There is quite an extensive literature about the pattern mentioned by TKR that irregular plurals are more acceptable as modifiers than regular plurals. This has nothing to do with whether the head noun is plural, as shown by examples in e.g. Haskell et al. (2003, in Cognitive Psychology 47):
- rat-eater, *rats-eater
- mouse-eater, mice-eater
Haskell et al. mention previous explanations based on rule ordering. On such accounts (they mention e.g. Kiparsky 1982; Pinker 1994, 1999), compounds and regular plurals are generated by rules, but irregular plurals are stored in the lexicon. Under the assumption that the compound formation rule applies before regular plural formation, regular plurals are unavailable in compounds, but irregular plurals are (I follow Pinker here; Kiparsky assumes that irregular plurals are generated by a rule prior to compound formation).
There are problems with these approaches, because of exceptions (awards ceremony; pilots union) as well as other problems that I will not go into here. To account for these exceptions, others have suggested that the rule-based account be extended with semantic and phonological constraints to allow exceptions where needed. What Haskell et al. propose is that these semantic and phonological constraints are powerful enough on their own, and that a rule-based account is no longer necessary:
We developed an alternative account in which the well-formedness of these constructions is a function of a constraint-satisfaction process that weighs multiple types of probabilistic information. [...] We began by identifying two primary constraints, one semantic and one phonological. Roughly speaking, on this account the acceptability of a modifier is a function of how semantically and phonologically similar it is to singular nouns.
Haskell et al. further explain how these constraints can be learned:
The phonological constraint reflects the fact that, although their phonological properties are highly varied, modifiers do not tend to have the phonological form of regular plurals [...] How this negative generalization could be learned is illustrated by connectionist models [...] The weights on connections between units are set on the basis of exposure to positive examples. The weights represent a set of simultaneous probabilistic constraints that are evaluated every time an example is processed. The well-formedness of a novel input depends on how well it fits the constraints embodied by the weights.
And:
The semantic constraint arises in a similar manner. The child learns that although the semantics of modifiers are highly varied, they do not tend to include number. Given a choice between a singular and a plural form, the singular form is preferred because it is a closer approximation to a number-neutral form.
The case of woman doctor is a bit different, because woman can be understood both as an attribute and as an object:
- Attribute: a doctor who is a woman (cf. woman birdwatcher)
- Object: a doctor who treats women (cf. woman hater; mouse-eater)
Mice-eater above corresponds to women doctor, which only has the latter interpretation. However, this objective interpretation licenses women doctors ('doctors who treat women'). Though I have not found literature on it just now, one might hypothesize that the pattern then spread from objective to attributive interpretations, so that women doctors can now mean 'female doctors' as well. This is a hypothesis that would have to be checked, and I'm open to alternatives.