Based on Zeus' having rescued his siblings from the belly of their father Kronos; and on the deal that he made with the Titans who eventually sided with him (which is the majority of the Titan population, by the way), starting with his personal bodyguard the four winged children of Pallas and Styx, namely Zelos, Kratos, Bia and Nike; and on his leadership in the war which led to Kronos' defeat, it would seem that it had already been decided that Zeus would be king of the gods and ruler over the entire universe.
As for the family estate which they inherited from the first Titan generation—consisting mainly of the realms of Earth, Sky, Sea and Underworld—Zeus, Poseidon and Haides [Hades] first decided that the Earth would be the domain of all three in common so that each of them would have some control over it from whichever realm one ended up with. Whether from the Sky, from which rain and lightning issued forth upon the ground; from the Sea, which "embraced" the world's land; or from the Underworld, which received the dead delivered through the ground and also rendered up mineral wealth.
The three brothers then cast lots to see who would get which realm, and thus Zeus became Ouranios, the Sky-God; Poseidon became Gaieokhos, "Earth's Embracer"; and Haides became Plouton [Pluton], the "Wealthy" One who owned all the Earth's buried treasure which mortals have to mine from it.
There is no hint in any original myth that Haides was either forced or reluctant to receive his cast lot. In fact if anything he is the source of the least drama and is supported by Zeus in almost every major action that he takes, most notably when he asks Zeus for his daughter Persephone's hand in marriage, against the wishes both of the prospective bride herself and of her mother Demeter, and Zeus nonetheless accepts, even though this literally changes the world.
Also, when Zeus' own grandson Asklepios [Asclepius] is depleting the population of Haides' realm by resurrecting so many of the dead, and Haides complains about this to Zeus, Asklepios is summarily zapped dead with a thunderbolt by his granddad, no negotiations apparently needed. This gives rise to the anger of Asklepios' father Apollon [Apollo], but by that point in the story, Haides has left the scene and is minding his own business again.
Haides' behaviour in the myths implies that he quite rather likes his kingdom under the Earth, which affords him a great deal of privacy and power. In a way, he rules the largest portion of the universe, housing the most subjects (eventually there must have been way more dead people than those alive), including the powerful ancient ones caged in Tartaros, which itself was as vast as the Sky.
Of especial note is the fact that Haides was considered to be as much and as powerful a king in his own right as Zeus was in the sky so much so that the king of the dead was sometimes referred to as Zeus Khthonios, "Zeus of the Underworld," and depicted in art the same way Zeus was: installed on a golden throne and wielding an eagle-tipped sceptre.
In essence, Haides was an upside-down version of Zeus. Orphic mythology further blurs the line between the two brothers, such as in Nonnus' epic the Dionysiaka, which has Zeus consorting with Persephone to produce Zagreus, a pre-incarnation of Dionysos [Dionysus], who occurs as a son of Haides in Aeschylus. The Underworld demoness Melinoe is another such child of Persephone who is referred to as the daughter of both Zeus and Haides.