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gwern comments on Stupid Questions August 2015 - Less Wrong Discussion
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There is a variable X, x belongs to [0, 100]. There are n ways of measuring it, among them A and B are widely used. For any given measurer, the difference between x(A) and x(B) can be up to 20 points. Between two any measurers, x(A)1 and x(A)2 can differ on average 10 points, likewise with B.
Measurer 1 wants to know if it is meaningful to compare her results, x(A)1, with Measurer 2's results, x(B)2. Does the interval in which the true x lies include 40 points?
If Measurer 1 herself establishes the difference between x(C)1 and x(D)1, where C and D are two other ways to measure x, how much more useful for any given Measurer 3 will be her results, if she also invites Measurer 2's opinion - that is, x(C)2 and x(D)2?
(Is this ok?)
Here are some examples in R of the mentioned approaches including EVSI. Syntax-highlighted on Pastebin: http://pastebin.com/8090dgvB
For another example of VoI, see my draft essay http://gwern.net/Mail%20delivery