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vigmeister

Many More Discursive Judges

Question

- Two suspects: Jacques & Gilles. It's been proven that one of them is guilty and deserves decapitation, but we do not know which one.

- Jacques is guilty if and only if both statements P and Q are true. Otherwise, Gilles gets the guillotine...

- There are 9 independent judges and an arbiter (you) who interprets their collective decision with no information about the case.

Situation A

- 4 judges think P&Q are true

- 3 believe only P is true and that Q is false

- 2 believe only Q is true and that P is false

Situation B

- 5 judges think both P&Q are true

- 4 judges think P is false and Q is false

Situation C

- 5 judges think P&Q are true

- 2 believe only P is true and that Q is false

- 1 believes only Q is true and that P is false

- 1 believes that P is false and Q is false

What is your verdict for each of these situations? Perhaps this thread needs to move to philosophical banter?

Cheers!

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3 answers to this question

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For B and C, it's obviously Jacques who has been found guilty. For A, I'd say Gilles because five of the judges find him guilty.

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There are 9 judges. So thre will be 9 opinions about P and 9 opinions about Q, total 18 opinions.

CASE [A]: 6 opinions are that Q is true, 7 opinions are that P is true.

Majority of opinions (12 out of 18) is that P & Q are true. So Jacques is guilty.
CASE : Here 5 opinions are that P is true and 5 opinions are that Q is true. So majority of opinions are that P & Q both are true. Again Jacques is guilty.
CASE [C]: Here also majority of opinions are that P & Q both are true. Again Jacques is guilty.

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If we assume P and Q are independent (I declare that they are!), then the subjective likelighood of P being true is 6/9 and for Q, it is 7/9 which implies overall, likelihood of P&Q is 42/81 which makes Jacques guilty in A.



In B and C, Gilles would be guilty by this method. Anyone agree?

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