Dilemma - who gets to go to the Awards Event Gala Dinner?

So as mentioned my team was nominated and made it to the finals of the Recognition Awards at work for 'Best Team'.

There are 18 of us. 17 testers and myself as manager.We have been told that a total of 13 can attend. My boss - head of our division, our nominator, myself & 10 of the testers.

So if you had a team of 17 in the finals for a Team Award, and only 10 are invited to attend the award ceremony gala event dinner. How would you chose who gets to go and who can't?!  

First thing I did was send out an email with voting options:

- YES. Pick me. PICK ME!

- Maybe - I wouldn't mind going.

- No - I'll be washing my hair that night.

True to form, I have pretty much all 'Pick me!'s and just a small few saying they'll stand down if they have to but would actually love to go. Which then caused a spontaneous and united anarchistic 'all for one and one for all', 'all or nothing' 'united we stand' 'no one gets left behind' stance where they've decided if they can't ALL attend then none want to go.

Aaai.

Now I respect and admire that stance and THAT is exactly why this team IS Team Awesome and is such a good and strong and cohesive team. But the fact is we'll be farting against thunder. This is a big corporate and rules are rules and our team is fairly large and fact is we need 'representatives' at the event and my boss has said I mustn't take this on and fight for it. We have fought and worked so hard to be recognised and rewarded (as relative outsiders to the rest of the company) that now that we ARE being notices we shouldn't look to be difficult, demanding, ungrateful etc.

So I have explained to the team that we have to pick 10. And the award/prize will absolutely be for the entire team - not being there does not imply not winning or not being part of the team/win - and it doesn't have to be divisive. 

But what would you do and how would you chose...?

- On merit?

- Length of Service?

- Random Draw?

- Democratic Vote?

What I have done is draw up a spreadsheet with categories for:

Length of Service, receiving Nominations in our recent company awards, submitting Nominations in our recent company awards, and then who WANTS to go. Each is weighed into 4 segments with a number assigned to each.

I have tabulated and ranked accordingly. The answer is then scientific and in the maths. 

What do you think does that sounds objective and fair enough?

Would you be happy if it was you and it was done that way?