Discussion: Should or should not P(Lying | Human) be above or equal to 0,5?

AndreasJ

Hi,

Condition: An human called X, in this specific case, according to game theory will win the most money and lose the least if applying a lying strategy about event Y happening. If he tells the truth about event Y not happening he will lose all the money and go to jail.

If I'm making a decision based on X:s testimony about Y, should I or should I not put P(Lying | Human X gives testimony) to be above or equal to 0,5 and ignore his statement to protect my epistemic vulnerability?

If I put P<0,5 I'm risking making a bad decision because of gullibility and trusting someone who has incentives to lie?

What would I be justified in doing according to you?

Many thanks,

tim wood

↪AndreasJ

I'm pretty sure you need to assign some probabilities to X's lying. You need those for the what-looks-like-an application of Bayes's theorem.

Of course what people might do is hard to figure, so maybe some hypothetical machine, or knights in white or black or grey armor that always act in some specified way.

AndreasJ

Thanks Tim. What I'm aiming for is what probability this would be and if it would be below chance or above chance?

tim wood

↪AndreasJ

i think if you look at some Youtube videos on Bayes's theorem, you will find what you're looking for.

TheMadFool

P(X is lying | X gives testimony) = [P(X gives testimony | X is lying)] * P(X is lying)]/P(X gives testimony]

If X's testimony is guaranteed, P(X gives testimony) = 100% = 1

P(X is lying | X gives testimony) = [1 * P(X is lying)]/1

P(X is lying | X gives testimony) = P(X is lying)

Makes sense because X can't lie until and unless X gives faer testimony.

Discussion: Should or should not P(Lying | Human) be above or equal to 0,5?

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