What's the algo got to do with it? Humans use the internet, robots just index it.
A bad website is not going to become an authority just because it does well in google. People won't return to the site - they go elsewhere.
A good website becomes an authority because it's a good website. A few good incoming links starts the traffic flow, word spreads, more links come in and then the search engines eventually recognise the site as authoritative (volume of incoming links goes high) and it does well in the SERPS.