How should leaders be selected?

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The way we have it in past years is that our Team captain is selected by popular vote(he/she's the person you want to follow) and then our department captains(mechanical, programming, electrical, communications) were nominated by receiving 20% of the team's vote. From this pool of nominees, the newly elected team captain selects his department captains so that they will work together.
I know that there are a lot of flaws in this system, but since our team is not at the point where I believe can have an application process, etc, this is what we do. Though some other members on the team and I who are going to be next year's officers are changing how our team works.