Let us assume that it is a constant percentage. That is, that for each new person who takes up the mantle, there is a specific and defined chance that they will abuse their position. In that case, then we might imagine that, with a starting count of x and a chance of c, the next “generation” will have x×c number of people who abuse their position. Then, in the generation after that, x×c².
We can notice that this is a simple sum of a geometric sequence, where the total sum is defined as S = a / (1-r), where a is the initial value and r is the rate of change.
If we assume that a is 400 people and r is 50 percent (0.5), then you will need to displace 800 people in total
Let us assume that it is a constant percentage. That is, that for each new person who takes up the mantle, there is a specific and defined chance that they will abuse their position. In that case, then we might imagine that, with a starting count of x and a chance of c, the next “generation” will have x×c number of people who abuse their position. Then, in the generation after that, x×c².
We can notice that this is a simple sum of a geometric sequence, where the total sum is defined as S = a / (1-r), where a is the initial value and r is the rate of change.
If we assume that a is 400 people and r is 50 percent (0.5), then you will need to displace 800 people in total