If I'm a recruiter, I then say: "Oh good...we're close. The salary approved for this position is 0.8Y. But we offer high-cholesterol lunches that have been 'catered' by the local fast-food meta-purveyors, health care, blah blah blah. Did I mention our free massage Fridays, and extensive selection of free, high-sugar, diabetes-inducing soft drinks?"
You then get to choose to counter or walk away. If you're a good negotiator (which you're not, since you've said the first number), we'll probably end up at 0.9Y.
Meanwhile, Joe Bloggs comes in, and doesn't say a number. The recruiter offers 0.8Y, and Joe finally says "I was thinking 1.2Y". Joe, being a savvy negotiator, ends up with at least Y, and maybe 1.1Y.
It doesn't matter what Y is, you always have a chance of doing better than your goal if you speak last. You lose that advantage if you speak first.