This question suggests 4 wives - but it says on Quora that KMG says he had more.
Out of Brahma, Daiva, Arsha, Prajapatya, Asura, Gandharva, Rakshasa, Paishacha, which style of marriage did Arjuna use with each of his brides?
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Arjuna rightfully participated in swayamwara organised by King Drupada and won Draupadi's hand. So this is Brahma marriage.
Bhishma said, 'Having enquired into the conduct and disposition of the person, his learning and acquirements, his birth, and his acts, good people should then bestow their daughter upon accomplished bridegrooms. All righteous Brahmanas, O Yudhishthira, act in this way (in the matter of the bestowal of their daughters). This is known as the Brahma
Anushasan Parva XLIV
The story of Arjuna and Uloopi marriage is as follows:-
When Arjuna was bathing in ganges, Uloopi dragged him inside the river. She asked Arjuna to marry her. But Arjuna denied as he was following Brahmacharya. But later he agreed and both of them married.
In this condition I think this is Gandharva marriage.
Manusmriti 3:32 The voluntary union of a maiden and her lover one must know (to be) the Gandharva rite, which springs from desire and has sexual intercourse for its purpose.
The king of Manipura had a daughter of great beauty named Chitrangada. And it so happened that Arjuna beheld her in her father's palace roving at pleasure. Beholding the handsome daughter of Chitravahana, Arjuna desired to possess her. Going unto the king (her father), he represented unto him what he sought. He said. 'Give away unto me thy daughter, O king! I am an illustrious Kshatriya's son.' Hearing this, the king asked him, 'Whose son art thou?' Arjuna replied, 'I am Dhananjaya, the son of Pandu and Kunti.' The king, hearing this, spoke unto him these words in sweet accents, 'There was in our race a king of the name of Prabhanjana, who was childless. To obtain a child, he underwent severe ascetic penances. By his severe asceticism, O Partha, he gratified that god of gods, Mahadeva, the husband of Uma, that supreme Lord holding (the mighty bow called) Pinaka. The illustrious Lord granted him the boon that each successive descendant of his race should have one child only. In consequence of that boon only one child is born unto every successive descendant of this race. All my ancestors (one after another) had each a male child. I, however, have only a daughter to perpetuate my race. But, O bull amongst men, I ever look upon this daughter of mine as my son. O bull of Bharata's race, I have duly made her a Putrika. Therefore, one amongst the sons that may be begotten upon her by thee, O Bharata, shall be the perpetuator of my race. That son is the dower for which I may give away my daughter. O son of Pandu, if them choosest, thou canst take her upon this understanding.' Hearing these words of the king, Arjuna accepted them all, saying, 'So be it.'
This is again Brāhma Vivan.
Subhadra was forcefully abducted by Arjuna.
Vasudeva answered, 'O bull amongst men, self-choice hath been ordained for the marriage of Kshatriyas. But that is doubtful (in its consequences), O Partha, as we do not know this girl's temper and disposition. In the case of Kshatriyas that are brave, a forcible abduction for purposes of marriage is applauded, as the learned have said. Therefore O Arjuna, carry away this my beautiful sister by force, for who knows what she may do at a self-choice.' Adi Parva CCXXI
It was Rakshasa marriage.
Manusmriti 3:31. When (the bridegroom) receives a maiden, after having given as much wealth as he can afford, to the kinsmen and to the bride herself, according to his own will, that is called the Asura rite.