There is a diagnostic screening test for a particular serious disease which has a 90% chance of testing positive if the patient has the disease. However, this test also has a 90% chance of testing positive for a common benign condition. As the test cannot distinguish between whether or not the person has the serious or benign condition, can we disregard the evidence of the positive test result?An important new paper by Toby Pilditch and colleagues (at UCL and Queen Mary) published today in the journal Psychological Science demonstrates that people assume that such evidence can be disregarded. Specifically, they assume that - as it is equally predicted by two competing hypotheses (in this case serious disease versus benign) - it offers no support for either hypothesis. However, this assumption is wrong. It only holds when the 'competing' hypotheses are mutually exclusive and exhaustive (i.e. exactly one is true). In the above example, if both the serious disease and the benign condition are equally likely (say, a 5% chance) in a random member of the population then the positive test result increases the probability of BOTH the serious disease and the benign condition to about 25% (assuming a 10% false positive rate for the test). The paper shows that this reasoning error is due to a 'zero-sum' perspective on evidence, wherein people wrongly assume that evidence which supports one causal hypothesis must disconfirm its competitor. Across three experiments the paper demonstrates this error is robust to intervention and generalizes across several different contexts. The paper also rules out several alternative explanations of the bias.
The implications of this work are profound, as the fallacy is made in many critical areas of decision-making including law and forensics as well as medicine. For example, in 2001 Barry George was convicted of the shooting of Jill Dando, a TV celebrity, outside her flat in broad daylight. The main evidence against him was a single particle of firearm discharge residue (FDR) found in his coat pocket. In 2007 the Appeal Court concluded that the FDR evidence was not ‘probative’ in favour of guilt, because, contrary to what had been suggested in the original trial, it was equally likely to have arisen due to poor police procedures (such as the coat being exposed to FDR during police handling) as from him having fired the gun that killed Dando. Hence, his conviction was quashed and a re-trial ordered, in which Barry George was set free. However, the appeal court argument assumed that if a piece of evidence (the FDR in the coat pocket) is equally probable under two alternative hypotheses (Barry George fired gun vs poor police handling of evidence) then it cannot support either of these hypotheses. But it is not necessarily the case that exactly one of these two hypotheses is true; it is possible that Barry George fired the gun and there was poor police handling of the evidence; and also that neither were true (e.g., the FDR particle came from elsewhere). Therefore, rather than being neutral, the FDR evidence may have been probative against Barry George (albeit weakly). The FDR evidence does not discriminate ‘Barry George fired the gun’ versus ‘poor police handling of evidence’, but it does discriminate ‘Barry George fired the gun’ from ‘Barry George did not fire the gun’: it is the latter hypothesis pair that was the target in this criminal investigation.
I have personally been involved in cases where defence evidence has also been wrongly deemed irrelevant because of the zero-sum fallacy. In particular, this happens when DNA from a crime scene does NOT match the defendant. The defence lawyer argues that this supports the hypothesis that the defendant was not at the crime scene. However, the prosecution and forensic experts argue (wrongly) that the lack of a match can be disregarded as this is equally likely to be the result of failure to collect a sufficient relevant sample of DNA from the crime scene.
The research was based upon work undertaken in the BARD project which was concerned with improving intelligence analysis with uncertain evidence using Bayesian networks. It was supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), under Contract [2017-16122000003].
The full reference:
Pilditch, T., Fenton, N. E., & Lagnado, D. A. (2019). "The zero-sum fallacy in evidence evaluation". Psychological Science, http://doi.org/10.1177/0956797618818484
Pdf of the accepted version.Related links:
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