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Volume weighting is a technique to compensate for the Malmquist bias (and which I think might be able to deal with the Eddington bias). It is actually weighting with the inverse of the volume, thus it is sometimes referred to as inverse volume weighting. The goal is handling systematic errors in the sampling of different luminosities (absolute magnitudes) in surveys. The method is to calculate a volume for each luminosity, consisting of the volume of space in which an object of that luminosity would be detected by the survey. Vmax is the term used for such a volume, i.e., a Vmax exists for each possible luminosity. When statistically using the counts of objects of a given luminosity, multiply the count times that luminosity's 1/Vmax (and the technique is also known as the 1/Vmax method). Examples of applicability would be in deriving (from the survey data) a mean luminosity of objects within some a volume of space, or a density function of luminosities over such a volume.