This is interesting, because it seems that you’ve proved the validity of the “Strong Adversarial Argument”, at least in a situation where we can say:
This event is incompatible with XYZ, since Y should have been called.
In other words, we can use the Adversarial Argument (in a normal Bayesian way, not as an acausal negotiation tactic) when we’re in a setting where the rule against hearsay is enforced. But what reason could we have had for adopting that rule in the first place? It could not have been because of the reasoning you’ve laid out here, which presupposes that the rule is already in force! The rule is epistemically self-fulfilling, but its initial justification would have seemed epistemically “irrational”.
So, why do we apply it in a courtroom setting but not in ordinary conversation? In short, because the stakes are higher and there’s a strong positive incentive to deceive.
This calculation just used the fact that Y would have been able to give stronger testimony than X, and that lawyers have incentives to present a strong case for their client where possible. In this scenario, the fact that Y was not called is evidence that Y’s testimony would have weakened the case for Z.
The actual objection against hearsay has nothing to do with this calculation at all, as I mentioned in my comment.
You can apply it in ordinary conversation too (to the extent that you apply Bayesian updates in ordinary conversation at all). It’s just that the update is stronger when the equivalent of E|XYZ is more unlikely, and in ordinary conversation it may not be very unlikely resulting in a weaker update.
This is interesting, because it seems that you’ve proved the validity of the “Strong Adversarial Argument”, at least in a situation where we can say:
In other words, we can use the Adversarial Argument (in a normal Bayesian way, not as an acausal negotiation tactic) when we’re in a setting where the rule against hearsay is enforced. But what reason could we have had for adopting that rule in the first place? It could not have been because of the reasoning you’ve laid out here, which presupposes that the rule is already in force! The rule is epistemically self-fulfilling, but its initial justification would have seemed epistemically “irrational”.
So, why do we apply it in a courtroom setting but not in ordinary conversation? In short, because the stakes are higher and there’s a strong positive incentive to deceive.
This calculation just used the fact that Y would have been able to give stronger testimony than X, and that lawyers have incentives to present a strong case for their client where possible. In this scenario, the fact that Y was not called is evidence that Y’s testimony would have weakened the case for Z.
The actual objection against hearsay has nothing to do with this calculation at all, as I mentioned in my comment.
You can apply it in ordinary conversation too (to the extent that you apply Bayesian updates in ordinary conversation at all). It’s just that the update is stronger when the equivalent of E|XYZ is more unlikely, and in ordinary conversation it may not be very unlikely resulting in a weaker update.