LogicalMANIPULATIVE

Defense Attorney's Fallacy

What it is

Arguing that because many people share an incriminating characteristic — “a million people match, so the odds he did it are one in a million” — the evidence is worthless, ignoring that it narrowed the field enormously and that other evidence combines with it.

How it works

This is the mirror of the prosecutor's fallacy, and Thompson and Schumann named both in the same 1987 paper. A match probability of one in a million in a country of 300 million gives about 300 people who match; the defense version stops there and says the defendant is one of 300, so the match proves nothing. But before the match he was one of 300 million, the evidence multiplied the odds against him by a million, and any further evidence — presence in the city, a motive, a second trace — multiplies again. The second form conditions on the wrong event. At the 1995 O. J. Simpson trial the defense argued that fewer than one in 2,500 men who batter their partners go on to kill them, so the history of abuse was irrelevant. I. J. Good's reply in Nature asked the right question: given that the woman was killed, how likely is it that the batterer did it? Worked in people: among 100,000 battered women in a year, about 40 are killed by their partners and about 5 are murdered by someone else, so of the 45 who are murdered, roughly 8 in 9 were killed by the partner. The lever is that a large number of possible matches sounds like reasonable doubt, and a small unconditional probability sounds like irrelevance.

Real-world examples

  • •In 1995 Alan Dershowitz, of the Simpson defense team, argued publicly that since only a tiny fraction of abusive husbands murder their wives, evidence of abuse had little bearing on guilt; Good's 1995 letter in Nature showed that conditioning on the murder having happened raised the relevant probability to well above one half, and Gigerenzer later put it near 8 in 9.
  • •Thompson and Schumann (1987) found that a substantial share of mock jurors, presented with a defense argument that a blood-type match shared by thousands of people “proved nothing”, discounted the evidence almost entirely, although it had excluded the large majority of the population.
  • •Cell-site location evidence is routinely met with the argument that thousands of phones connected to the same tower; that is a fair objection when the location is the only evidence, and a fallacy when the location is combined with a match, a motive and a timeline that each independently narrow the field.
  • •Defense responses to DNA database matches sometimes note that several people in a database of millions are expected to match by chance, which is true, and then treat the defendant as no more likely than any of them, which ignores whatever else connects him to the crime.

Ethical guidelines

  • ●When arguing that a characteristic is widely shared, state how much the evidence narrowed the field and what other evidence must be weighed with it; presenting the number of matches as the odds of guilt is the fallacy.
  • ●Condition on the right event: the probability of interest is given what actually happened, not the unconditional rate of the outcome in the population.
  • ●A large-population argument is legitimate when the shared characteristic really is the only evidence; it is deceptive when other evidence exists and the argument is designed to make the tribunal weigh the pieces separately.
  • ●Advocates on either side should not present a probability to a jury without saying what it is conditioned on.

How to defend against it

  • ►When told “thousands of people match”, ask how many people there were before the match; the ratio is the strength of the evidence, and it is usually large.
  • ►Ask what the probability is conditioned on. “Few batterers kill” and “most murdered battered women were killed by their batterer” are both true and only the second bears on the case.
  • ►Ask what other evidence exists and whether it is independent of the match; pieces of independent evidence multiply, and the argument that treats each as worthless on its own is avoiding the product.
  • ►Rewrite the argument in a population of 100,000 people with the numbers filled in; the wrong conditional usually shows itself in the first line.

From the Defense Playbook

The Base-Rate Checkminutes

Before accepting what a test result, a profile, or a striking detail seems to prove, ask how common the thing is in the first place, because evidence that sounds accurate can still be wrong most of the time when the underlying condition is rare.

Every playbook entry states how strong its evidence is and when not to use it. Browse the full playbook.

References

  1. Thompson, W. C., & Schumann, E. L. (1987). Interpretation of statistical evidence in criminal trials: The prosecutor's fallacy and the defense attorney's fallacy. Law and Human Behavior, 11(3), 167-187
    The naming of the defense attorney's fallacy and the mock-juror evidence that it works.
  2. Good, I. J. (1995). When batterer turns murderer. Nature, 375(6532), 541
    The correct conditioning in the Simpson battering argument: given the murder, the batterer is the likely killer.
  3. Gigerenzer, G. (2002). Calculated Risks: How to Know When Numbers Deceive You. Simon & Schuster
    The natural-frequency working of the Simpson argument to roughly 8 in 9, and the general treatment of both courtroom fallacies.
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