I was told it's a "random" principle, but I still see the same few projects being featured, and none of the many times I have reloaded the home page did I see a glimpse of ours. Clearly, selection is not random.
You are correct that selection is not random. The homepage featured projects are selected based on a number of metrics including page views, number of backers, along with a other metrics. The algorithm determines the projects that are featured. The featured projects are entirely determined by the algorithm with no human interference.
Pageviews, seriously? The projects featured on the homepage of a high-traffic site will get more page views, and that accounts for the self-perpetuating system where the same few projects keep getting shown. Do you not see the flaw in this principle? What are the other metrics?