  Imposing fairness in resource allocation incurs a loss of system throughput,
known as the Price of Fairness ($PoF$). In wireless scheduling, $PoF$ increases
when serving users with very poor channel quality because the scheduler wastes
resources trying to be fair. This paper proposes a novel resource allocation
framework to rigorously address this issue. We introduce selective fairness:
being fair only to selected users, and improving $PoF$ by momentarily blocking
the rest. We study the associated admission control problem of finding the user
selection that minimizes $PoF$ subject to selective fairness, and show that
this combinatorial problem can be solved efficiently if the feasibility set
satisfies a condition; in our model it suffices that the wireless channels are
stochastically dominated. Exploiting selective fairness, we design a stochastic
framework where we minimize $PoF$ subject to an SLA, which ensures that an
ergodic subscriber is served frequently enough. In this context, we propose an
online policy that combines the drift-plus-penalty technique with
Gradient-Based Scheduling experts, and we prove it achieves the optimal $PoF$.
Simulations show that our intelligent blocking outperforms by 40$\%$ in
throughput previous approaches which satisfy the SLA by blocking low-SNR users.
