first question here, so I hope that I'm doing everything correctly.
Let's say that I have a certain number of objects. Each object is defined by two properties, $x$ and $y$.
$x$ and $y$ both vary from $0$ to $100$, and the higher the value, the better. So for example the object with properties $(0, 0)$ is the worst possible, and the one with $(100, 100)$ is the best possible. There is no preference of one property over the other.
The question is: given two objects, how to determine which is "better"?
Here's my line of reasoning: first thing first, I imagined each object as a single point in a cartesian space limited on both axis on $[0, 100]$. Then I thought about some metrics I could use:
1) The first I thought about was simply $x*y$, the area of the rectangle with sides $x$ and $y$.
2) Second metrics: the average of the two properties, i.e. $\frac{x+y}{2}$.
These two metrics looked really simplistic to me, so I didn't really give much thought about them. What I reasoned about most were these other two:
3) Distance from the worst point, $(0, 0)$. The longer the distance, the better the object.
4) Distance from the best point, $(100, 100)$. The shorter the distance, the better the object.
So I wrote a short python program that casually generates objects, and then order them using the four metrics described above. To my surprise, I got four different orders.
To give a practical example of the metrics 3 and 4: given the objects $A = (37, 32)$ and $B = (90, 7)$.
The distances from the worst point are respectively about $48.92$ and about $90.27$. So object $B$ is better, being further away from the worst.
The distances from the best point are instead about $92.7$ and $93.54$, so object $A$ is better, being closer to the best.
So, again, my question is (are): What's the best metrics to use? Is there a "correct" metric? Using metric 3 instead of 4 what characteristics am I maximizing?, and of course How is this problem called?, because obviously I can't be the first to think about it, but I didn't find anything online.
Thanks to you all.
P.S. If you want examples of points that give four different orders, here it is: $A = (28, 0)$, $B = (23, 76)$, $C = (24, 75)$, $D = (92, 19)$, $E = (49, 86)$, $F = (5, 97)$.
First metric: $A, F, B, D, C, E$.
Second metric: $A, B, C, F, D, E$.
Third metric: $A, C, B, D, F, E$.
Fourth metric: $A, F, D, B, C, E$.
(from worst to best)