Solving for a Probability Distribution P(ei) from a Simpler Constraint for a Subset of P(ei) Derived from a Constraint Over All P(ei)

   In (1), it is suggested that there are two formal mathematical approaches for solving for a probability distribution. The first is the uniform probability approach, called the principle of indifference in (1) which apparently goes back to Laplace. The second is maximization of Shannon’s entropy subject to constraints (Jaynes), if constraints exist. In this case, it is assumed that in general the constraint applies to the entire probability distribution p(ei). We argue here that for a certain kind of constraint, i.e. one which implies the conservation of the variable ei upon which p(ei) depends, one may consider a subset of p(ei) which are then linked to a uniform probability distribution through a product p(ei)p(ej)=p(ei+ej) for an unnormalized p(ei). This then represents another way in which to solve for a distribution. In other words, one is not forced to use maximization of entropy subject to constraint in such a case.