I need some advice

I know there are scads of adages advising against asking for advice, but I need some input. Here's the situation, ...

Pretty soon (next few months) my department will be moving into a renovated building. As you might expect, the first question to be decided is, "Who gets a window?" This is very important in departmental hierarchies. Seeing as how I'm still almost brand new, I never considered that I'd be one of the fortunate ones -- especially since there are only two offices with windows. It turns out, though, my current boss doesn't want to pick one of the windowed offices because she's retiring in the next year or so and that would just make everyone go through the office shuffle again. Since she's not taking a window and there are only 4 full-time instructors in the business division, that means there is one window available for either me or the junior accounting instructor (we'll call her Lucy).

Now Lucy and I came in at the same time (last fall) so we should both be equal in terms of seniority. The problem is that due to some weird paperwork thing I actually have A DAY of seniority on Lucy. Since all things here at this institution run by seniority that legally gives me picking rights over her. Why is that a problem? Well, I don't think it's fair that I get to pick over her. I have done nothing special to earn the extra day of seniority. In fact, I don't even know how that happened. So, in all fairness, we should flip a coin or something to see who gets the office, right?

This would solve the problem if not for the fact that I WANT THE OFFICE WITH A WINDOW! It's not just that it has a window, actually 2 narrow windows, but the windows actually open! Yes, I could open the window and enjoy the breeze. I hate to be petty, but in my defense I am a huge fan of open windows. Except for the very hottest part of the summer, I keep my windows open at home. I just like the feel of natural air rather than stale, recycled, artificial air. The fact that I'd also be able to look outside also plays a role, but mostly it's just that I'd be able to open my window. You may not believe me, but it's really not a status thing. Regardless, I want the window, but I don't want to be an ass and try to use my one day of seniority to grab the window.

So, dear readers, what do I do? Do I just bite the bullet and look out for my own desires or do I take fairness into consideration and take the chance that I lose out on the window? A couple of things to keep in mind. I will have to work with Lucy for the foreseeable future (I hope), so there may be a cost to bear if I alienate her. Second, this decision likely will last for a long time. The other guy who will get a window has many years to go before retirement. So whoever doesn't get a window likely won't have a window for a long, long time.

Being an economist, I came up with a solution -- I should offer to pay Lucy to let me have the window. I figure that plan wouldn't go over so well among the general public (or the rest of the college). I sense that they would see that as dirty or tainted whereas it makes perfect sense to me. Who should get the office? The one who values it more? How do we determine that? See who will pay more.

Still, I don't think that plan is feasible. So, what do I do? Go for what I want or be fair? Help.