Here is a youtube explanation of consensus: https://www.youtube.com/watch?v=pj1QVb1vlC0
and here is an explanation on the Ripple wiki: https://ripple.com/wiki/Consensus
and a brief explanation on stackexchange: https://bitcoin.stackexchange.com/questions/7550/how-does-ri...
You are correct that I am involved in the project. I think Ripple consensus is a more practical, faster, more secure, and less wasteful solution to the double spend problem than proof of work. Happy to entertain your arguments to the contrary.