We have a group of employees and their company will assign a prize to as many employees as possible by finding the ones probably better than the rest. The company assigned the same 2 tasks to every employee and scored their results with 2 values x,y both in [0,1]. The company selects the best employees among the others, if there is no other employee with a better score in both tasks.
Knowing that both scores are uniformly distributed in [0,1], how can i proof that the number of the employees receiving the price is estimated near to logn, with n the number of the employees, having high probability?
I need to use Chernoff bound to bound the probability, that the number of winning employees is higher than logn.