/sci/ - Science & Math

I'm creating a genetic algorithm and there's a couple of questions I'd like to ask.

However, first some background information:
if I have 2N individuals I'd always want to kick out the N worst performing. However, that wouldn't be realistic and might cause some hindrances to calculations so I created a selection method where the better you were, the smaller the chance is that you are kicked and vice versa.

In this picture, I have 1000 individuals ordered in how good they were at a task. the Y-axis tells the chance that an individual is kicked out. The selection algorithm I've made ensures that exactly have of the individuals are selected, while also maintaining the 'randomness of getting selected' (as in, it's still completely random whether individual C gets kicked out or not).

Here are my questions:
1) Is that curve some known function? It starts at (0,0) and ends at (0.8,1) with a total area of 0.5 (duh!)
2) Does there exist an algorithm that would create a straight line from (0,0) to (1,1) while always maintaining the 'randomness of getting selected'
3) I'm reinventing the wheel, aren't I?