The order of names on the 1871 census is possibly incorrect. It records him as 'William A' but both the birth registration and 1861 census state 'Arthur William'.
Sources
↑Birth Registration:
"England & Wales General Register Office" GRO Online Indexes - Birth (accessed 6 March 2023)
Widdowson, Arthur William (Mother's maiden name: Lowe). GRO Reference: 1856 Oct-Nov-Dec in Radford Volume 07B Page 164.
↑1861 Census:
"1861 England Census"
Class: Rg 9; Piece: 2452; Folio: 146; Page: 26; GSU roll: 542973; ED, institution, or vessel: 13; Household schedule number: 141 Ancestry Sharing Link - Ancestry uk Record 8767 #22194282 (accessed 6 March 2023)
Arthur William Widdowson (4) son in household of Thos Widdowson (33) in Snenton in Radford registration district in Nottinghamshire, England. Born in Sneinton.
Birth Registration: "England & Wales General Register Office" GRO Online Indexes - Birth (accessed 27 October 2021) Widdowson, Arthur William (Mother's maiden name: Lowe). GRO Reference: 1856 Oct-Nov-Dec in Radford Volume 07B Page 164.
1861 Census: "1861 England Census" Class: RG 9; Piece: 2452; Folio: 146; Page: 26; GSU roll: 542973 Ancestry uk Record 8767 #22194282 (accessed 27 October 2021) Arthur William Widdowson (4) son in household of Thos Widdowson (33) in Radford registration district. Born in Sneinton.
1871 Census: "1871 England Census" The National Archives; Kew, London, England; 1871 England Census; Class: RG10; Piece: 3525; Folio: 49; Page: 13; GSU roll: 839752 Ancestry uk Record 7619 #4932633 (accessed 27 October 2021) William A Widdowson (14) son in household of Thomas Widdowson (42) in Nottingham registration district. Born in Sneinton, Nottinghamshire, England.
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Widdowson-1186 and Widdowson-692 appear to represent the same person because: Both are profiles for Arthur William Widdowson born in Sneinton to father Thomas Widdowson. Duplicate profiles for the father also need merging. I've attached a birth registration showing the correct birth year is 1856.