Discursive Judges

[BMAD]

The accused is brought forth in front of the tribunal. The three judges must hear the accusations and the defense to make a determination of innocent or guilt. In this particular case, the accused is found guilty ( C ) if the action in question is defined as illegal (P) and the accused committed the action (Q) or in other words . Judge number 1 found both P and Q true, Judge number 2 found only Q true, and Judge number 3 found only P true. Should the accused be found guilty?

Edited May 5, 2013 by BMAD

[BMAD]

This is actually a famous scenario in social choice theory (known as the discursive dilemma) showing a paradox of aggregating group thought.

As seen in the chart: The majority opinion is that the individual is guilty but the conclusion based on

how the law works (did you commit the act and is the act illegal) would lead to a logical conclusion of innocence. And thus the paradox: the majority think he is guilty but the majority ruling is innocence.

Edited May 6, 2013 by BMAD

[vistaptb]

I don't think the accused should be found guilty; two of the three judges would find him innocent. Say we extended this to 101 judges. If 50 judges say that the action is illegal but the defense didn't undertake it, 50 judges say that the defense did the action and that it was perfectly legal, and only 1 judge said that the defense was actually guilty, it would be ridiculous to convict him based on that.

[bonanova]

OP says

the accused is found guilty ( C ) if the action in question is defined as illegal (P) and the accused committed the action (Q) or in other words .

That is implication: P and Q -> C.

Do you mean if and only if?

Or does it matter?

[bonanova]

He should not be found guilty. Implication is enough.

Two of the three judges voted not guilty.

• J1: P and Q => C.
• J2: ~P => ~C.
• J3: ~Q => ~C.

[BMAD]

OP says

the accused is found guilty ( C ) if the action in question is defined as illegal (P) and the accused committed the action (Q) or in other words .

That is implication: P and Q -> C.

Do you mean if and only if?

Or does it matter?

In other words, the judges agree that a defendant should be liable only if P and Q are both true.

[bonanova]

And that's all we need to solve.

[BMAD]

And that's all we need to solve.

Yes. there is no additional information needed.

[bonanova]

Which leads to the posts, #2 and #4, where the solution is given.

[witzar]

It obviously depends on jurisdictional procedure. If each judge votes guilty/not guilty, then the accused will be released, since only 1 out of 3 judges votes "guilty". But if judges vote on P, then vote on Q - he will be convicted (both P and Q will be voted "true" with 2 votes out of 3).

[vigmeister]

Actually I feel even there mathematically, the judges are 2/3 sure of P and 2/3 of Q which means they are probabilistically only 4/9 certain of the man's guilt. I think a not guilty decision is fair, but this got me thinking (in another thread...)