This seems consistent so long as U(Certainty) > 1⁄34 U($27,000).
I’m not committed to the notion there is a rational independent value to certainty, I’m just not seeing how it can be dismissed with quick algebra. Maybe that wasn’t your goal. Forgive me if this is my oversight.
I think I missed something on the algebraic inconsistency part...
If there is some rational independent utility to certainty, the algebraic claims should be more like this:
U($24,000) + U(Certainty) > 33⁄34 U($27,000) + 1⁄34 U($0)
0.34 U($24,000) + 0.66 U($0) < 0.33 U($27,000) + 0.67 U($0)
This seems consistent so long as U(Certainty) > 1⁄34 U($27,000).
I’m not committed to the notion there is a rational independent value to certainty, I’m just not seeing how it can be dismissed with quick algebra. Maybe that wasn’t your goal. Forgive me if this is my oversight.