Besides the missing parenthesis, there’s a crucial conceptual problem with that statement. If “uv(v(1), b(0))” means “a utility function as defined by the VNM theorem”, then the statement does not follow. VNM says that a utility function exists; it does not say that the function is unique. Since uv(v(1), b(0)) is not uniquely defined, asking whether it is greater than another number doesn’t make sense.
No. The post says, “Betty likes apple pies, but Veronica loves them, so uv(v(1), b(0)) > ub(v(0), b(1)).” It says that Betty’s utility, in the situation where she has one pie and Veronica does not, is less than Veronica’s utility in the situation where she has one pie and Betty does not. That is a constraint that we impose on the two utility functions.
This post is incomplete, as was noted at its beginning, and you really shouldn’t be trying to figure it out now. “Incomplete” is very bad, in mathematics. I’m moving it into Drafts.
No. The post says, “Betty likes apple pies, but Veronica loves them, so uv(v(1), b(0)) > ub(v(0), b(1)).” It says that Betty’s utility, in the situation where she has one pie and Veronica does not, is less than Veronica’s utility in the situation where she has one pie and Betty does not. That is a constraint that we impose on the two utility functions.
This post is incomplete, as was noted at its beginning, and you really shouldn’t be trying to figure it out now. “Incomplete” is very bad, in mathematics. I’m moving it into Drafts.