This post is meant to set the stage for a follow-up post in which I will argue that the Euthyphro Dilemma provides a definitive (or as close to definitive as we can reasonably expect to get) objection to divine command metaethics (even the modern so-called modified divine command theories associated with Robert Adams, Edward Wierenga, C. Stephen Evans and others). In this post I want to talk not about divine commands or love or metaethics, but rather supreme executive power, reasons, motives, and arbitrariness. We’ll start with this:

https://www.youtube.com/watch?v=JvKIWjnEPNY

Upon learning how Arthur became King of the Britons, Dennis the constitutional peasant says, “Strange women lying in ponds distributing swords is no basis for a system of government. Supreme executive power derives from a mandate from the masses, not from some farcical aquatic ceremony.”
Dennis is here presenting a democratic theory of the basis of government. Presumably, he would be unmoved even if he were assured that the Lady of the Lake had perfect knowledge of any presumed candidate’s qualifications and only tossed swords to candidates that were well-qualified. After all, defenders of democracy recognize that their preferred system does not always result in the most qualified leadership. Their claim is, rather, that legitimate government is only that which is elected via popular referendum. So, from Dennis’ perspective, the Lady of the Lake’s choice is completely arbitrary with respect to the issue at hand. But notice that his concern is not that it is arbitrary because it is ungrounded in reasons; Dennis does not care whether she had reasons or what those reasons might be (more on this, including an important ambiguity involved in ‘reason’ below). The problem, from Dennis’ perspective, is that the feature of Authur Pendragon, in virtue of which he is King, namely that the Lady of the Lake threw Excalibur to him, is totally unrelated to the task he was chosen for, that is, being King. In that sense, the fact that he was the recipient of Excalibur is just an arbitrary reason to think that he deserves to be King.
A basis or ground of something can be arbitrary when the purported ground is completely unrelated to the thing for which it is supposed to be serving as the ground. Here is another example: Suppose that passengers on a damaged aircraft, which is running low on fuel, have determined that the plane stands a good chance of making it to a safe landing spot only if its weight is significantly reduced; and the only way to do that is for one of the passengers to jump from the plane. Since there are no volunteers, the passengers decide to draw straws to see who will have to jump. Bob draws the short straw. Given that Bob agreed to the procedure, he is now obligated to jump. But here’s the thing: Bob does not deserve to be sacrificed just in virtue of having drawn the short straw. Drawing the short straw is not the kind of thing that could make someone deserve to be sacrificed. It is an arbitrary reason to think that Bob deserves to die.
It is important to note that there may be a non-arbitrary method for deciding who deserves to die. But time is running out and given the difficulties involved in discovering a mutually agreed upon method, the passengers are better off just going with the arbitrary method of drawing straws. But that the method is expedient does not make it less arbitrary. In this case the ground–drawing the short straw–is not the kind of thing that could serve as the basis for the relevant feature; that is it cannot make it the case that a person should die. This is what makes the method arbitrary.
One more point: even if it is true that the Lady of the Lake (LoL) had reasons for her decision to throw the sword to Arthur, that does not mean that her decision was non-arbitrary. To see this we need only remind ourselves that ‘reason’ is ambiguous between ‘motive’ and ‘justifying reason.’ If, when we say that the LoL has reasons for choosing Arthur, what we mean is merely that she has motives for choosing him, then we are not saying that she has a justifying reason for her decision. She can have a motive that would render her decision arbitrary. Suppose, for example, that she is acting on a threat, the ghosts of Arthur’s deceased ancestors have threatened to reveal scandalous information about the LoL’s proclivities for hippo-love; or suppose she is personally smitten with Arthur’s considerable charms.  In such a case, while LoL has a motive to choose Arthur as King, she lacks a justifying reason. And (and this is very important) her decision is therefore arbitrary.
We will miss this point so long as we neglect the very significant distinction between motives and reasons. We use the word ‘reason’ to talk about both, but this obscures the following important difference: motives explain while reasons justify. One can therefore have a motive without having a reason (in the justifying sense). Therefore the fact that a decision was based on a motive does not make the decision non-arbitrary.
Stay tuned for my follow-up post in which I apply some of these lessons to the Euthyphro based objections to DCT.