I'm a software engineer, and lately I've been working on a project that ranks US states based on subscriptions. Thanks to Math.SE we're closer now with the equation we will be using.

In any case, the last step was implementing what's called an increasing function that has a horizontal asymptote, in order to manage extreme cases where x/y > 1 and breaks the ranking. $$A+B - \frac {x/y} {x/y + 1}$$

Mathematically-speaking, this equation returns the correct ranking, and that's great.

But we have departments that may say that the x/y in the question has more weight than the rest of the components. Or maybe A+B is more important, etc. I tried to ask the question here, and not having a math background, maybe the question was not correctly written.

I guess my question is: how can I improve this math question?

  • As you relate the issue, different departments may dispute the relative importance of the values used for rankings. Any combination of values might in theory be the subject of such a dispute. You cannot expect Readers to supply a reasoned mathematical argument that resolves the issues of concern to those departments. Rather you might be responsible (or not) to listen to their concerns and address them through a compromise weighting. It simply goes outside the strengths of Math.SE to propose such a compromise. – hardmath Aug 7 at 16:22
  • I'm not asking for a solution to the company's needs. I'm simply asking if there's a way to give a part of an equation more weight. – rbhat Aug 7 at 18:09
  • Is it clear that you can choose weights to calculate the value on which states are ranked, $w_1 A + w_2 B - w_3 \frac{x/y}{x/y + 1}$? The case you mention in the note above is the case of equal weights, but you can choose them to be unequal. – hardmath Aug 7 at 20:18

What you're asking is help with mathematical modeling: translating a real-world problem into mathematics (rather than most questions here, which ask for help using mathematics to solve an already-mathematical problem). I'd argue that this question is still in-scope here, but understand that you're asking for an answer that is ultimately subjective, and so need to give as much information as possible: what do the variables mean? Can you tell us, as precisely and in as much detail as possible, how you want your formula to behave as you change the values of these variables?

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