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

AndreasJ December 10, 2020 at 20:18 1600 views 4 comments

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,

Comments (4)

Deleted User December 10, 2020 at 20:46 #478849 0 likes

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AndreasJ December 10, 2020 at 21:00 #478852 0 likes

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

Deleted User December 11, 2020 at 01:29 #478893 0 likes

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TheMadFool December 13, 2020 at 18:47 #479731 0 likes

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.