That's counter to all proven negotiating strategy. Studies show the person who throws out the first number creates an anchor point, and the final number always

That's counter to all proven negotiating strategy. Studies show the person who throws out the first number creates an anchor point, and the final number always ends up closer to the first number than the desired number of the second person. You say "We can work up" and "they can work you down" - you'd much rather be worked down from a high number than work up from a low number.