Robot assistant social etiquette

The new wave of excellent scheduling assistants seems to have given birth to a new online etiquette question. Do we use my robot or your robot, Andrew or Doodle? Should we trade every time? Is it related to whether you are I are "more important" or have "less time." Somewhat akin to the Manhattan or Brooklyn, my neighborhood or your neighborhood dilemma...And then the occasional earthling protests - I don't want to schedule with your robot anymore!