Tuesday, April 20, 2010

Elements of Legal Claims and Affirmative Defenses

In a comment about L.J. Cohen's conjunction paradox I said:
Footnote: If you believe (as I do) that all probabilities about factual hypotheses are conditional probabilities [e.g., P(element 1| evidence x)], then the product rule, if applied at all, should be applied to such conditional probabilities (and not to freestanding, or unconditional, probabilities [e.g. P(element 1)].
My own comment gave me the following thought(s):

Although the elements of claims or affirmative defenses -- more precisely stated, although the facts that satisfy the elements of legal claims or affirmative defenses -- may be "random variables" in the sense that they can take on various probability values, they are not random variables in the sense in which an evenly balanced die is a random variable.

The probability of an element (or, more precisely stated, the probability of a fact that satisfies an element) is conditional on evidence: i.e., P(Element n|Evidence x) -- or, more precisely stated, P(Fact n| Evidence x). That expression yields a probability: the resulting probability is a function of (i) the prior probability Fact n and, (on a Bayesian view of things), (ii) on the ratio of P(Evidence X|Fact n)/P(Evidence x|~Fact n). The same will be true for every other element of the claim or affirmative defense.

  • Note: Even the "prior probability" Fact n is not "absolute," or unconditional: The prior probability of Fact n is conditional on "background evidence," of evidence that is present, that is there, before Evidence x "comes along," or is considered. See Hajek's convincing argument that all probabilities are conditional probabilities.
  • Is there any reason to assume that the chance of any probability value (between and inclusive of 0 to 1) for some Fact n given some Evidence x is equal to the chances of any other probability value between and inclusive of 0 and 1? I can't think of a valid reason why we should make this assumption. Can you? So a material fact in issue conditional on some evidence is not that sort of random variable: The correct analogue is not the equiprobability that we attach to each of the possible outcomes of an evenly-balanced die or an evenly-balanced roulette wheel, is it?

    If that's correct, just what, precisely, does the expression P(Fact n| Evidence x) represent or "stand for"? If the expression represents someone's epistemic uncertainty, ... whose uncertainty would a numerical value for P of Fact n given Evidence x represent? And once we have an answer to that question, what would our answer imply (if anything) for the chances of success for a proponent of a legal claim or an affirmative defense?

    These are murky waters. Perhaps it is better for me to stay away from them. (I'm no mathematician or logician. I'm just a poor ol' befuddled law teacher.)

    &&&

    The dynamic evidence page

    It's here: the law of evidence on Spindle Law. See also this post and this post.

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