Value interdependency: difference between “ratio”, “proportion”, “rate”, and “relation”

In the context of decision-making, I'm looking for a word that describes the relation of two values: "even if value a increases, value b decreases". For this relation, I have found ratio, proportion, rate and relation. Which is the most suitable, when I want to use it in the following sentence: "To weigh out possible advantages, ??? between the values have to be established"?

-
a and b are inversely proportional See here – SmokerAtStadium Mar 21 '13 at 16:52
@Radu, that is not clear from the question. "even if value a increases, value b decreases" is stated. But maybe if value a decreases, value b would decrease even faster... – GEdgar Mar 21 '13 at 17:32
That would be black magic! – SmokerAtStadium Mar 21 '13 at 18:30

The relation you specify is an "inverse dependency" or an "inverse proportion".

-

The even if phrase at the beginning of “even if value a increases, value b decreases” suggests that value b decreases independently of what value a does. The phrase could be used in a sentence like “In previous times, b followed a; but in this time frame, even when a increases, b decreases.”

If instead you mean to say that increase in a implies decrease in b, and conversely when a decreases, you can say b changes oppositely to a, and might say b changes inversely to a. However, inverse typically refers to a multiplicative inverse. If a·b = k for some constant k, then a and b are inversely related. If instead a+b = k, you might speak of a zero-sum game.

In the sentence you ask about, none of ratio, proportion, rate, relation, inverse, opposite, zero-sum or variants thereof are appropriate. Instead write

To maximize advantage, tradeoffs between values must be established.

A tradeoff is “An advantage or improvement that necessitates the corresponding loss or degradation of something else”.

-