[Heory]

Oxy, I like your initial idea better. Base is not present according to the problem. I think the major product depends on the confirmation of the carbamate.

[Oxy]

After stewie griffin posted the document and due to calculation of Chem3D, I'm not sure about the first idea. I'm try finding a more reasonable way. Base is not required if proton isn't lost. Hmm... Heory, could you get the answer?

[Heory]

No I don't have the answer, nor would I have the chance to get it.

[tmartin]

    I really got my hopes up waiting for the answer too... now we'll just have to argue these points over and over again like Groundhogs Day! 

[Oxy]

I asked a friend for help . Here is his solution.
Due to inductive effect, the C-Br sigma* MO (b) has lower energy than the other one.
The lone pair (1) interact with C-O sigma* MO better than the other one and lower its energy.
So energy between lone pair (1) and C-Br sigma* MO (a) is larger than energy between lone pair (1) and C-Br sigma* MO (b).
Conclusion, path A is preferred.