I certainly have changed my behaviour since bin collection was privatised.
Don't get me wrong, I'm not saying my behaviour has not changed. Rather it is hard to identify any real significant reduction in waste.
I compartmentalise my waste but that by itself is not reducing waste. I may buy a box of cereal that uses recycled cardboard but I don't consider that a reduction of my waste rather the producer has reduced waste. I still dump a cardboard box into my recycling bin. Recycled or not, my waste level is the same.