The Dark (Frank) Knight

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2 Responses

  1. A.J. Sutter says:

    As you probably know, there is a very old pedigree for this issue, namely the debate between the frequentist and Bayesian interpretations of probability.

    Under the frequentist interpretation, a probability is a limit of the relative frequency of an event in a large number of trials. Most techniques of statistical inference are based on this interpretation, at least implicitly. But it’s hard to know this of a particular coin. All the less so of the many other things we deal with in life, where (i) many outcomes are not often, or ever, repeated, and (ii) there may also be threshold issues just in defining those outcomes. (E.g., are lawsuits always “won” or “lost” in a clear-cut binary way?)

    Without this knowledge, how can you have “risk”? Maybe one of the more interesting results of these definitions is that (subjective) risk first requires some level of trust.

  2. Edward Swaine says:

    Check plus for the title of your post. I’m being boring, but I think Two-Face’s coin illustrates a more basic risk. In situation # 1 (who will chair the trial), Rachel Dawes may be questioning the fairness of the coin, but I think it’s equally plausible that she is expressing doubt that Dent would abide by any adverse result. Same for situation #2: it’s not that bad guy has changed his mind, or misunderstood probability, but rather that Dent’s behavior indicates that he will not abide by any result favorable to the bad buy (i.e., that Dent will keep flipping until it comes up tails). These are simply commitment problems, reinforced by his disclosure that he actually would not have abided by tails either.

    I don’t remember the third incident, but the final situation speaks more to your issue. As I recall from the comics, once one side of the coin is scarred (I think he does the defacing himself in at least one of the versions), Two-Face is in fact quite good about abiding by the result. Indeed, I think that in his psycho-world, it is of the utmost importance that he NOT influence the result; were that understood, and coupled with the fact that the coin’s original construction obviated any need to weight one side relative to the other, the kid should be pretty confident that the flip would be fair.

    The kid doesn’t know any of this, however. And he also doesn’t have a choice, which is relevant to the fairness assessment — not just because we think forcing such games on people is unfair, but also in a way that bears on the fair coin issue. Two-Face chooses the occasions on which he flips the coin, and does not solicit advance approval. This is pretty awful, in most respects, but if we suppose (as the kid would, though it is not in fact consistent with Two-Face’s character) that Two-Face would have been at liberty to do the worst thing possible without even subjecting matters to a flip — to “cheat” with total likelihood of the bad result prevailing, not 51% or 52% — we should be relatively comfortable with the probable fairness of the coin. More so than if you and I were trying to decide who should spring for lunch.

    If you think this is bad, don’t get me started on Dark Knight’s ending.