Scotts theorem and other theorems give conditions under which a qualitative ordering (>= for at least as probable than) which satisfies certain constraints (total pre-order, finite cancellation axioms and others) is such that it is represented by some P on [0,1] that is such that 'if A>= B iff P(A)>P(B)' that is a finite additive probability function.
When conditions are relaxed so that we have only the conditional rather than the bi-conditional, whereby 'if A>=B then P(A)>P(B)' P is a finitely additive probability function, this is call almost or weak representation. What are the disadvantages of weak representation, does it only ensure the compatibility rather than the necessity of a finitely additive structure or is that the strong representation entails that the numerical probability function P is unique is something similar
Is this just me - but what has this got to do with qualitative analysis? When has qualitative analysis had anything to do with statistical analysis (although some qualitative meta fans might want to challenge that) - or probability issues?
William - have you invented a new order methodology?
I'm both intrigued and completely perplexed.
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