Are bright $\gamma$-ray bursts a fair sample?

We conjecture that bright gamma-ray bursts (GRBs) are bright because they come from sources which are intrinsically over luminous and not because they come from nearby sources. We show that this hypothesis is supported by theoretical and observational arguments and that it explains some well-known properties of GRBs such as their Hardness-Intensity Correlation or the No-Host problem. We discuss the consequences of this hypothesis on our understanding of the properties of the GRB population