I was gold five before the changes to ranked in which I got moved up to gold four. Before I moved up I was getting about 22 lp per win and lost 18 per loss, which infers that i had mmr greater than my rank. When I moved up to gold four though, I immediately went to 0 lp and had a warning sign that said I was dangerously close to deranking. I started only getting 13 lp per win and lost 26 per loss, even though op.gg said I had gold four mmr. Even after winning most my games and doing well in them, I was still only getting 13 lp per win. Eventually I went on a two game losing streak and went back down to 0 lp. Then, I played another game, went 17/9/8 with 50% kp as jungle, and got deranked to silver. There's something really wrong with mmr in this new ranked system, at least for people who were division five before the changes.
Edit: From many comments, it seems like this deranking is intentional from Riot. Incase anyone from Riot sees this post, I'd just like to say this: Deranking players that have spent hundreds of hours to acquire their current rank is unfair and unappreciative to the player base.