It just goes in player order. When it's a player's turn to choose, that player automatically bids on the faction with the largest difference between that player's max bid and the faction's current bid.
Let's take a quick example. Let's say the bids look like this:
* Faction A: Current bid is 4. Your max bid is 6. The difference is 2 (because 6-4 = 2)
* Faction B: Current bid is 2. Your max bid is 5. The difference is 3 (because 5-2 = 3)
* Faction C: Current bid is 0. Your max bid is 0. The difference is 0 (because 0-0 = 0)
When it's your turn to bid in this example, you're going to automatically bid on Faction B because it has the largest difference (3). It's not your max bid that determines which faction you bid on, it's the difference. You'll automatically increase the bid by one, so you'll bid 3 (because it's one higher than the current bid of 2).
If that's super helpful, I can add it to the How To Play wiki. If not, let's figure out what's confusing and talk about it.
