vigmeister Posted May 6, 2013 Report Share 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! Quote Link to comment Share on other sites More sharing options...

0 vistaptb Posted May 6, 2013 Report Share 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. Quote Link to comment Share on other sites More sharing options...

0 bhramarraj Posted May 7, 2013 Report Share 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. Quote Link to comment Share on other sites More sharing options...

0 vigmeister Posted May 7, 2013 Author Report Share 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? Quote Link to comment Share on other sites More sharing options...

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## vigmeister

- 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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