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That sort of works with sportsman and helmsman, less well with draftsman, and not well at all with spokesman. I think rather it's a suffix creating generic and abstract nouns. We have it also in news, sports, etc.

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Generic and plural are closely related semantically, so it's not a surprising shift. I've argued elsewhere that the -s sound on independence and other such -nce words is the same abstract nominalizer, a suffix added to adjectives ending in -nt.

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The standard spelling -nce disguises this analysis, which morphologically would be -nt+s. It may have originate as a plural or a genitive, but by the early 17th century it became an abstract noun suffix.

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You can see variation suggesting this in Shakespeare and other contemporary writers.

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