I'm going to go out on a limb here and suggest again that multiplayer winner-take-all is the most arbitrary system that could have been used, that still involved actual gameplay. And I'm actually not convinced that using a poll would have been more arbitrary, especially given the total of only four games used, all with the same four people. Not a single qualifier demonstrated superiority of play over more than three people here.
The seat rotation method used was poor too, since we're bringing up flaws. With two excellent players and two people who bought cards at random in a pod, it was possible for one of the excellent players to go before the other one three times.
Are you sure you're using "arbitrary" correctly?
See definition 4.
Here's what I'd suggest:
A-B-C-D
D-C-B-A
B-A-D-C
C-D-A-B
Everyone gets every seat, and you're only sitting before/after the same person in games 1 and 4.
And since the person you're directly before or after doesn't make much difference, that last part isn't an issue. What you've posted is perfect, as every player goes before every other player twice. Thanks for taking the time to actually do that.
You're welcome! Made sense to me
Although I disagree about the "who you're sitting before and after" part - Possession, Masquerade, and final turn dynamics care about those things.
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I disagree strongly to your assessment that winner-take-all is arbitrary based on that definition of the term, and now I have an ace-in-the-hole reason:
From the Dominion rulebook, page 8: "Game End"
The player with the most victory points wins.
If the highest scores are tied at the end of the game, the tied player who has
had the fewest turns wins the game.
If the tied players have had the same number of turns, they rejoice in their shared victory.
Nowhere in the rulebook does it state anything about players who did not finish with the most points, only that they were not victorious. There's no talk about second-place points, third-place, etc. None.
The only distinction made is between players who won, and players who did not win. According to the actual Dominion rules, there's only one prize handed out: victory (shared or outright). Therefore, winner-take-all seems like the LEAST arbitrary system to employ, in my observation and opinion.
EDIT: I don't really want to open this can of worms again, but the use of "arbitrary" really bristled me, and I just remembered to use the rules as evidence. So I have.