Right, but what is the purpose of the spreadsheet? It's aggregating a bunch of variables to get a final, composite ranking. So the actual, cardinal numbers used in the variables are arbitrary. What we need are to transform the variables so that they are comparable to each other. That's what normalization does. If the substantive differences among the states are not important, as in the example you give, the solution is to give the normalized variable a very small weighting so that it does not much affect the final result.

I see your point about weighing, but I don't agree with it.

The fundamental function of assigning weights, is to decide for yourself how important that criterion should be in contributing to what state we choose. One should be able to assign it

*without having to look at the data itself.* You shouldn't need to fudge your weights in order to account for poor choices in the normalization algorithm that cause non-real-world representations of the data (such as that 49% is very different from 50%).

It's hard enough assigning weights, only taking into account the importance of criteria. We don't need to pile this other function on to it.

But Ted's solution can create paradoxes if you're not very sophisticated about the way in which you do the ranking. For example, imagine the ranking is "government ownership above 48%." Then state A scores 2% and state B scores 1% even though the fundamental, underlying concept is the same. Ted's solution would give B a 5 and A a 10.

Well, I'm not suggesting you can't pick a criterion in such a way as to break this simple nomalization algorithm. But you have to admit, you had to go out of your way to do it!

On the other hand, we did not go out of our way at all to break the current normalization algorithm (in such a way as to require fudging weights to compensate); in fact we used criteria that are already in the spread sheet!

Generally I think you have to look at each criterion, then pick one of several nomalization algorithms that would best display the data in real-world terms, and that doesn't give nonsense answers when you apply different data to the criterion. (Obviously the criterion having to do with borders and coasts has to have a different normalization algorithm than this one.)

This is similar to what I picked up long ago when I was a Physics major at the University. One way we used to verify that an equation matched the system under study, was to take each variable in the equation and set it to its maximum possible or minimum possible value, then verify that the results the equation predicts still makes sense. If it does, for every variable, then we can be pretty sure the equation is right.