Matthew Lewis Vaughan-Davies, 1st Baron Ystwyth (17 December 1840 – 21 August 1935) was a Welsh Liberal Party politician. He was Liberal MP for the Cardiganshire Division from 1895 until 1921.
He was born at Tan-y-Bwlch, Cardiganshire, the only son of Matthew Davies of Tan-y-Bwlch. He was educated at Harrow School, but only stayed for a year. He married, in 1889, Mrs Mary Jenkins. She died in 1926. They had no children.
He served as High Sheriff of Cardiganshire in 1875. He served as a Justice of the Peace and a Deputy Lieutenant in Cardiganshire. He was the Conservative candidate in the seat in 1885 but then went over to William Gladstone.
In 1889, Vaughan Davies sought election as Conservative candidate for Llanfarian at the inaugural Cardiganshire County Council elections but was defeated by another Conservative, Morris Davies, by fifteen votes. Three years later, however, Davies stood as a Liberal candidate. This was an unexpected development as he had been a pillar of Conservatism in Cardiganshire for many years, and one factor may have been his marriage to Mrs. Mary Jenkins, a wealthy widow from Swansea, in 1889. She was later elected president of the Aberystwyth Women's Liberal Association, and was a keen supporter of women suffrage.
Vaughan Davies captured the seat, and remained a member of the County Council for over fifteen years.
Having actively supported the sitting member, William Bowen Rowlands at the 1892 General Election it soon became known that Davies was interested in the Liberal nomination. This was strongly resisted by leading figures in the local Liberal Association, such as the Aberaeron merchant J.M. Howell who suspected Davies's commitment to Liberal policies, a suspicion later borne out by embarrassing evidence of his behaviour towards tenants on his own Tanybwlch estate.