I don't understand why MA has such difficulty figuring a way to give everyone a chance at winning; It seems easy enough to me to just use the existing system to determine the "winners". First of all - all items in the game have a unique identifier - then for each item assigned to you - you get a certain number of entries into a "lottery".
There will Always be a problem to give everyone the same chance of winning.
First, given nothing at all, the ones with better gear and higher skills, will of course have the top hand.
If you divide into classes depending on a certain skill or attribute, the ones at the top of the class and with better gear (for instance tier 7 foeripper, mod fap and shadow armor - either own or borrowed from a family member) will have the upper hand of the people that are on the lower side in the class and having lesser gear (let's say p5(L), UR-125(L) and gremlin). Or even if just there is a difference of weapon options for those in upper and lower half.
If you do it totally random, given no time constraint, it will give those an upper hand who can take time off (from work, school etc) during the period.
And with a too small time constraint, you will give those an advantage who have a gazillion of alts.
So as the players comes with different backgrounds (skill level, gear, available time etc) it's hard to set up rules that are fair to everyone.
One thing thought what didn't work out well last year was how looting of the mission items worked, and that the "tokens" are looted more evenly, so those who "team up" with someone and enter a cave when a friend just hands in his pumpkins won't get those pumpkins in 5 minutes.
And as for fair play; teams can be allowed but only with rules that are hard to cheat with, let's say you are only allowed to enter caves with by damage rule and with 0% fapper option; and that in the end check so that none (at least of winners) have handed in more pumpkin(-point)s than they have actually looted themselves.