This is where a vote kick could make/break this game. Could be useful in situations like this but could be hella abused. I still don't understand why your able to go other places in a strike in the first place! You're there for the strike so do the strike and quit wasting everyone else's time.
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Any system can be abused given enough greed and ingenuity. But I think my suggestion is as close to "neutral" as any can be. It requires that all players 1) be in the final boss arena, and 2) participate at least to the bare minimum of picking up the controller, aiming, and shooting something; while 3) it protects against an unlucky break killing a player before the boss appears, in a position where his allies can't revive him. It even allows for the cherished tradition of carrying lower-level friends through an event- just pop one shot at the Dreg in that cave over there, then hide for the rest of the boss fight while your buds do the rest. There's no way to sit out the entire strike. It's not perfect, but I've put a lot of thought into it. I think it's pretty good.