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The stated assumptions are that all people are equal with respect to morals; that morals apply equally to all persons; that individuals are sovereign.

We originally got onto this by way of your post to me at #197, wherein you attempted to counter my comment from #67, "One can't derive morality or theology from science, as science is necessarily agnostic," with some commentary from Plato. I'll return to Plato in a moment, let's look at the attempt you cite of a deduced morality, the libertarian principle.
I suggested to lexcorp, at #191, that if one attempted to do so, they would "soon be making arbitrary and unscientific pronouncements."
When, in your libertarian principle, you cite "stated assumptions," you've done exactly that. Why are those assumptions, "that all people are equal with respect to morals; that morals apply equally to all persons; that individuals are sovereign," more valid than say, survival of the fittest?
Let me suggest that they are arbitrary, or else they wouldn't have needed to be assumed, you'd have deduced them.

Now, as for Plato...
The link you provided suggests the following dilemma...
Why is the Euthyphro dilemma important for philosophy of religion? Although many believers consider God to be the ground of morality, what exactly does this mean in practice? Is it that God is the ground of morality in that what God wills is good and trustworthy? If so, then God's commands are arbitrary and it is perfectly reasonable to argue that one day God might decree that committing adultery is a good thing to do. Or is it? If one questions the viability of this possibility is it because of an innate sense that committing adultery is wrong? If so, God's commands are not arbitrary but are formed on the basis of what is good. But this implies that there is a moral standard greater than God to which God's decrees must conform. In other words, if God cannot decree adultery to be good it is because the notion that adultery is wrong exists outside the Divine realm. But if this is so then who, or what, has instigated this supramoral realm? Here the problem is clearly exposed. Is an act morally good because God wills it or is it good because God agrees that it is good? We place an enormous amount of trust in the character of God if the former is true (E.g. we assume God is all-good but we cannot know for sure), whilst we are led to question the status of God in the presence of the latter (E.g. God's Omnipotence).

Let's break it down...
"Although many believers consider God to be the ground of morality, what exactly does this mean in practice? Is it that God is the ground of morality in that what God wills is good and trustworthy? If so, then God's commands are arbitrary and it is perfectly reasonable to argue that one day God might decree that committing adultery is a good thing to do."

It is an error to suggest that God's commands are arbitrary. The appropriate adjective is "sovereign." Whatever our inability to understand the basis of His commands, they are no more arbitrary than our command to a dog to stay off the sofa, though our reasons are well beyond canine understanding (we just don't want their hair on the furniture).
Therefore it is an error to suggest that "it is perfectly reasonable to argue that one day God might decree that committing adultery is a good thing to do," since it hinged on a belief that His will was arbitrary.
More...
"If one questions the viability of this possibility is it because of an innate sense that committing adultery is wrong? If so, God's commands are not arbitrary but are formed on the basis of what is good. But this implies that there is a moral standard greater than God to which God's decrees must conform. In other words, if God cannot decree adultery to be good it is because the notion that adultery is wrong exists outside the Divine realm."

Here is the key to misunderstanding... "But this implies that there is a moral standard greater than God to which God's decrees must conform."
God doesn't require an external, supramoral standard by wich He must conform. God is eternal, irreducible Virtue. Morality is intrinsice to His nature. God is good, and good is God.
Isn't that a tautology? Sure, because that's the type of explanation we finite beings of four-dimensional space-time are going to get when trying to perceive the Eternal the Omnipotent, and the Omniscient. That's not due to God's limitations, but to ours.
For example, in the Bible, God said to Moses, "I am, that I am." (Exocus 3:14)
Yet He also said to Job from the whirlwind (Chapter 38)...

2 "Who is this that darkens counsel by words without knowledge?
3 Gird up your loins like a man, I will question you, and you shall declare to me.
4 "Where were you when I laid the foundation of the earth? Tell me, if you have understanding.
5 Who determined its measurements--surely you know! Or who stretched the line upon it?
6 On what were its bases sunk, or who laid its cornerstone,
7 when the morning stars sang together, and all the sons of God shouted for joy?

Further (Ch. 40)...

1 And the LORD said to Job: 2 "Shall a faultfinder contend with the Almighty? He who argues with God, let him answer it."

Most attempts to put God into a box, including Plato's Euthyphro dilemma, revolve around attempts to undermine God's nature... "Can God make a mountain bigger than He can lift? If no, He's not omnipotent, if yes, He's not Omnipotent."
This reduces to, "Can God make Himself not Omnipotent? If no, He's not Omnipotent, if yes, He's not Omnipotent." And...
"If Omnipotent, then not Omnipotent," and...
"If omnipotent, then not God."
And the paradoxes just keep coming, getting sillier and sillier. As with the earlier tautology, our inability to fully grasp Omniscience and Omnipotence is exactly that: our inability.
Not God's.

Just to clarify, although I initially responded to a later post, what first sparked my attention was your following statements to lexcorp in posts 48 and 67:

How do you "know that some things are just wrong?"

Who decides?

Your assertion that morality can be derived from experience, intuition, and a consensus of society is as mystical as any appeal to a higher power.

I do not doubt your sincerity in your beliefs. But not everone is sincere as you. You choose to live your life according to a belief in God. But not everyone around you believes in God, and of those that do, not everyone believes in your God.

To hold all men to the standards of YOUR religion is not proper, unless the intent is to establish a theocratic society enforcing a single religion. (I don't mean to imply you have suggested that, of course, but that is the only way to enforce a divinely dictated morality.)

In order for people of all religions to hold a common standard of morality, such assumptions as I postulated must be necessary. "It's self-evident that all men are created equal," so on and so forth. To assume the equality of all men with respect to rights and morals is a logical assumption. From there, morals and rights can be deduced.

The danger of assuming that the only legitimate source of morality is via religion is the automatic and necessary assumption that atheists are immoral. This position is obviously false, as is the assumption that an atheist must by definition hold arbitrary standards of morality.

The short answer is that we disagree. I appreciate your courtesy.

It is an error to suggest that God's commands are arbitrary. The appropriate adjective is "sovereign." Whatever our inability to understand the basis of His commands, they are no more arbitrary than our command to a dog to stay off the sofa, though our reasons are well beyond canine understanding (we just don't want their hair on the furniture).

Therefore it is an error to suggest that "it is perfectly reasonable to argue that one day God might decree that committing adultery is a good thing to do," since it hinged on a belief that His will was arbitrary.

It's perfectly reasonable to say that God could change His inscrutable mind & declare adultery moral all of a sudden. Maybe God bought a new couch & put the old one in the basement, so He now lets us shed on the old couch at will. Does He have to explain his actions to you? NO, he's sovereign, and He assures us that He's beyond our understanding! So just receive His new commands, that go against everything you believe is right regarding adultery, and just have faith that He has good reasons of His own. (Now who's putting God in a box???)

Here is the key to misunderstanding... "But this implies that there is a moral standard greater than God to which God's decrees must conform."

God doesn't require an external, supramoral standard by wich He must conform. God is eternal, irreducible Virtue. Morality is intrinsice to His nature. God is good, and good is God.

Equating God == good is a reification error. Just like saying God == a supernatural man on a supernatural throne would be an anthropomorphization error, a specific kind of reification error. It's like saying "God is profit and profit is God", or "God is the color blue and the color blue is God", or "God is hurry up and hurry up is God". It's a category error. The Good is a class of actions and attitudes, and God is a supernatural person. They're fundamentally different things. So you can't solve the Euthyphro dilemma that way.

Isn't that a tautology? Sure, because that's the type of explanation we finite beings of four-dimensional space-time are going to get when trying to perceive the Eternal the Omnipotent, and the Omniscient. That's not due to God's limitations, but to ours.

Maybe if you defined God as the universe itself you could say that. But then God would equal Bad as well as Good. If God equals everything, then making any kind of moral distinctions based on God's existence would be pretty much a moot point, and you're right back where you started with the dilemma.

Most attempts to put God into a box, including Plato's Euthyphro dilemma, revolve around attempts to undermine God's nature... "Can God make a mountain bigger than He can lift? If no, He's not omnipotent, if yes, He's not Omnipotent."
This reduces to, "Can God make Himself not Omnipotent? If no, He's not Omnipotent, if yes, He's not Omnipotent." And...
"If Omnipotent, then not Omnipotent," and...
"If omnipotent, then not God."
And the paradoxes just keep coming, getting sillier and sillier. As with the earlier tautology, our inability to fully grasp Omniscience and Omnipotence is exactly that: our inability.
Not God's.

But don't you see, what you dismiss as "trying to put God in a box" is merely our attempt to reconcile God with logic! The box IS the constraints of logic. If you don't want your God to have to be limited to being logical then that's your choice, but you really have to shut your mind off at that point, IMO. Then the only thing that's left is chanting.