Somewhere in the company will be a database. In it, there will be one column for every property of a city, one column for each property of the bid received (tax breaks included of course). I'll bet there will be hundreds of columns. And then there will be a very large formula that takes every property, assigns it a value to Amazon over the next 25 years, and adds it all up.
It's probably quite a complex formula. I have a friend with a master's degree in computational geometry who used to work on fulfillment center placement optimization. Lots of software dedicated to that I hear. Amazon is a data-driven company- it would never leave such problems to human intuition.
Once the data entry was done, and probably a few dozen formula updates were made as new factors were realized and added in, the decision would have been made automatically. The only problem left would be announcing it at the best time to further profit Amazon- another factor the formula probably spit out.
My guess is that we'll know when Q4 results are published. I'd love it to be my home city of Toronto, but I think the lack of tax breaks offered may push it down in the formula's ranking.