I'm not really sure that there is a clear sense of what "fairness" means here. These variable are negatively correlated -- if one if them is high in its range, the others have to be lower in their ranges so it all sums to 100.

For example, when the sum of midpoints exceeds 100, there will be more combinations that work when variables are below their midpoints.

Put differently, one definition of fairness is that all potential combinations are equally likely. Another definition would take into account the implications of the overlapping ranges.

Our algorithms perform quite differently as a result. Here are the means for each variable from our two algorithms:

# Original constraints (xdg algorithm)
Expected:  20.0  30.0  50.0
Means      19.5  30.5  50.0

# Pathological constraints (xdg algorithm)
Expected:  50.0  50.0  50.0
Means      49.5  24.8  25.7

# Original constraints (gen3 algorithm)
Expected:  20.0  30.0  50.0
Means      22.6  23.2  54.2

# Pathological constraints (gen3 algorithm)
Expected:  50.0  50.0  50.0
Means:     33.5  33.4  33.1

[download]

-xdg

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In reply to Re^4: Need technique for generating constrained random data sets by xdg
in thread Need technique for generating constrained random data sets by GrandFather

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