As pointed out by GeneM here
Armageddon Chess is a fair tie-break system only if the two players bid for how much time Black should have.
My guess is yes but they do 1-time only bids for practical reasons like with plurality voting. Of course it could be that either 1-time only is actually more fair than bid or somehow, the results will end up the same regardless of the kind of auction.
Consider recently in 2023 champions chess tour Airthings Masters magnus vs hikaru, where the bids were Hikaru 8:59 and Magnus 8:58.
2 ways to look at it:
I think with 1-time only, they're bidding far lower than what they normally would bid in an English auction - something like they're bidding not how much they want black (or white, if you can choose colour) but how much they don't want their opponent to get black. I think if they did an English auction, then black would end up with maybe 10-12 minutes.
But here, there's only a 1 second difference. Maybe they'd bid even lower. If the bids would continue - let's say the next bid must be at least 10 seconds lower than your opponent's bid - then the might go as low as 6 minutes.
- If I were to bid exactly 15 minutes because my opponent thinks I'd go as low as 9 minutes. Then I'd trick my opponent to do like 8:30 whereas my opponent wouldn't even have gone lower than 10 minutes otherwise. I think this can be fixed with Vickrey auction as pointed out actually by Jim Ratliff in the same thread with GeneM.