What if there's constant up/down traffic on two opposite sides of the ribbon? Wouldn't ascending cars try to pull the ribbon "back" (from orbital direction), whereas descending cars would try to push the ribbon "forward"?
I'm pretty tired now and I can't think very well, but my gut feeling tells me the two effects would compensate each other to a pretty large fraction of 100%.
But where will that extra downward traffic come from? The total weight of all space debris is only around 6000 tons[0] so that'll get exhausted within a matter of years (assuming we're even capable of collecting said debris). The only other alternative seems to be pulling near-Earth asteroids into geosynchronous orbit and using that.
There could be bounty hunters, who wrangle asteriods and other debris to serve the ever-hungry fleet of elevators. Also, there's legit asteriod/moon mining possibilities to at least partially counter the up-traffic.
I'm pretty tired now and I can't think very well, but my gut feeling tells me the two effects would compensate each other to a pretty large fraction of 100%.