First of all, I recommend clearing away the moral language (value, good, and must) unless you want certain perennial moral controversies to muddy the waters.
Example phrasings of the case you may be trying to make:
Bayesian predictions made from (100% certain) information set {N}U{M} are usually more accurate than those made from {N} alone
I suppose this is true.
Bayesian predictions made from (100% certain) information set {N}U{M} are always more accurate than those made from {N} alone
If you’ve ever done a jigsaw puzzle, you can probably think of a counterexample to this.
Here’s a counterexample. There is an urn filled with lots of balls, each colored either red or blue. You think there’s a 40% chance that the next ball you pull out will be red. You pull out a ball, and it’s red; you put it back in and shake the urn. Now you think there’s a 60% chance that the next ball you pull out will be red, and you announce this fact and bet on it. You pull out one more ball, and it’s blue. If you hadn’t seen that piece of evidence, your prediction would have been more accurate.
First of all, I recommend clearing away the moral language (value, good, and must) unless you want certain perennial moral controversies to muddy the waters.
Example phrasings of the case you may be trying to make:
I suppose this is true.
If you’ve ever done a jigsaw puzzle, you can probably think of a counterexample to this.
You’ve never done a jigsaw puzzle using optimal Bayesian methods.
(Or he just believes you probably haven’t!)
Here’s a counterexample. There is an urn filled with lots of balls, each colored either red or blue. You think there’s a 40% chance that the next ball you pull out will be red. You pull out a ball, and it’s red; you put it back in and shake the urn. Now you think there’s a 60% chance that the next ball you pull out will be red, and you announce this fact and bet on it. You pull out one more ball, and it’s blue. If you hadn’t seen that piece of evidence, your prediction would have been more accurate.