The most coherent formulation that I’ve seen is from Terence Cuneo’s The Normative Web. The basic idea is that moral norms have the same ontological status as epistemic norms. 

Unpacking this a little, when we’re talking about epistemic norms we’re making a claim about what someone ought to believe. For example:

• You ought to believe the Theory of General Relativity is true.
• You ought not to believe that there is a dragon in your garage if there is no evidence.

When we say ought in the sentences above we don’t mean it in some empty sense. It’s not a matter of opinion whether you ought to form beliefs according to good epistemic practices. The statements have some normative bite to them. You really ought to form beliefs according to good epistemic practices.

Similarly, you could cast moral norms in a similar vein. For example:

• You ought to behave in a way which promotes wellbeing
• You ought not to behave in a way which causes gratuitous suffering.

The moral statements above have the same structure as the epistemic statements. When I say you really ought not to believe epistemically unjustified thing X this is the same as saying you really ought not to behave in morally unjustified way Y.

There are some objections to the above:

• You could argue that epistemic norms reliably track truth whereas moral norms reliably track something else like wellbeing which you need an additional evaluative function to tell you is “good.”

The point is that you also technically need this for epistemic norms. Some really obtuse person could always come along and ask you to justify why truth-seeking is “good” and you’d have to rely on some external evaluation that seeking truth is good because XYZ. 

• The standard formulation of epistemic and moral norms is “non-naturalist” in the sense that these norms cannot be deduced from natural facts. This is a bit irksome if we have a naturalist worldview and want to avoid positing any “spooky” entities.  

Ultimately I’m pretty skeptical that we need these non-natural facts to ground normative facts. If what we mean by really ought in the above are that there are non-natural normative facts that sit over-and-above the natural facts then maybe the normative statements above don’t really have any “bite” to them. As noted in some of the other comments, the word really is doing a lot of heavy lifting in all of this. 

My intuition that there's something "real" about morality seems to come from a sense that the consensus process would be expected to arise naturally across a wide variety of initial universe configurations. the more social a species is, the more they seem to have a sense of doing-well-by other beings; the veil of ignorance seems intuitive in some sense to them. It's not that there's some thing outside us, it's that, if I'm barking up the right tree here, our beliefs and behaviors are a consequence of a simple pattern in evolutionary processes that generates things like us fairly consistently.

If we imagine a CEV process that can be run on most humans without producing highly noisy extrapolations, and where we think it's in some sense a reasonable CEV process; then for me, I would try to think about the originating process that generated vaguely cosmopolitan moralities, and look for regularities that would be expected to generate it across universes. Call these regularities the "interdimensional council of cosmopolitanisms". I'd want to study those regularities and see if there are structures that inspire me. call that "visiting the interdimensional council of cosmopolitanisms". if I do this, then somewhere in that space, I'd find that there's a universe configuration that produces me, and produces me considering this interdimensional council. It'd be a sort of LDT-ish thing to do, but importantly this is happening before I decide what I want, not as a rational bargaining process to trade with other beings.

But ultimately, I'd see my morality as a choice I make. I make that choice after reviewing what choices I could have made. I'd need something like a reasonable understanding of self fulfilling prophecies and decision theories (I currently am partial to intuitions I get from FixDT), so as to not accidentally choose something purely by self-fulfilling prophecy. I'd look at this "real"ness to morality as being the realness of the fact that evolution produces beings with cosmopolitan-morality preferences.

It's not clear to me that morality wins "by default", however. I have an intuition, inspired by the rock-paper-scissors cycle in game theory evolutionary prisoner's dillema experiments (note: citation is not optimal, I've asked a claude research agent to find me the papers that show the conditions for this cycle more thoroughly and will edit when I get the results), that defect-ish moralities can win, and that participating in the maximum-sized cooperation group is a choice. the realness is the fact that the cosmopolitan, open-borders, scale-free-tit-for-tat cooperation group can emerge, not that it's obligated by rationality a priori to prefer to be in it. What I want is to increase the size of that cooperation group, avoid it losing the scale-free property and forming into either, isolationist "don't-cooperate-with-cosmopolitan-morality-outsiders" bubbles, or centralized bubbles; and ensure that it thoroughly covers the existing moral patients. I also want to guarantee, if possible, that it's robust against cooperating with moralities that defect in return.

see also eigenmorality as a hunch source.

I suspect that splitting LDT and morality like this is a bug arising from being stuck with EUT, and that a justified scale-free agency theory would not have this bug, and would give me a better basis for arguing for 1. wanting to be in the maximum-sized eigenmorality cluster, the one that conserves all the agents that cooperate with it and tries to conserve as many of them as possible 2. that we can decide for that to be a dominant structure in our causal cone by defending it strongly.

For those who give significant weight to the possibility that morals are real, in the "actually have some effect on the universe" sense...

This sense of "real" is contested in contemporary philosophy. As a sketch, here are a few things that are often considered quite plausible:

1. There are abstract objects and abstract facts
   1. Plausible examples: numbers (or sets), shapes, propositions
2. Abstract objects are real
3. Moral facts are abstract facts

If (1-3) are plausible, then it's also plausible that (4) moral facts are real. I'm not exactly offering this as an argument, but merely a set of (what contemporary philosophers consider to be, at least) plausible theses. A philosopher who accepts (4) will usually be referred to as a moral non-naturalist. 

What IS it, if not "just" our beliefs and preferences about each others' behaviors?

This is an interesting question for moral non-naturalists; but they would respond that this question is no more mysterious for morality than it is for mathematics (or any other abstract domain). And they'd certainly reject that moral facts (and mathematical facts) are "just" reflections of our beliefs and preferences. 

I find the premise that it's anything but a social consensus of human preferences to be ... incoherent.

Of course, many philosophers will reject 1-4 above, as well as this thought of yours. Such philosophers think that moral facts simply reduce to natural facts. E.g., facts about wrongness reduce to facts about units of pain, in the same way that facts about water reduce to facts about H2O. If they're right about that, then all we need to do is figure out how to measure pain-units -- or whatever natural property morality corresponds to.

Minimally, moral realism is just the theory that moral propositions have mind independent truth values. The often derided idea that MR requires a domain of supernatural truth makers is a maximal form.

For those who give significant weight to the possibility that morals are real, in the “acually have some effect on the universe” sense

Minimal MR does not require such causal influence.

So, how do you justify MR without exotic ontology,?

*Some natural facts are also moral facts (Sam Harris seems to believe something like this)

*It evolved (possible amounting to the above)

*It works like logic ...

*..or decision theory..

*...or game theory...

*Or it's constructed (possibly the same as some of the above).

Arguments against subjectivism and constructivism are to some extent arguments for realism. (Not entirely because nihilism, error theory and non cognitivism are options).

We often have posts exploring morality, and I find the premise that it’s anything but a social consensus of human preferences

The classic argument is the open question argument...for any socially constructed system of morality, it's seems reasonable to ask whether it's really true (whereas it makes a lot less sense to ask whether a personal preference is really a personal preference).

Some forms of mild realism can answer the Open Question: if morality is constructed by societies for a purpose , it can fail at the purpose, and therefore be "wrong" in a sense. Compare with things like financial and political systems which are constructed but can still be better or worse ..under the circumstances. Moderate realism can avoid the central problem of relativism , which is that any society is good by its own standards.

Societies need to create morality, because their interests as a whole can conflict with the interests of their members...societies need brave soldiers to sacrifice themselves on foreign field, but their members do not want to be sacrificed.

My intuition that there’s something “real” about morality seems to come from a sense that the consensus process would be expected to arise naturally across a wide variety of initial universe configurations. the more social a species is, the more they seem to have a sense of doing-well-by other beings

It's hard to see how an asocial society would need morality at all..if you were alone on a desert island , there is no one one to steal from , murder, etc. But it doesn't follow from that , that all societies will converge on the same morality...only that they need some kind of morality. Circumstances differ.

@lesswronguser123

pretty much depends on how you define real. I buy more into [Valence series] 1. Introduction

That only describes how individuals make decisions in their own interests. Morality is about doing things you otherwise wouldn't. That's why it needs to be backed by persuasion and threats.

@Dagon

Thanks. Can you describe a bit more about #2 “Abstract objects are real”? I don’t see how this could be believed. There are elements of reality that correspond pretty well to abstract objects, but never (AFAIK) precisely—there are always variants or finer-grained measurements that don’t match the abstraction

The idea is not that there is some material object that perfectly exemplifies an abstraction, -- it's the idea is that abstract objects exist immaterially and eternally.

@Richard_Kennaway

The concepts of mathematics exist of themselves, independent of the relationships that some of them have to physical reality

That's a theory, not a fact.