  :The same way that whenever you walk towards the west the earth is insignificantly slowed (and insignificantly sped up when you walk to the east). The great disparity of mass of the earth versus your body (or indeed a space elevator and payload) means that the actual slowing experienced is so infinitesimal as to not warrant worry, but does deserve a breif entry into the physics section of the Space Elevator wiki. Also, presumably an operational space elevator would have mass coming down as well as going up, so there's your countermeasure.  