Here is the dictionary definition of arbitrary.
Definition of arbitrary
1a
: existing or coming about seemingly at random or by chance or as a
capricious and unreasonable act of will an arbitrary choice When a task is not seen in a meaningful context it is experienced as being arbitrary.— Nehemiah Jordan
b
: based on or determined by individual preference or convenience rather than by necessity or the
intrinsic nature of something an arbitrary standard take any arbitrary positive number
2a
: not restrained or limited in the exercise of power
: ruling by absolute authority an arbitrary government
b
: marked by or resulting from the unrestrained and often
tyrannical exercise of power protection from arbitrary arrest and detention
3 law
: depending on individual
discretion (as of a judge) and not fixed by law The manner of punishment is arbitrary.
Some of those parameters do apply to election.
It does "seem" to be random and capricious. It does " seem" to be unreasonable.
But - when seen in the "meaningful context" of the scriptures it is experienced as meaningful.
Some of the definition is, of course, absolutely correct. God is not restrained by any one or anything other than His own nature and He does things for His own convenience.
But our election is not from necessity. God was perfectly happy without us in His Kingdom.
It is true that He exercises election by His own discretion.
But no one in Calvinism says that He is a tyrant for doing so.
When anti-Calvinists describe the Calvinist God as being arbitrary and capricious - they are saying that He would be a tyrant if election is true.
But Calvinists affirm that God has a good purpose for everything He does and that, although it may "seem" random and purposeless, it is not.
Calvinists do state, however, that there is nothing found in us that deserves such grace as our election and calling.
While Arminians say that God's calling and election is because of our reception of Him and His will - Calvinists recognize that no one can come to the Son in the first place without that calling, election, drawing and special enlightenment.
As the Lord says: "Flesh and blood did not reveal this to you, but My Father in Heaven."