There are three main reasons for European Exploration. Them being for the sake of their economy, religion and glory. They wanted to improve their economy for instance by acquiring more spices, gold, and better and faster trading routes.
Answer:
The answer is simple. First you would want to gain control over the other idiots you were stranded with. To do this you would kill a few of them to show your strength (preferably the older ones since the younger ones would be easier to control) Then you can use the bodies of your victums as food and fertilizer to plant a new food source. Then, use their bones to create a shelter. And forget democracy, just make yourself the king and once the others on the island begin to repopulate you will soon have your own nation. :) your welcome
Explanation: