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Several reasons.  
Saw this crusade as a blessing from God.  
Christians would stop fighting themselves.  
Christians that would fight would go to heaven or be right with God.  
To take back the holy lands, from the Muslims would be a righteous cause.  

The way this small state - large state compromise guards against tyranny is that small states and large states have one note: i am sorry but i was not able to give you the full answer. but i got this answer from