Wait a minute, do you think it's fair when the quest organizer or the retailer (as I suggested) participate? They will know which quest or cards everybody has, which isn't the idea I think.
For example, I am quest organizer, and I give an earth player the quest to kill my whole team (with his team). This way, we would be able to prepare, and other teams don't.
On the contrary; I think it'll be fair if the Quest Organizer/Retailer are people who would willingly sign up as elements of 'Other', thus having no affiliation with any other element in terms of alliances. Not to mention, since this is Beta, the general concept is to test out basic mechanics and systems (such as reporting statuses of players, moving people on a daily/round basis, organizing battles, keeping track of player decks/cards/electrum/etc.). Small things like 'providing advantages to an element' is a moot point at the beginning, because the beta should be based around doing the simple things and not worrying about backstabbing/excess advantages in quest-based allegiances.
Advantages in terms of extreme map-based positioning (having Outlaw city too close to an element that's already well protected), resources (one element having a plethora of areas to gain items from after conquering it), or Wonders (having special things like salvaging excess cards/gaining other unique benefits that outweigh the other elements) - those are problems that should be addressed within the Beta first and foremost.
...short version: Make the Quest/Fight/Main organizers non-affiliated with any element, thus allowing them to perform their jobs without compromising the other elements (Movers) as they fight each other and attempt to 'Win' the game. Major issues based on resources, location of cities/wonders, and other systems of WoE will be fixed then.