Whereas the Mythbusters confirmed it. Of the two shows, I’d give far more weight to the Mythbusters.
Above either, I’d go with Cecil, and above that is Google Scholar, where you can look through actual research which has been done on the subject.
Now if you look through Google scholar, you’ll find that there are (simplistically speaking) studies which prove that polygraphs work and there are studies which prove that they don’t. That could either mean that the results are indeterminate (i.e. sometimes you’ll get a positive result and sometimes you won’t) OR it means that the methodology of the studies causes different results.
That I’ve seen, there are two key findings in the literature:
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Lie detectors are wholly ineffective unless a person fears the outcome of the test. Telling lies doesn’t cause people to become so ashamed of themselves that they demonstrate measurable signs of stress. Fear of getting caught and punished causes people to become stressed, whenever any question comes up which, if they answered honestly, would lead to them being punished. The vast majority of lie detector tests fail to find any results because they expect the machines to detect lies, rather than to detect stress. The name “lie detector” for a polygraph is a misnomer. It should be “stress detector”.
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It is amazingly easy to beat a polygraph. Simple training in a few easily accomplished techniques can completely destroy the effectiveness of the polygraph.
In the real world, there is the real threat of punishment if you are guilty of the crime that you’re under the polygraph for, so while item #1 is relevant to the testing of polygraphs, it isn’t relevant to the usage of polygraphs as a tool.
And, in the real world, the grand majority of criminals are uneducated morons. They have almost certainly not researched methods for beating a polygraph, nor have they practiced them. So item #2 is also not relevant.
In the real world, it’s almost certain that polygraphs are highly effective.
Where they break down is with the following three classes of people (one can infer):
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Anyone who feels no guilt in their crime or concern for their future - sociopaths, psychopaths, etc. - are liable to pass the test with no issue because they don’t get stressed out about the situation.
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Anyone who is simply a worrywart is liable to fail the test because, even though they didn’t do anything wrong, they know which questions would reveal guilt and become stressed just by hearing such questions. They’re worried what their body might show that they’re lying even when they’re not, since they can’t control their body. And of course, that’s just what happens.
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Anyone who is reasonably intelligent could probably come up with a few potential methods to fool the polygraph, if not research a couple beforehand.
In prosecuting crime, everything should come down to odds. I should be able to say that, unless someone has utilized a method to beat the polygraph, the test will give a valid result ~85% of the time. (The other 15% of the time, the person is either a sociopath or a worrywart.) Though if they have an IQ higher than 100, there’s a 50% chance that they’ve utilized a method to beat it, and if they’re above 120 IQ then they almost certainly would have. In all of those cases, a polygraph showing someone as guilty is only false in the case of unintelligent worrywarts, which might only be 4% of all cases tested. The other 96% of guilty results, the person is genuinely guilty.
Compared to fingerprint evidence or DNA evidence, polygraph results aren’t very good, but paired with even one more item of evidence, and the odds that the accused isn’t guilty become impressively low.