Clarification required - what does it mean for everyone to have the "same" utility system? The obvious answer is "every situation gives everyone the same utility", but if I like chocolate, I should gain utility from eating chocolate. If my brother doesn't like eating chocolate, he shouldn't gain utility from it. So if it's not the seemingly obvious answer, how are we defining it?
Also, you've mentioned that the negation of an event is it "not happening", and it has the opposite utility of the original. There are two main objections here:
1) A coworker unexpectedly brings in cookies and hands them out to everyone. This should be a positive utility boost. But am I really getting negative utility every day that doesn't happen? Conversely, am I really getting just as much utility from having my friends alive each and every moment as I lose when they die and I'm stricken with grief?
2) There are an infinite number of things Not Happening at any given time, all of which would in theory play into the utility value. How do we even remotely consider the idea of negations given this?
One way to address this would be to do things like considering probability - we're not terribly happy/sad about the non-occurence of wildly improbable events - but that's just a start.
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.