watch almost any episode of "Law and Order". The detectives separate the prisoners and promise the one who talks first the best deal. It is not necessary to compare their utility functions. It is only necessary to assume that each of the prisoners prefers less time in jail to more. Okay, the show is fiction, but scenes like that are played out in interrogation rooms in police departments all over the country.

• Published: June 19, 2006 12:12 PM

• Paul Marks

• The whole "prisoners dilemma" thing is a particularly bad example of "economic man" a concept that the Austrian school rejects.

  If I have committed a crime (I mean a real crime a violation of the nonaggression principle by force or fraud - not a violation one of the government's arbitary and contraditory regulations) then I should confess my guilt and accept my punishment.

  If someone else committed the crime with me (for example a gang rape) then I should "give them up" (justice for the victim demands this).

  Whether I get time off prison for "informing" is not relevant - indeed I should refuse time off in any case (as my reptentance is not genuine if I try and make such deals).

  One can treat honour as a form of "utility" if one wants to ("you are maximising your utility by repenting of your crime and accepting punishment") but then one can say that about any action or nonaction.

  This is certainly not a form of utility that can be measured in "utils" or mathematically manipulated.
  

• Published: June 25, 2006 10:27 AM