Posted May 6, 2013 - 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! 0 Share this post Link to post Share on other sites

0 Posted May 6, 2013 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. 0 Share this post Link to post Share on other sites

0 Posted May 7, 2013 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. 0 Share this post Link to post Share on other sites

0 Posted May 7, 2013 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? 0 Share this post Link to post Share on other sites

Posted

- 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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