I just did my first game with auctions and lost on a faction I feel like I should have won. Its taking a lot of parsing through the rules to understand why and I'm beginning to see where the contention is coming from. I bid 12 points on my first pick and 9 points on my second pick. Another player bid 9 points on my first pick but less (I think zero, but I'm not sure) on my second pick. When the bid on my first pick hits four points, my bid shifts away from my preferred faction to my second choice because the second choice has larger differential. (Nine minus zero on my second pick is larger than 12 minus four on my first pick.) The auction rules assume that I would rather bid on a race I have smaller bid on than continue to bid on a faction I have a higher bid on. What this ends up doing is creating a situation where, with my 12pt-1st/9pt-2nd bid, I'm effectively not going to bid any higher than 3 points on my 1st choice unless there is also competition on my second choice. So even though I'm willing to pay more for my preferred faction than the second player, that player is going to end up winning it. So here are the specific ways in which I feel like the linked explanation is insufficient.
1) The "power" of your highest bid is tempered by the size of your second highest bid. In my example, the bidding on my favored faction stops at 4 because the difference between my two highest bids was three. If my second bid had been, say six instead of nine, the other player would have had to bid up to seven before triggering my bids into switching to a different faction. If winning my favored faction was that important to me, the strategy here is not to increase my bid for my favored faction, but rather to decrease the bid for my second choice.
2) It does not specifically call out the fact that you can lose a faction for which you are the highest bidder. In the help file example, this is demonstrated by the fact that Player B wins AMBAS even though player C had a higher bid for that faction. But the point I'm making here is that
the help file neither specifically calls this fact out nor explains why it can happen. You have to manually parse out the logic to understand that the bidding system is not only forcing you to switch which faction you bid on, but effectively blocks you switch back unless you subsequently get knocked out of the "new" faction you are bid into.
3) The net effect of the two items above means that the lowest bid you submit is equally valid for any faction you are bidding on at all. Most people are going to assume that if I bid 10 on Alpha and 7 on Beta, that I only want to bid 7 on Beta if I actually lose on Alpha. But the way the rules work, the system is assuming that any bid of seven or less is equally good for either Alpha or Beta. And that isn't to say that the auction system is wrong or invalid, only that its not intuitive to the way people conventionally think about how real-life auctions work. In the real world, I'm going to bid on purchasing something, I'm going to bid on the item I want the most, not the item I have the least contention against. The down side here is that players may not end up getting their favored choice even if they are willing to pay more than the winner while the up side is that the system generally guarantees that all participants end up paying the least amount necessary.
And the overall point here is that the problem with the help file is not that it is technically inaccurate, but rather that it fails to explain the kinds of non-intuitive outcomes it can produce, why they can happen, and what the strategic implications of a second choice bid actually are.