Player Roles in a Draft

Cyclades does a draft through bidding. X roles are placed randomly in a column and players take turns bidding for roles. If player 1 bids 1 for role Y and then later player 2 bids 2 for role Y, player 2 gets the role (until somebody else bids higher) and player 1 has to bid on something else. This continues until every player has a role that they're the highest bidder for. Players then pay their bid money to the bank.

One role, always located at the bottom of the column, doesn't need to be bid for, can be taken by more than one player, and rewards a bonus to the first player who moves on it.

Once a player moves on a role, he can't bid on others to move off of it; a player can only bid again if another player dislocates him from the role by bidding higher (and you can't be dislocated from the bottom role).

The order of roles on the column determines bidding order in the next round (top of column goes first; bottom goes last).

After bidding, each player takes 1 turn to use powers associated with the role they chose (these powers often cost gold), then roles are placed randomly in a column again and players bid.

I haven't played Eminent Domain, but that example reminds me of a personal favorite, Puerto Rico. The entire game is players trying to pick the best role. X roles are laid out to choose from. On a player's turn he chooses a role and everyone does its effect (e.g. Builder: everyone gets to buy a building). The player who picks the card goes first and also gets a slight benefit (for Builder: pay 1 less gold to purchase the building). Unlike Eminent domain, each role can only be picked once per round. At the end of the round, all roles that were not chosen get 1 gold placed on them, and the next player to pick the role gets all the gold on it. The next player to the left starts the next round.

Puerto Rico works because
1) It offers a lot of timing windows for players to screw others over by picking a role at the right time (e.g. places that players want to put resources in have limited capacities, and you can try to pick builder when other players are too poor to buy anything).

2) Through selection of buildings (which often alter how the roles work for the player who gets them) and plantations (these determine what resources players get), each individual player's needs become very different.