Can Mathematical Certainty be Achieved for Common Claims?

[Ivan Seeking]

Assuming that the most sophisticated lie detectors can yield results with a known degree of accuracy given a large enough sample, is it possible to state with any mathematical certainty whether or not a common claim is true or false, given a large enough sample of alleged witnesses. Assume that we have a clearly identified type of event, but not the same event common to all alleged witnesses.

For example, if 1000 people all claim to have seen a automobile accident at close range [described as absolute certainty] - again, not the same accident, but an accident - and if we can say that our lie detector yields results accurate to 90% in 75% of the people in any large sample, with the other 25% being completely unreliable, and if 900 of the 1000 alleged witnesses pass the lie detector test as truthful, do we have a mathematical statement of certainty as to whether or not automobile accidents happen?

 

[matt grime]

The short answer is no. The longer answer is "that isn't how statistics work", and there's an even longer answer abuot what you're doing isn't maths, and all you're doing is proving something in a model of something, though what the thing you are proving is, and what the model is of are hazy.

 

[Hurkyl]

Ack, the C-word!


All other issues aside, the best result you could get is that there is a segment of the population that believes they've seen a car accident at close range.

 

[Ethereal]

In a court case, that may be sufficiently rigorous as evidence. Brain fingerprinting also works on somewhat the same basis.

 

[Ivan Seeking]

I seem to be getting conflicting answers. I realize that the interpretation of events "believed" by the claimants is what's really tested. I was allowing for absolute certainty with the understanding that this is really a subjective term. However, from what Hurkyl said, we could get a result indicative of truth?

 

[matt grime]

Ok, let me put it this way:

you've produced an argument that proves something in the larger sense of the word proved, proved in legal terms, provided evidence that it is more than reasonable to believe. That argument involves mathematics. But it is not, in my opinion, something that would be called a "mathematical proof" in the sense that a mathematician may use the phrase - it proves nothing about or in mathematics, and arguable not in any mathematical model of something, at least not of the thing you seem to be claiming. We may arguablu have shown mathematically, that some people think they have seen something that they consider to be an accident.

 

[Ivan Seeking]

Okay thanks; I see your point. This was a poor choice of words on my part.

 

[Ivan Seeking]

Okay one more question...getting to the heart of things [watch Hurkyl gasp and fall over dead! ]

Since we are so found of ideal [perfect] devices in physics, let's assume for a moment that we have lie detector test that uses perfect questions! In principle, could a well designed test of claim X as described be used to interpret anecdotal evidence for X, as scientific evidence for X?

 

[matt grime]

please define your terms: what is scientific evidence; what is a perfect question; anecdotal evidence...?

Maths is essentially about definitions. If we know what you mean we can sau, if we don't we're having a semantic argument about things we do not agree upon.

 

[Ivan Seeking]

Please use your own defintions.

 

[cantormath]

Good research is like finding a sequece or function that has a limit; but not, yeah know?

"A Mathematician is a machine for turning coffee into theorems." -Erdös, Paul Nov. 1992

 

[Dr.ThinkDeep]

Sure you can do it statistically - but not for an individual

There are two questions you can try to answer:
1. Is the lie detector better than a coin?
2. What is the probability for
a) a person with a positive test result to have actually lied
b) a person with a negative test result to have actually told the truth.
Question 1 can be dealt with with a Fisher 2x2 contingency table test and it is rather straight forward.
If you want more detail, you will find that there is some threshold involved in interpreting the lie detector test, e.g. some minimal increase of skin conductivity to diagnose a lie. In addition there is a proportion of liars in your population.
Both variables enter in the probabilities 2a and 2b and one should be fine tuned to the other bearing in mind the cost of wrong decisions one way or the other.

The basic problem for application in a trial is to find a population for which the witness is a representative, because the single witness is unique and has not been found according to some definite inclusion/exclusion criteria. The individual comes with a certain stress resistance, a social background, childhood experiences, vegetative stability etc. All of these are covariates that would have to be tested before one can apply the population statistics to the single individual. No soap. Any decent lawyer/statistician team could tear such a result to pieces, imho - well unless the poor guy is in Guantanamo. But then you are into the virtual reality business anyway.
Remember, the price for lying is that you start to believe your own lies and then no lie detector can help you.