This analysis reveals the applications of relative divergence and maximum relative divergence principles for grading functions on partially ordered sets, indicating insights into probability theory.
Relative Divergence (RD) and Maximum Relative Divergence Principle (MRDP) for grading (order-comonotonic) functions (GF) on posets are used as an expression of Insufficient Reason Principle under the given prior information (IRP+). Classic Probability Theory formulas are presented as IRP+ solutions of MRDP problems on conjoined posets. RD definition principles are analyzed in relation to the poset structure. MRDP techniques are presented for standard posets: power sets, direct products of chains, etc. "Population group-testing" and "Single server of multiple queues" applications are stated and analyzed as "IRP+ by MRDP" problems on conjoined base posets.
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Alexander Dukhovny (2025) studied this question.
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