with the mass-luminosity relation derived from the counting method, however. As noted by @iro, the fact that the mass function is decreasing with increasing mass causes an effect similar to the Malmquist bias: for any given mass bin, more objects are scattered into it from lower mass bins than are scattered out of it. If we then take our base mass-luminosity relation to be the average one in the CLF distribution, because of this effect we will end up with a calculated luminosity function that greatly overestimates the abundance of very bright galaxies when compared to the observed one.

To get the correct matching to the observed luminosity function, it is then necessary to modify the average mass-luminosity function we take for the basis of the CLF. This is achieved by introducing an additional term, of the form:

$$\label{eq:mlmod}
L(M)=L_{ref}(M)(1+M/M_s)^a \, ,$$

where $L_{ref}(M)$ refers to the base mass-luminosity relation of equation (\[mlfit\]). In practice, $a$ is going to be negative since we need to lower the luminosity corresponding to any given high-mass halo in order to drive the value of our calculated luminosity function down.

There is one final, potentially important point about this issue: once scatter is introduced, 