My experience with the honor crests
I have a green Great Teammate ribbon since the honor initiative was released. At first it was really fun. I felt proud that I was one of the most positive players in the game and I tried to set an example for others. Initially it truly was an honor to get this crest and I am convinced it improved behavior across the board.
But then the years passed and Riot neglected the honor initiative. The ribbon was made smaller to make room for Champion Mastery icons and in Teambuilder you can't even see the honor crests. Fair enough, Riot had other priorities. But at this point I feel like the ribbon has a negative influence on player behavior.
In one of Lyte's talks in 2013 he showed the results of their Optimus Prime project. They looked how messages on the loading screen affected negative behavior. One surprising result was that the sentence "Who will be the most sportsmanlike player in the game?" resulted in around 15% more reported toxic behavior. I am afraid the same thing is true for honor ribbons.
Being a 'Great Teammate' makes you a target for negativity. "I will report you so you lose your ribbon." "You only defend him to get honor." For me the negative side no longer outweighs the positive side. So Riot, it is time to make sure honor crests lead to more positive play. Right now it is not working.
Source Optimus Prime project Minute 22.30: http://www.gamasutra.com/view/news/191262/