Yes, in certain ways, says mathematician at the University of Adelaide.
From Science Daily:
The old adage that says ‘If it sounds too good to be true, it probably is’ has finally been put to the test — mathematically. A team of researchers has found that overwhelming evidence without a dissenting opinion can in fact weaken the credibility of a case, or point to a failure of the system.
The team put three different scenarios to the test based on mathematical probability: the use of witnesses to confirm the identity of a criminal suspect; the accurate identification of an archaeological find; and the reliability of a cryptographic system.
They found in each case that there was a point at which “too much of a good thing” actually weakened confidence in the result.
“In our first example, we imagine there are 13 witnesses who all confidently identify a criminal suspect after seeing the suspect briefly. But getting a large group of unanimous witnesses in these circumstances is unlikely, according to the laws of probability. It’s more likely the system itself is unreliable,” says Professor Abbott.
“In our scenario, the probability that a suspect is guilty is strong after three positive identifications by witnesses. But our tests showed that the more positive confirmations you have beyond those three, the more it erodes our confidence that this is the right person being identified. More.
The number of people who are quite legitimately quite certain probably won’t exceed three under normal circumstances.
But wait… where did we hear the phrase “overwhelming evidence” repeated ad nauseam? Oh yes,
Asix-week trial over the issue yielded “overwhelming evidence” establishing that intelligent design “is a religious view, a mere re-labeling of creationism, and not a scientific theory,” said Jones, a Republican and a churchgoer appointed to the federal bench three years ago.
Well, we’ll see how that plays out, but one wonders if anyone would have predicted that in 2016, the Royal Society would start to get serious about seeing past Darwin.
Lachlan Gunn and his team were using Bayesian analysis.
But see also: Bayes’ supercool theorem promotes “superstition”?
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Here’s the abstract:
Is it possible for a large sequence of measurements or observations, which support a hypothesis, to counterintuitively decrease our confidence? Can unanimous support be too good to be true? The assumption of independence is often made in good faith, however rarely is consideration given to whether a systemic failure has occurred.
Taking this into account can cause certainty in a hypothesis to decrease as the evidence for it becomes apparently stronger. We perform a probabilistic Bayesian analysis of this effect with examples based on (i) archaeological evidence, (ii) weighing of legal evidence, and (iii) cryptographic primality testing.
We find that even with surprisingly low systemic failure rates high confidence is very difficult to achieve and in particular we find that certain analyses of cryptographically-important numerical tests are highly optimistic, underestimating their false-negative rate by as much as a factor of 280. (Public access) – Lachlan J. Gunn, François Chapeau-Blondeau, Mark McDonnell, Bruce Davis, Andrew Allison, Derek Abbott. Too good to be true: when overwhelming evidence fails to convince. Proceedings of the Royal Society A, January 2016