  In this paper we present a new, essentially empirical, model for the relation
between the mass of a dark matter halo/subhalo and the luminosity of a galaxy
hosted in it. To estimate this, we replace the assumption of linearity between
light and mass fluctuations with the assumption of monotonicity between galaxy
light and halo or subhalo mass. We are enabled to proceed with this less
restrictive ansatz by the availability of new, very high resolution dark matter
simulations and more detailed and comprehensive global galactic luminosity
functions.
  We find that the relation between halo/subhalo mass and hosted galaxy
luminosity is fairly well fit by a double power law, while that between halo
mass and group luminosity is fairly well fit by a two branch function, with
both branches double power laws. Both relations asymptote to $L\propto M^4$ at
low $M$, while at high mass the former follows $L\propto M^{0.28}$ and the
latter $L\propto M^{0.9}$.
  We also derive results for the occupation number, luminosity function of
cluster galaxies, group luminosity function and multiplicity function. Then,
using some additional assumptions, we further derive results for biasing
between mass and light and mass and galaxy number, light distribution function
and the void probability distribution. Our results for the most part seem to
match well with observations and previous expectations. We feel this is a
potentially powerful way of modelling this relation, since the main inputs are
readily testable against dark matter simulation results and galaxy surveys.
(abridged)
