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Alsadius comments on Variables in Arguments as a Source of Confusion - Less Wrong
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Normalize the results - put each person on a 0-1 scale, where 0 is them being unable to do anything at all that they want to, and 1 is them being able to do everything they want to. Don't bother with dot products, just take the mean(probably the geometric mean, to preserve minority rights).
Sure, each element of the usefulness matrix is between 0 and 1. You need the freedom vector to quantify how valuable each freedom is in general before scaling it by the usefulness of it to each individual. Feel free to explicitly write out your expression for the overall freedom and try it out on some simple examples.
Given input of a list of the value of various freedoms, divide by the sum to normalize the result. I don't care if they make each individual freedom worth 3 points or 3450121 points, but I hold it self-evident that all men are created equal, and normalize their values in the algorithm as a result.