The objections to your concept of negation still stand, I think—there are an infinite number of possible events, an infinite number of which don’t happen. Only finitely many things happen, but the utility of each is similar to the utility of the things that didn’t happen, since things that don’t happen have the same absolute value as they would if they did. We can’t just say that they cancel out, because they eat up the available utility space, so every individual event has to have an infinitesimal value...
I’m not sure that this is really a fixable system, because it has to partition out a bounded amount of utility among an infinite number of events, since every possible event factors in to the result, because it either A) happens or B) doesn’t, and either way has a utility value. It would need to completely rebuild some of the axioms to overcome this, and you only really have normalizing to the −1 to 1 utility values and the use of negations as axioms.
The objections to your concept of negation still stand, I think—there are an infinite number of possible events, an infinite number of which don’t happen. Only finitely many things happen, but the utility of each is similar to the utility of the things that didn’t happen, since things that don’t happen have the same absolute value as they would if they did. We can’t just say that they cancel out, because they eat up the available utility space, so every individual event has to have an infinitesimal value...
I’m not sure that this is really a fixable system, because it has to partition out a bounded amount of utility among an infinite number of events, since every possible event factors in to the result, because it either A) happens or B) doesn’t, and either way has a utility value. It would need to completely rebuild some of the axioms to overcome this, and you only really have normalizing to the −1 to 1 utility values and the use of negations as axioms.