The sum of the utility of an event and its negation is 0.
If two events are independent then the utility of both events occurring is the sum of their individual utilities.
Utilities are defined over outcomes, which don’t have negations or independence relations with other outcomes. There is no such thing as the utility of an event in standard expected utility theory, and no need for such a concept.
Given an outcome X, there are many outcomes other than X, which generally have different utilities. Thus there isn’t one utility value for X not happening.
I didn’t say that. Is there any part of the post you what me to clarify?
Utilities are defined over outcomes, which don’t have negations or independence relations with other outcomes. There is no such thing as the utility of an event in standard expected utility theory, and no need for such a concept.
An event is any outcome from which an individual can derive utility.
The negation of an event is the event not happening.
Given an outcome X, there are many outcomes other than X, which generally have different utilities. Thus there isn’t one utility value for X not happening.