Principle of Insufficient Reason
Statement
In the absence of any relevant evidence, agents should distribute their credence equally among all the possible outcomes under consideration. I.e., If there is not enough reason for two quantities to be different (i.e. they're indistinguishable), the extrema occurs when the quantities are the same. So basically, a symmetric expression is maximized or minimized when the 
quantities are the same. This is what enabled us to say WLOG.
Proof
Problems
Introductory
Intermediate
Olympaid
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