Yet Another Derivation of The Principle of Maximum Entropy

A new derivation is presented of the principle of maximum entropy, for assigning probability distributions given equality constraints linear in the probabilities. In common with the Shannon—Jaynes derivation the idea involves an invariance under arbitrary partitioning of the points on which probabilities are defined. However, the Shannon—Jaynes derivation is a two-stage process: assert that a particular functional of the probabilities, that has a certain interpretation, should be maximised; then use that interpretation to generate an equation for the functional itself. This equation is routinely solved to give the usual p log p form. By contrast the derivation presented here is a one-stage process which does not rest on any interpretation.