Why too much evidence can be a bad thing

(Phys.org)—Under ancient Jewish law, if a suspect on trial was unanimously found guilty by all judges, then the suspect was acquitted. This reasoning sounds counterintuitive, but the legislators of the time had noticed that unanimous agreement often indicates the presence of systemic error in the judicial process, even if the exact nature of the error is yet to be discovered. They intuitively reasoned that when something seems too good to be true, most likely a mistake was made.

In a new paper to be published in The Proceedings of The Royal Society A, a team of researchers, Lachlan J. Gunn, et al., from Australia and France has further investigated this idea, which they call the "paradox of unanimity."

"If many independent witnesses unanimously testify to the identity of a suspect of a crime, we assume they cannot all be wrong," coauthor Derek Abbott, a physicist and electronic engineer at The University of Adelaide, Australia, told Phys.org. "Unanimity is often assumed to be reliable. However, it turns out that the probability of a large number of people all agreeing is small, so our confidence in unanimity is ill-founded. This 'paradox of unanimity' shows that often we are far less certain than we think."

The researchers demonstrated the paradox in the case of a modern-day police line-up, in which witnesses try to identify the suspect out of a line-up of several people. The researchers showed that, as the group of unanimously agreeing witnesses increases, the chance of them being correct decreases until it is no better than a random guess.

In police line-ups, the systemic error may be any kind of bias, such as how the line-up is presented to the witnesses or a personal bias held by the witnesses themselves. Importantly, the researchers showed that even a tiny bit of bias can have a very large impact on the results overall. Specifically, they show that when only 1% of the line-ups exhibit a bias toward a particular suspect, the probability that the witnesses are correct begins to decrease after only three unanimous identifications. Counterintuitively, if one of the many witnesses were to identify a different suspect, then the probability that the other witnesses were correct would substantially increase.

The mathematical reason for why this happens is found using Bayesian analysis, which can be understood in a simplistic way by looking at a biased coin. If a biased coin is designed to land on heads 55% of the time, then you would be able to tell after recording enough coin tosses that heads comes up more often than tails. The results would not indicate that the laws of probability for a binary system have changed, but that this particular system has failed. In a similar way, getting a large group of unanimous witnesses is so unlikely, according to the laws of probability, that it's more likely that the system is unreliable.