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Discursive Judges


BMAD
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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 5f05ad1c81b996c02d8ea766ce370e72.png. 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?

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

post-53485-0-12373100-1367876164_thumb.p

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.

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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.

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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 5f05ad1c81b996c02d8ea766ce370e72.png.

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.

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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).

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