I don’t think a formal proof is needed. An agent with imperfect knowledge does not, by definition, know what ‘the truth’ is. It may be able to judge the impact of extra information on another agent and whether that information will move the other agent closer or further from the first agent’s own probability estimates but it cannot know whether that has the result of moving the second agent’s probability estimates closer to ‘the truth’ because it does not know ‘the truth’.
Point taken. If we assume the Court-agent can effectively communicate all of its knowledge to the Jury-agent, then the Jury can make decisions at least as good as the Court’s. Or the Jury could communicate all of its knowledge to the Court and then we wouldn’t need a Jury. You’re right about this.
But as long as we’re forced to have separate Court and Jury who cannot communicate all their knowledge to one another—perhaps they can only communicate all the knowledge directly relevant to the trial at hand, or there are bandwidth constraints, or the Judge cannot itself appear as witness to provide new information to the Court—then my point stands.
I don’t think a formal proof is needed. An agent with imperfect knowledge does not, by definition, know what ‘the truth’ is. It may be able to judge the impact of extra information on another agent and whether that information will move the other agent closer or further from the first agent’s own probability estimates but it cannot know whether that has the result of moving the second agent’s probability estimates closer to ‘the truth’ because it does not know ‘the truth’.
Point taken. If we assume the Court-agent can effectively communicate all of its knowledge to the Jury-agent, then the Jury can make decisions at least as good as the Court’s. Or the Jury could communicate all of its knowledge to the Court and then we wouldn’t need a Jury. You’re right about this.
But as long as we’re forced to have separate Court and Jury who cannot communicate all their knowledge to one another—perhaps they can only communicate all the knowledge directly relevant to the trial at hand, or there are bandwidth constraints, or the Judge cannot itself appear as witness to provide new information to the Court—then my point stands.