Many people have heard the expression "Garbage In -- Garbage Out" -- which is not too surprising an expression.  However there are two other sayings that can be associated with the letters GIGO that you might not have thought about before....

"Genius In -- Garbage Out" can happen when we take good information (genius might be too strong a word, but you get the idea), combine that information with other 'good' information, but in ways that mathematically meaningless.  For example, averaging ordinal numbers (such as 4 for an 'A' in a graduate course, 3 for a 'B', etc.  is mathematically meaningless and the resulting average can be considered 'garbage' even though the letter grades were well thought out and appropriate evaluations of a student's performance.  As another example, using some 'mathematical model' that does not adequately represent reality can produce 'garbage' results even though input to the model might be good.  As another example, experiments have shown that weights and scores spreadsheets to evaluate choice alternatives produce inadequate results because people who might be well versed in the decision, cannot 'assign' weights for the importance of the criteria accurately enough.

"Garbage In -- Genius Out" might seem like magic, but we can convert ordinal pairwise comparisons to ratio scale priorities using AHP verbal comparisons provided we have enough redundancy and variety.  Whereas ordinal measures cannot be used in arithmetic operations such as addition and multiplication, ratio scale numbers can and so we can produce measures with a higher level of meaning by computing the principle right hand eigenvector of a set of pairwise verbal judgments.



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