Difference between 'principal of indifference' vs 'the assumption of equal a priori probabilities'? Is there a difference between the "principal of indifference" and "the assumption of priori probabilities" and if so what? If there is no difference why the use of two different terms? 
EDIT
I have also read about the "principal of insufficient reason" which again seems similar to the above.
 A: Operationally, no, but the latter is misleadingly worded.  The principle of indifference is not an assumption.  The principle of indifference is a (very simple) special case of both the principle of maximum entropy and (transformation group) symmetry.  In both cases, the only "assumption" involved is that you've provided all the information you know.
As a concrete example, say you trust me.  I tell you I'm going to flip a coin and that the coin is severely biased, say 90%, but I don't tell you what way, heads or tails, it's biased.  What is the probability of getting heads?  It's still 50/50.  The reason isn't because you assumed they were equally probable events — you know they're not.  The reason is that the options are symmetric between heads or tails.  Any argument you could make for heads, you could just swap "heads" and "tails" everywhere and have an equally good argument for tails.  Of course, you may have relevant prior information which changes that.  Maybe you know that I have a obsessive fascination with faces and thus I'm much more likely to prefer a coin biased towards heads.  The principle of indifference would no longer apply (though it could be used for a prior that you update with this background information.)
