I think the recent uproar over the acquittal of Casey Anthony clearly shows how our internal system of inference can be at odds with the American judicial system. For those of you who don’t pay attention to the mainstream media, Casey Anthony was a young mother of a toddler that was found dead. What captivated the American public was that the toddler had been missing for a month before Anthony reported it. She lied to her parents and the authorities about the whereabouts of the child and even appeared celebratory in public during the period of the child’s disappearance. In the court of public opinion, Anthony was clearly guilty. The fact that a mother showed no anxiety whatsoever over the disappearance of a child clearly indicates that she was the culprit.
The American judicial system requires that if there is any reasonable doubt of guilt then a person must be acquitted. The burden of proof is on the prosecution. In this case, there were no witnesses and no physical evidence linking Anthony to the death of the child or that the child was even murdered. Thus there was the remote possibility that Anthony was not responsible for the child’s death but simply took advantage of the situation, as macabre as that may be. Even though the probability of these two unlikely events – a mother wishing to be free of her child and a child going missing – is exceedingly low, it is still non zero and thus the jury was forced to acquit.
Now if a single piece of evidence had linked Anthony to the crime, say a fingerprint or DNA sample, then she most likely would have been found guilty. The interesting aspect of this is that there is also an equally low probability that someone could have planted the evidence to frame her. Thus, reasonable doubt is not a global quantity according to the law. It is not sufficient that the total probability that the accused is guilty be high, it also matters if it is high in each of several categories, i.e. motive, opportunity, and direct physical evidence or witnesses. Circumstantial evidence is insufficient to convict a criminal. However, it appears that our brains do not work this way. We seem to take the global probability of guilt and go with that.