I don't think so.
We may and often have to choose to restrict ourselves to some family of conceptions of deities in order to even meaningfully talk about them.
But when push comes to shove, deities may or may not have some sort of humanly understandable attributes; may have or lack a role in the creation of existence; may have or lack a plan for it; may be symbolic or literal; may be finite or infinite; natural or supernatural; mundane or cosmic.
In short, there is no clear requisite or restriction for anything at all being considered a deity, except perhaps that someone must raise the matter and declare whatever a deity.
What do you think?
"luisDantas",
Some of these imaginations could be correct, if we were not talking about the Almighty Creator, of heaven and earth, the whole creation, whether A Universe, or Polyverses.
The simplest logic would tell us that The One who created everything has the right to give laws to His creation, both inanimate and animate.
If you think about it, you would have to recognize that His creation NEEDS laws, to keep from chaos in the inanimate world, and trouble, at the least, and death to His living creation. Man, because he is so limited in his knowledge, needed guidence, because seems like the right path to take might very well, lead to death, in the unforeseeable future, Prov 14:12, 16:25.
Let us think for a minute; what exactly is the definition you are using of Arbitrary.
The usual definition is; making laws because you can or have the right to, the authority to. That is definitely not God's way. God loves His creation and gave man rules to help him live without problems, Isa 48:17-19, Deut 10:12,13.
God did not make rules, just because He had the right, He gave rules to help his creation, because man cannot see how things will turn out in the future, unless God directed him, Jere 10:23,24. Remember, God is perfect in knowledge, Job 36:4, 37:16, and is Good in every way, Job 34:10,12, Deut 32:4, Ps 32:8,9.
God loves those who love Him, Prov 8:17, and He has purposes to make a paradise earth for all who love Him, and His son, Jesus, Rev 21:3-7.
Even when God judges the earth, it will be because of love for His creation. It is an impossibility to make a paradise for His people, if there are others who have no love for man or God, Rom 3:5,6. God wants all to repent and live, but the time has almost run out, we only have a short time to show God we are worthy to be preserved into the New Earth, mentioned at Rev 21:1, where even death will be done away with, 1Cor 15:26.