Ralph's leadership is the result of a democratic vote by the boys. They have elected him chief because he has a certain stillness about him and is attractive and quite big. Most importantly, though, he is the one who has the conch, the instrument that summoned them all together. This, more than anything, is what makes the boys choose him instead of Jack, who is only voted for by the choirboys.
Ralph's vision is made clear by what he says. After he has been voted leader, one of the first things he says with regard to what he wants is the following:
We can't have everybody talking at once. We'll have to have "Hands up" like at school.
Ralph's dream is, in this instance, that they should have an ordered, disciplined society in which there are rules. His wish is later, ironically, supported by Jack when he states that Ralph is right. In saying this, Jack also alludes to the English being the best at everything and that they have to do "the right things."
Ralph also sees them having fun on the island, for he says:
While we’re waiting we can have a good time on this island.
In this he is expressing the desire of every young boy: to have fun and adventure, free from the strictures of their parents. As they wait for rescue, they can enjoy themselves. This brings us to another of his goals:
And we want to be rescued.
For this purpose a signal fire has to be made and maintained. Ralph here again expresses his dream for order and discipline--there should be a duty toward a greater cause. Everyone should understand their purpose. He states:
We’ve got to have special people for looking after the fire. Any day there may be a ship out there...
Jack magnanimously volunteers his hunters in this regard. They will look after the fire and work according to a duty roster.
Another concern that Ralph expresses is the fear of a beast, especially prominent with the little ones. He at first exclaims that there is no such thing but later comes to accept that its existence is a reality for many of the boys.
Ralph wants everyone to feel safe and secure. It is for this reason that the building of shelters becomes imperative. In a later discussion with Simon he says:
And they keep running off. You remember the meeting? How everyone was going to work hard until the shelters were finished?
Ralph is clearly frustrated that the building of the shelters is not progressing as well as he would like it to. He believes that they need shelters "as a sort of home." He later has a major confrontation with Jack who continuously goes off hunting with the choirboys instead of building shelters.
Ralph's authority is repeatedly questioned by Jack, who later reneges on all that he has promised. Jack becomes absorbed in hunting and indulges only his desire whilst neglecting his duties. During confrontations, he criticizes the rules which he so strongly supported initially. This results in Ralph's role as a leader being eroded.
Eventually, it is Jack's appeal to the boys' innate lust for blood and destruction and his violent threats that draw them to him, leaving Ralph vulnerable and without authority. Ralph is then finally left with no one to rely on but himself.