Etymology
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willy-nilly 
c. 1600, contraction of will I, nill I, or will he, nill he, or will ye, nill ye, literally "with or without the will of the person concerned." See nill + will (v.1).
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nill (v.)

Old English nylle, nelle "to be unwilling," from ne "no" (from PIE root *ne- "not") + will (v.). Often paired with will; the once-common construction nill he, will he, attested from c. 1300, survives principally in willy-nilly, which, however, reverses the usual Middle English word order. Latin expressed a similar idea in nolens volens.

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self-willed (adj.)

"obstinate, unmindful of the will or wishes of others," late 15c., from self-wille "obstinate or perverse insistence on one's own desires or opinions" (mid-14c.); see self + will (n.). Old English selfwill, selfwyll meant "free will."

Self-willedness "quality or condition of being self-willed" is from mid-15c., though it is not certain whether "obstinacy" or "self-reliance" is implied.

Middle English also had an adjective self-willy (15c.), and the adverb self-willes is attested from late 12c. as "willingly, voluntarily;" late 14c. as "willfully, stubbornly."

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