Michael Van Biesbrouck
You could bid points for turn order like they do in Puerto Rico tournaments.
2010 World Boardgaming Championships wrote:
Going around in [random order], each player will [mark] a bid value ranging from 0 to 5.0 VP (in increments of 0.5 VP) on a chart to be furnished by the GM. Bids may be zero but in all instances must be higher than any previous bids for a particular seat. Any player who has been outbid will have his/her marker removed and will, when his or her turn comes, bid again--either a higher value for the same seat or a different amount for another seat. A player whose bid is not topped by another bid does not get another bid -- instead the bidding goes around to the next player without a bid marker in play. The process continues until all players' bid markers are on a different seat, with the resulting bid representing the VP handicap to be assigned for that particular game. These VP handicaps will be noted at the top of the particular seat position (1, 2, 3 or 4) on the scoresheet above the player's name and will be subtracted from that player's VP total at the end of the game.
You should use fractional bid values. It might actually be best to work in thirds, but it doesn't really matter. I believe that going first is worth at least 4/3 of a point over last place. If your bids stabilize over several games, please report what they are. You might want bidding to follow distribution of private orders, in which case there may be some variability.