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Why too much evidence can be a bad thing January 4, by Lisa Zyga, Phys. 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.
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 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.
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.
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.
The researchers say that this paradox crops up more often than we might think. Large, unanimous agreement does remain a good thing in certain cases, but only when there is zero or near-zero bias. Abbott gives an example in which witnesses must identify an apple in a line-up of bananas—a task that is so easy, it is nearly impossible to get wrong, and therefore large, unanimous agreement becomes much more likely.
On the other hand, a criminal line-up is much more complicated than one with an apple among bananas. In these situations, it would be highly unlikely to find large, unanimous agreement.
Wide implications The paradox of unanimity has many other applications beyond the legal arena. One important one that the researchers discuss in their paper is cryptography. Data is often encrypted by verifying that some gigantic number provided by an adversary is prime or composite.
One way to do this is to repeat a probabilistic test called the Rabin-Miller test until the probability that it mistakes a composite as prime is extremely low: The systemic failure that occurs in this situation is computer failure.
Most people never consider the possibility that a stray cosmic ray may flip a bit that in turn causes the test to accept a composite number as a prime. After all, the probability for such an event occurring is extremely low, approximately per month.
But the important thing is that it's greater thanso even though the failure rate is so tiny, it dominates over the desired level of security. Consequently, the cryptographic protocol may appear to be more secure than it really is, since test results that appear to indicate a high level of security are actually much more likely to be indicative of computer failure.
In order to truly achieve the desirable level of security, the researchers advise that these "hidden" errors must be reduced to as close to zero as possible. The paradox of unanimity may be counterintuitive, but the researchers explain that it makes sense once we have complete information at our disposal.
For instance, an experiment tests not only a certain phenomenon, but also the correction function of the experimental tools. In the paradox of unanimity, it's the methods the "auxiliary hypotheses" that fail, and in turn reduce confidence in the main results.
More examples Other areas where the paradox of unanimity emerges are numerous and diverse. Abbott describes several below, in his own words: The company fraudulently programmed a computer chip to run the engine in a mode that minimized diesel fuel emissions during emission tests.Melissa Conrad Stöppler, MD.
Melissa Conrad Stöppler, MD, is a U.S. board-certified Anatomic Pathologist with subspecialty training in the fields of Experimental and Molecular Pathology.
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