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## Making something out of nothing: the inconclusive fallacy

K. Kulick, M. W. Perlin, "Making something out of nothing: the inconclusive fallacy", American Academy of Forensic Sciences 74th Annual Scientific Conference, Seattle, WA, 25-Feb-2022.

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Abstract

"You can’t get something for nothing" – First Law of Thermodynamics
"0 + 0 = 0" – Immediate from the Peano Postulates of Natural Numbers
"Nothing will come of nothing" – King Lear, Act I, William Shakespeare

It is well known in science, mathematics and literature that one can't create something out of nothing. Adding together an infinite number of zeros still sums to zero. But in forensic science, some lawyers argue that the absence of forensic evidence implies guilt. That "inconclusive" DNA evidence means that the defendant is "included" in DNA evidence. This fallacious reasoning is wrong and dangerous.

The argument goes like this. First, a forensic expert reports that some evidence (DNA, for example) is "inconclusive" for a defendant. Then, an attorney has their expert agree that, based on these "inconclusive" results, the defendant "cannot be excluded" from the DNA evidence. The lawyer goes on to tell the jury that since the defendant cannot be excluded, he "must be included" in the DNA evidence. And therefore, is guilty as charged.

This logical fallacy misapplies the "law of the excluded middle." The lawyer is incorrectly saying that the defendant must either be "excluded" or "included" from the evidence; there is no other possibility. But there is a third possibility – the evidence is "inconclusive" – and so no "excluded" or "included" determination can be made.

Expressed as a likelihood ratio (LR), when a LR match statistic equals one, there is no support in the evidence for a hypothesis (e.g., defendant inclusion) or its alternative (exclusion). Scientists use the logarithm of the LR to express information. The log of 1 is 0. So, there is zero information about inclusion or exclusion. Zero is not a positive log(LR) supporting inclusion, nor is zero a negative log(LR) supporting exclusion. A zero log(LR) means zero information.

Many crime laboratories apply thresholds to their statistical LR results. Even though they calculate an informative match statistic (say, an inclusionary LR = 1000, or an exclusionary LR = 1/1000), they do not report this LR and instead call the result "inconclusive." Better science would have them report the LR value, along with an error rate that provides context for the jury. For example, giving the chance that someone who didn't leave their DNA in the evidence would have a match statistic as strong. That helps prevent the unscientific transformation of informative DNA evidence into inconclusive results.

Arguing that "inconclusive" forensic non-results imply guilt is not admissible evidence. An "inconclusive" statement has no probative value – it has no ability to make a relevant disputed point more true or less true. Moreover, FRE Rule 403 on relevant evidence permits courts to exclude even relevant evidence, should its probative value be substantially outweighed by a danger of unfair prejudice, confusing the issues, or misleading the jury.

This presentation introduces the "inconclusive fallacy," where lawyers concoct something nonsensical out of nothing forensical. We illustrate the fallacy's misuse in recent criminal cases where "inconclusive" arguments harmed justice. We discuss the ethical implications of misleading a jury through nonprobative forensic evidence. Practicing trial lawyers need to be aware of this maneuver so that they can raise timely objections to vacuous arguments that subvert forensic science.

Links

• American Academy of Forensic Sciences 74th Annual Scientific Conference - Program