At its core,

[CoccoBill]

Of course there are grey areas, but like I said, there's plenty of questions where the differences between two options are clear as day. Happiness is hard to measure, for sure, suffering is a little bit easier. For example insurance companies and justice systems have already for a long time put numeric values on loss of life and mental or physical harm. Obviously these are not perfect and they likely never will be, but they're a start.

For most questions we don't need to measure these things exactly. Take for example capital punishment, genital mutilation of children, honor killings and banning contraception. Consider the subjective suffering they cause and weigh it against the subjective happiness they cause. You're absolutely right, I personally do not have a complete formula to objectively demonstrate which one's greater, but for most people I think it should be crystal clear. Even a pretty crude algorithm could easily deal with these issues.

When we get to the grey areas, say, is it worse to kill one child or two pensioners, or whether it's ok to physically hurt someone to make 10 million people happy, there maybe isn't a clear answer, not from science and not from anything else, since as mentioned, these are subjective questions and depend on a variety of things. I'd still claim that however imperfect, at least for now, science is better equipped to answer these questions than anything else. Science can describe the norms of different cultures, and use set rules with adequate safety margins to compare them, then make decisions on the clear cases. This could be done right now, and get rid of an enormous amount of unnecessary suffering and injustice, the most glaring cases.

I see no fundamental reason why moral questions could not be subjected to rational empirical scientific examination just as well as other social branches of science.

[MadMojoMonkey]

I see no fundamental reason why moral questions could not be subjected to rational empirical scientific examination just as well as other social branches of science.

You can certainly apply scientific method to study anything.

Scienctific method, simplified:
observe, hypothesize, experiment, analyze, evaluate
repeat

Being able to formulate scientifically stable models which make specific, unambiguous, verifiable predictions is a whole other issue.
Having those predictions reproduced by independent scientists, who are diligently trying to disprove your assertions, is a high bar that ethical and moral questions simply have never been able to surmount.

***
Note, in science, a single counter-example to a posited model is enough to disregard the model.