The natural symmetry of the retrieval situation as between documents and
queries suggests that we could treat within-query term frequency (
) in a similar fashion to within-document term frequency. This
would suggest, by analogy with equation 8, a weighting function
thus:
where 
is another unknown constant.
In this case, experiments (section 7) suggest a
large value of 
to be
effective---indeed the limiting case, which is equivalent to
appears to be the most effective. This may perhaps suggest that an S-shaped function like equation 9 could be better still, though again none has been tried in the present experiments.
The experiments are based on combining one of these
multipliers with the within-document term frequency and
document length functions defined above. However, it should be pointed
out that (a) the ``natural symmetry'' as between documents and queries,
to which we appealed above, is open to question, and (b) that even if we
accept each model separately, it is not at all obvious that they can be
combined (a properly constructed combined model would have fairly
complex relations between query and document terms, query and document
eliteness, and relevance). Both these matters are discussed further by
Robertson [12]. In the meantime, the combination of either
multiplier with the earlier functions must be regarded as
not having a strong theoretical motivation.
