one-uppersonship
(wun.up.PUR.sun.ship) n. The practice of one person trying to do better than or to prove themselves superior to another person.

Example Citation:
In the book world, we're proclaiming sunshine (at least when it's not pouring) and the open air; we're discussing Tent City, conviviality, occasional verbal punchups, the excitement of ideas, a crush of communality and highlevel one-uppersonship, all awash in a sea of South Australian wines.
—Murray Waldren, "All roads lead to Adelaide," The Weekend Australian, February 28, 1998

Earliest Citation:
And talking of bankers, what did the best-dressed guests at the official opening of a new bank in Singapore last year wear to the occasion? One trusts they did not take the dress-code indicated in the invitation literally. Dress: Lounge suite, it advised. No doubt the opportunity for one-uppersonship immediately presented itself to the purely vain and fashion-conscious with a full wardrobe of furniture who decided to eschew the two-piece for the more formal three-piece (settee and two chairs).
—Louis Beckerling, "1993: The Year of the Stag," The Straits Times, January 2, 1994

Notes:
This word is the gender neutral version of one-upmanship (1952) and the earlier Word Spy entry one-upwomanship (1977).

The earliest citation I could find was the single-word heading "One-uppersonship" over a letter to the editor in the October 8, 1988 edition of The Globe and Mail.

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