What does the phrase “the greatest balance of happiness over unhappiness” mean?

Question

A utilitarian defines ‘good’ as ‘whatever brings about the greatest total happiness’. This is sometimes known as the Greatest Happiness Principle or the Principle of Utility. For a utilitarian the right action in any circumstances can be calculated by examining the probable consequences of the various possible courses of action. Whichever is most likely to bring about the most happiness (or at least the greatest balance of happiness over unhappiness) is the right action in those circumstances

Philosophy: The basics. Nigel Warburton

What does "the greatest balance of happiness over unhappiness" mean? And I don't understand the use of "over" there. Could your explain it to me?

Answer 1

The meaning is as described at wiktionary, etymology 1, definition 2–3:

(in certain collocations) As compared to.
Sales are down this quarter over last.

The meaning is that, if an action cannot be taken that will result in pure happiness, the action to be taken should result in the best ratio of happiness to unhappiness (which is, not coincidentally, similar to definition 4.)

Answer 2

The "over" hear means simply "compared to". So the amount of happeiness should exceed the amount of unhappiness by as much as possible.

Comment on the answer from @randomhead

In mathematics "A over B" would be the ratio or fraction A/B and the statement would mean that A/B should be as much greater than 1 as possible.

Then the quote would say the goal was to make that fraction (the "balance") as large as possible: much greater than 1. I don't think everyday usage calls for interpreting "over" as creating a fraction. Making the difference A - B as large as possible has the same everyday meaning.