The ratio of people to cake is too big.
Excuse me, I believe you have my stapler...
Re:Question about Alliance tiles
The only limitation on the number of alliance tiles you can have is the actions it takes you to collect them. You can use the alliance tiles anywhere they apply, but most of them are restricted to a single region. Note that you can only use alliance tiles when you are directly involved in the conflict. You can lend troops, but not alliance tiles to assist an "ally" (another player) in their battle.
Remember that all alliances tiles are returned to the supply at the end of each war. We missed that rule in our first playing and it made a big difference.